12a
0164
(K12a
0164
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 12 10 11 4 8 7 1 6
Solving Sequence
3,9 4,5,12
6 2 1 8 10 11 7
c
3
c
5
c
2
c
1
c
8
c
9
c
11
c
7
c
4
, c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1
I
u
1
= h798299739247u
24
+ 2218887488039u
23
+ ··· + 14116099211116d − 8843381349140,
− 364885635753u
24
+ 1117648334550u
23
+ ··· + 28232198422232c − 44559223365168,
458802669672u
24
+ 367351897733u
23
+ ··· + 7058049605558b − 1244576019090,
− 1687329917173u
24
− 1804551705088u
23
+ ··· + 28232198422232a − 30643572770096,
u
25
+ 2u
24
+ ··· − 16u − 8i
I
u
2
= hd + 1, 2u
10
a + u
10
+ ··· − 4a + 4, −u
10
a + u
10
+ ··· + b − 2, −3u
10
a + u
10
+ ··· + 2a
2
− 2a,
u
11
− 3u
10
+ 6u
9
− 7u
8
+ 7u
7
− 3u
6
− 2u
5
+ 8u
4
− 7u
3
+ 5u
2
− 2u + 2i
I
u
3
= hd + 1, −u
7
a − 3u
5
a + u
5
− 2u
3
a − 3au + c + a + u, −u
7
a + u
7
+ u
5
− u
3
a + 2u
3
+ b + u − 1,
2u
8
a − 2u
8
+ ··· + 2a − 2, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
4
= hd + 1, 2u
7
c − u
8
+ 2u
6
c + 2u
5
c − u
6
+ 2u
4
c + u
5
+ 4u
3
c − 2u
4
+ 2u
2
c + c
2
− u
2
+ c + 2u,
− u
7
− u
5
− 2u
3
+ b − u, −u
5
+ a − u, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
5
= h2u
8
+ 2u
7
+ 4u
6
+ 4u
5
+ 6u
4
+ 4u
3
+ 4u
2
+ d + 4u, 2u
8
+ 2u
6
+ 4u
4
+ 2u
2
+ c + 1, −u
7
− u
5
− 2u
3
+ b − u,
− u
5
+ a − u, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
v
1
= ha, d + 1, c + a + 1, b − 1, v + 1i
I
v
2
= hc, d + 1, b, a − 1, v −1i
I
v
3
= ha, d + 1, c + a, b − 1, v −1i
I
v
4
= ha, da − c − 1, dv + v −1, cv + av − a + v, b − 1i
* 8 irreducible components of dim
C
= 0, with total 95 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h7.98 × 10
11
u
24
+ 2.22 × 10
12
u
23
+ · · · + 1.41 × 10
13
d − 8.84 ×
10
12
, −3.65×10
11
u
24
+1.12× 10
12
u
23
+· · ·+ 2.82 ×10
13
c −4.46 ×10
13
, 4.59×
10
11
u
24
+ 3.67 × 10
11
u
23
+ · · · + 7.06 × 10
12
b − 1.24 × 10
12
, −1.69 × 10
12
u
24
−
1.80 × 10
12
u
23
+ · · · + 2.82 × 10
13
a − 3.06 × 10
13
, u
25
+ 2u
24
+ · · · − 16u − 8i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
0.0597662u
24
+ 0.0639182u
23
+ ··· − 0.107083u + 1.08541
−0.0650042u
24
− 0.0520472u
23
+ ··· + 0.578878u + 0.176334
a
12
=
0.0129244u
24
− 0.0395877u
23
+ ··· + 0.145173u + 1.57831
−0.0565524u
24
− 0.157188u
23
+ ··· − 1.05131u + 0.626475
a
6
=
0.0747149u
24
+ 0.105730u
23
+ ··· + 0.724685u + 0.690091
0.00202430u
24
+ 0.0813992u
23
+ ··· + 0.686595u − 0.973634
a
2
=
0.0597662u
24
+ 0.0639182u
23
+ ··· − 0.107083u + 1.08541
0.0375166u
24
+ 0.0396045u
23
+ ··· − 0.990575u − 0.621247
a
1
=
0.0972828u
24
+ 0.103523u
23
+ ··· − 1.09766u + 0.464165
0.0375166u
24
+ 0.0396045u
23
+ ··· − 0.990575u − 0.621247
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
0.0159383u
24
− 0.0332769u
23
+ ··· − 0.0633916u + 1.31412
−0.0587766u
24
− 0.139007u
23
+ ··· − 0.788077u + 0.624033
a
7
=
0.0395277u
24
+ 0.0675081u
23
+ ··· + 0.598270u + 0.845409
−0.0839809u
24
− 0.0749523u
23
+ ··· + 1.66833u + 0.315163
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
8058725701665
7058049605558
u
24
+
10736954342885
7058049605558
u
23
+ ··· −
38478403451674
3529024802779
u −
29622418287164
3529024802779
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
25
+ 12u
24
+ ··· + 3u + 1
c
2
, c
4
, c
5
c
12
u
25
− 2u
24
+ ··· − u + 1
c
3
, c
8
u
25
− 2u
24
+ ··· − 16u + 8
c
6
, c
7
, c
10
u
25
+ 2u
24
+ ··· + 8u + 4
c
9
u
25
− 6u
24
+ ··· + 64u + 64
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
25
+ 8y
24
+ ··· − 13y −1
c
2
, c
4
, c
5
c
12
y
25
− 12y
24
+ ··· + 3y −1
c
3
, c
8
y
25
+ 6y
24
+ ··· + 64y −64
c
6
, c
7
, c
10
y
25
− 22y
24
+ ··· + 88y −16
c
9
y
25
+ 14y
24
+ ··· + 43008y −4096
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041130 + 0.234144I
a = 0.494693 + 0.148943I
b = 0.853442 − 0.558038I
c = 0.755058 + 0.911073I
d = 1.06504 + 1.52742I
3.14377 + 4.46824I −1.00511 − 6.27335I
u = 1.041130 − 0.234144I
a = 0.494693 − 0.148943I
b = 0.853442 + 0.558038I
c = 0.755058 − 0.911073I
d = 1.06504 − 1.52742I
3.14377 − 4.46824I −1.00511 + 6.27335I
u = −0.804646 + 0.457350I
a = 0.661026 + 0.327338I
b = 0.214886 − 0.601608I
c = 0.598042 + 0.576553I
d = 0.536475 + 0.287592I
2.41327 − 0.90505I 1.24488 − 0.76686I
u = −0.804646 − 0.457350I
a = 0.661026 − 0.327338I
b = 0.214886 + 0.601608I
c = 0.598042 − 0.576553I
d = 0.536475 − 0.287592I
2.41327 + 0.90505I 1.24488 + 0.76686I
u = −0.336133 + 1.048560I
a = 0.23291 − 1.77170I
b = −0.927060 + 0.554841I
c = −2.44072 − 0.00843I
d = 1.28789 + 1.63373I
0.70247 + 6.59785I −2.96140 − 9.56947I
u = −0.336133 − 1.048560I
a = 0.23291 + 1.77170I
b = −0.927060 − 0.554841I
c = −2.44072 + 0.00843I
d = 1.28789 − 1.63373I
0.70247 − 6.59785I −2.96140 + 9.56947I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926049 + 0.758012I
a = 0.437271 + 0.092989I
b = 1.187970 − 0.465287I
c = 1.33714 + 0.95866I
d = 2.30915 + 1.75468I
−7.68831 + 5.75962I −10.13195 − 4.49272I
u = 0.926049 − 0.758012I
a = 0.437271 − 0.092989I
b = 1.187970 + 0.465287I
c = 1.33714 − 0.95866I
d = 2.30915 − 1.75468I
−7.68831 − 5.75962I −10.13195 + 4.49272I
u = −0.759240 + 0.251838I
a = 0.519076 − 0.093919I
b = 0.865432 + 0.337523I
c = 0.49147 − 1.32874I
d = 0.46170 − 2.46248I
−2.09943 − 2.64913I −8.26724 + 7.08829I
u = −0.759240 − 0.251838I
a = 0.519076 + 0.093919I
b = 0.865432 − 0.337523I
c = 0.49147 + 1.32874I
d = 0.46170 + 2.46248I
−2.09943 + 2.64913I −8.26724 − 7.08829I
u = −0.169266 + 0.764490I
a = 1.154810 + 0.812291I
b = −0.420684 − 0.407489I
c = 0.77118 + 1.56321I
d = 0.194809 − 0.625745I
1.62680 − 1.08260I 3.35440 + 3.89731I
u = −0.169266 − 0.764490I
a = 1.154810 − 0.812291I
b = −0.420684 + 0.407489I
c = 0.77118 − 1.56321I
d = 0.194809 + 0.625745I
1.62680 + 1.08260I 3.35440 − 3.89731I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096683 + 1.217070I
a = 0.512583 − 1.088800I
b = −0.646064 + 0.751814I
c = −0.430370 − 0.686592I
d = 0.984764 + 0.859225I
8.85704 + 0.98974I 4.51267 − 2.53049I
u = 0.096683 − 1.217070I
a = 0.512583 + 1.088800I
b = −0.646064 − 0.751814I
c = −0.430370 + 0.686592I
d = 0.984764 − 0.859225I
8.85704 − 0.98974I 4.51267 + 2.53049I
u = −0.661369 + 1.057320I
a = 0.574734 + 0.631929I
b = −0.212320 − 0.866068I
c = 0.370547 + 0.605496I
d = 0.879125 − 0.241772I
4.06909 + 6.32284I 1.86961 − 4.09954I
u = −0.661369 − 1.057320I
a = 0.574734 − 0.631929I
b = −0.212320 + 0.866068I
c = 0.370547 − 0.605496I
d = 0.879125 + 0.241772I
4.06909 − 6.32284I 1.86961 + 4.09954I
u = −1.024310 + 0.754591I
a = 0.432415 − 0.103048I
b = 1.188320 + 0.521494I
c = 1.26644 − 0.88578I
d = 2.18015 − 1.59332I
−3.22783 − 10.10170I −5.60475 + 6.88322I
u = −1.024310 − 0.754591I
a = 0.432415 + 0.103048I
b = 1.188320 − 0.521494I
c = 1.26644 + 0.88578I
d = 2.18015 + 1.59332I
−3.22783 + 10.10170I −5.60475 − 6.88322I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425565 + 1.220260I
a = −0.00331 + 1.51391I
b = −1.001440 − 0.660540I
c = −1.51553 − 0.69262I
d = 1.55274 − 1.36521I
6.70868 − 9.75196I 0.64851 + 8.69449I
u = 0.425565 − 1.220260I
a = −0.00331 − 1.51391I
b = −1.001440 + 0.660540I
c = −1.51553 + 0.69262I
d = 1.55274 + 1.36521I
6.70868 + 9.75196I 0.64851 − 8.69449I
u = 0.797713 + 1.033120I
a = −0.66380 + 1.63521I
b = −1.213130 − 0.525024I
c = −1.11526 − 2.93778I
d = 2.23603 − 1.53373I
−6.80818 − 12.11480I −8.50713 + 8.67244I
u = 0.797713 − 1.033120I
a = −0.66380 − 1.63521I
b = −1.213130 + 0.525024I
c = −1.11526 + 2.93778I
d = 2.23603 + 1.53373I
−6.80818 + 12.11480I −8.50713 − 8.67244I
u = −0.832592 + 1.087810I
a = −0.64807 − 1.52933I
b = −1.234910 + 0.554337I
c = −0.80559 + 2.69461I
d = 2.22655 + 1.42478I
−2.1296 + 16.8657I −4.74649 − 10.33694I
u = −0.832592 − 1.087810I
a = −0.64807 + 1.52933I
b = −1.234910 − 0.554337I
c = −0.80559 − 2.69461I
d = 2.22655 − 1.42478I
−2.1296 − 16.8657I −4.74649 + 10.33694I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600838
a = 0.591322
b = 0.691126
c = −0.564782
d = −1.82889
−1.26593 −6.81200
10
II. I
u
2
= hd + 1, 2u
10
a + u
10
+ · · · − 4a + 4, −u
10
a + u
10
+ · · · + b −
2, −3u
10
a + u
10
+ · · · + 2a
2
− 2a, u
11
− 3u
10
+ · · · − 2u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
u
10
a − u
10
+ ··· − u + 2
a
12
=
−u
10
a −
1
2
u
10
+ ··· + 2a − 2
−1
a
6
=
−
3
2
u
10
+
5
2
u
9
+ ··· +
1
2
u
2
−
3
2
u
−u
10
+ 2u
9
− 3u
8
+ 2u
7
− 2u
6
− u
5
+ 3u
4
− 4u
3
+ u
2
− u + 1
a
2
=
a
−u
10
a + u
10
+ ··· + u − 2
a
1
=
−u
10
a + u
10
+ ··· + a − 2
−u
10
a + u
10
+ ··· + u − 2
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−
3
2
u
10
+
9
2
u
9
+ ··· −
3
2
u + 3
2u
9
− 3u
8
+ 5u
7
− 3u
6
+ 4u
5
+ 3u
4
− 4u
3
+ 6u
2
+ 3
a
7
=
−
1
2
u
10
+
1
2
u
9
+ ··· +
1
2
u
2
+
1
2
u
−u
10
+ 2u
9
− 3u
8
+ 3u
7
− 2u
6
+ 3u
4
− 2u
3
+ 2u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
10
− 8u
9
+ 10u
8
− 10u
7
+ 4u
6
− 4u
5
− 14u
4
+ 12u
3
− 6u
2
− 8u − 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 11u
21
+ ··· + 40u + 16
c
2
, c
4
, c
5
c
12
u
22
− u
21
+ ··· − 4u + 4
c
3
, c
8
(u
11
+ 3u
10
+ 6u
9
+ 7u
8
+ 7u
7
+ 3u
6
− 2u
5
− 8u
4
− 7u
3
− 5u
2
− 2u − 2)
2
c
6
, c
7
, c
10
(u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 4u
6
− 5u
5
+ 3u
4
− 3u
3
− 5u
2
+ 3u − 1)
2
c
9
(u
11
− 3u
10
+ ··· − 16u + 4)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
22
− 3y
21
+ ··· − 544y + 256
c
2
, c
4
, c
5
c
12
y
22
− 11y
21
+ ··· − 40y + 16
c
3
, c
8
(y
11
+ 3y
10
+ ··· − 16y −4)
2
c
6
, c
7
, c
10
(y
11
− 11y
10
+ ··· − y −1)
2
c
9
(y
11
+ 7y
10
+ ··· + 24y −16)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992754
a = 0.541424 + 0.181355I
b = 0.660661 − 0.556253I
c = −0.173971 + 0.420983I
d = −1.00000
3.69004 0.666830
u = −0.992754
a = 0.541424 − 0.181355I
b = 0.660661 + 0.556253I
c = −0.173971 − 0.420983I
d = −1.00000
3.69004 0.666830
u = 0.762686 + 0.875309I
a = 0.432041 + 0.071853I
b = 1.252300 − 0.374583I
c = −1.077570 − 0.728230I
d = −1.00000
−7.89368 − 2.87937I −10.41286 + 3.23335I
u = 0.762686 + 0.875309I
a = −0.83899 + 1.92556I
b = −1.190170 − 0.436468I
c = −0.92410 + 2.27150I
d = −1.00000
−7.89368 − 2.87937I −10.41286 + 3.23335I
u = 0.762686 − 0.875309I
a = 0.432041 − 0.071853I
b = 1.252300 + 0.374583I
c = −1.077570 + 0.728230I
d = −1.00000
−7.89368 + 2.87937I −10.41286 − 3.23335I
u = 0.762686 − 0.875309I
a = −0.83899 − 1.92556I
b = −1.190170 + 0.436468I
c = −0.92410 − 2.27150I
d = −1.00000
−7.89368 + 2.87937I −10.41286 − 3.23335I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958422 + 0.661375I
a = 0.580062 − 0.402139I
b = 0.164345 + 0.807203I
c = 0.034579 − 0.677196I
d = −1.00000
−0.20533 + 5.20915I −2.55774 − 3.72118I
u = 0.958422 + 0.661375I
a = 0.445846 + 0.101514I
b = 1.132380 − 0.485520I
c = −0.435696 + 0.436381I
d = −1.00000
−0.20533 + 5.20915I −2.55774 − 3.72118I
u = 0.958422 − 0.661375I
a = 0.580062 + 0.402139I
b = 0.164345 − 0.807203I
c = 0.034579 + 0.677196I
d = −1.00000
−0.20533 − 5.20915I −2.55774 + 3.72118I
u = 0.958422 − 0.661375I
a = 0.445846 − 0.101514I
b = 1.132380 + 0.485520I
c = −0.435696 − 0.436381I
d = −1.00000
−0.20533 − 5.20915I −2.55774 + 3.72118I
u = −0.273627 + 1.210650I
a = 0.547051 + 0.920222I
b = −0.522674 − 0.802934I
c = 1.04176 − 1.12578I
d = −1.00000
8.10965 + 4.33574I 3.31243 − 3.68401I
u = −0.273627 + 1.210650I
a = 0.21367 − 1.45637I
b = −0.901383 + 0.672173I
c = 0.872371 − 0.074382I
d = −1.00000
8.10965 + 4.33574I 3.31243 − 3.68401I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273627 − 1.210650I
a = 0.547051 − 0.920222I
b = −0.522674 + 0.802934I
c = 1.04176 + 1.12578I
d = −1.00000
8.10965 − 4.33574I 3.31243 + 3.68401I
u = −0.273627 − 1.210650I
a = 0.21367 + 1.45637I
b = −0.901383 − 0.672173I
c = 0.872371 + 0.074382I
d = −1.00000
8.10965 − 4.33574I 3.31243 + 3.68401I
u = 0.764438 + 1.080520I
a = 0.535931 − 0.594839I
b = −0.163987 + 0.927905I
c = 0.36336 + 1.80240I
d = −1.00000
1.11929 − 11.51290I −1.55919 + 7.44023I
u = 0.764438 + 1.080520I
a = −0.56921 + 1.60575I
b = −1.196120 − 0.553243I
c = −0.063151 + 0.595914I
d = −1.00000
1.11929 − 11.51290I −1.55919 + 7.44023I
u = 0.764438 − 1.080520I
a = 0.535931 + 0.594839I
b = −0.163987 − 0.927905I
c = 0.36336 − 1.80240I
d = −1.00000
1.11929 + 11.51290I −1.55919 − 7.44023I
u = 0.764438 − 1.080520I
a = −0.56921 − 1.60575I
b = −1.196120 + 0.553243I
c = −0.063151 − 0.595914I
d = −1.00000
1.11929 + 11.51290I −1.55919 − 7.44023I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215541 + 0.601634I
a = 0.466364 − 0.019525I
b = 1.140500 + 0.089613I
c = −1.154200 + 0.288451I
d = −1.00000
−2.97495 + 0.92758I −6.11605 − 7.40073I
u = −0.215541 + 0.601634I
a = 2.14581 − 3.56073I
b = −0.875845 + 0.206022I
c = 2.01661 − 3.69343I
d = −1.00000
−2.97495 + 0.92758I −6.11605 − 7.40073I
u = −0.215541 − 0.601634I
a = 0.466364 + 0.019525I
b = 1.140500 − 0.089613I
c = −1.154200 − 0.288451I
d = −1.00000
−2.97495 − 0.92758I −6.11605 + 7.40073I
u = −0.215541 − 0.601634I
a = 2.14581 + 3.56073I
b = −0.875845 − 0.206022I
c = 2.01661 + 3.69343I
d = −1.00000
−2.97495 − 0.92758I −6.11605 + 7.40073I
17
III. I
u
3
= hd + 1, −u
7
a − 3u
5
a + · · · + c + a, −u
7
a + u
7
+ · · · + b − 1, 2u
8
a −
2u
8
+ · · · + 2a − 2, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
u
7
a − u
7
− u
5
+ u
3
a − 2u
3
− u + 1
a
12
=
u
7
a + 3u
5
a − u
5
+ 2u
3
a + 3au − a − u
−1
a
6
=
u
7
a + 2u
5
a − u
5
+ u
3
a + 2au − a − u + 1
u
7
a + u
3
a + 1
a
2
=
a
−u
7
a + u
7
+ u
5
− u
3
a + u
2
a + 2u
3
+ u − 1
a
1
=
−u
7
a + u
7
+ u
5
− u
3
a + u
2
a + 2u
3
+ a + u − 1
−u
7
a + u
7
+ u
5
− u
3
a + u
2
a + 2u
3
+ u − 1
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−u
8
a − u
6
a − u
7
− u
4
a − u
5
− u
2
a − u
3
+ au + u
2
− u
−u
8
a − u
7
a + ··· + a − 1
a
7
=
u
8
a + u
6
a + u
7
+ u
4
a + u
5
− u
3
a + u
2
a + u
3
− u
2
+ u
u
8
a + u
7
a + u
6
a + u
7
+ u
5
a + u
4
a + u
3
a + u
2
a + u
3
+ au − u
2
− a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 13u
17
+ ··· + 12u + 1
c
2
, c
4
, c
6
c
7
, c
10
u
18
+ u
17
+ ··· − 2u − 1
c
3
, c
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
2
c
5
, c
12
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
2
c
11
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 17y
17
+ ··· − 156y + 1
c
2
, c
4
, c
6
c
7
, c
10
y
18
− 13y
17
+ ··· − 12y + 1
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
c
5
, c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
c
11
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.848261 − 1.052190I
b = −0.535620 + 0.576021I
c = 1.90798 + 1.04029I
d = −1.00000
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 + 0.966856I
a = 0.432824 + 0.012312I
b = 1.308540 − 0.065670I
c = −0.899132 − 0.444549I
d = −1.00000
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = 0.848261 + 1.052190I
b = −0.535620 − 0.576021I
c = 1.90798 − 1.04029I
d = −1.00000
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.140343 − 0.966856I
a = 0.432824 − 0.012312I
b = 1.308540 + 0.065670I
c = −0.899132 + 0.444549I
d = −1.00000
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = 0.435786 + 0.058681I
b = 1.253840 − 0.303492I
c = −0.559107 + 0.407789I
d = −1.00000
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = −0.55382 + 2.15000I
b = −1.112360 − 0.436175I
c = 0.109615 + 1.224890I
d = −1.00000
−0.61694 − 2.45442I −2.32792 + 2.91298I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628449 − 0.875112I
a = 0.435786 − 0.058681I
b = 1.253840 + 0.303492I
c = −0.559107 − 0.407789I
d = −1.00000
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = −0.55382 − 2.15000I
b = −1.112360 + 0.436175I
c = 0.109615 − 1.224890I
d = −1.00000
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = 0.633756 + 0.458467I
b = 0.035822 − 0.749326I
c = 0.123475 + 0.714951I
d = −1.00000
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 + 0.733148I
a = −1.21946 − 2.08021I
b = −1.209730 + 0.357771I
c = −1.26364 − 2.41694I
d = −1.00000
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = 0.633756 − 0.458467I
b = 0.035822 + 0.749326I
c = 0.123475 − 0.714951I
d = −1.00000
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −0.796005 − 0.733148I
a = −1.21946 + 2.08021I
b = −1.209730 − 0.357771I
c = −1.26364 + 2.41694I
d = −1.00000
−4.37135 + 1.33617I −7.28409 − 0.70175I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = 0.583232 + 0.580415I
b = −0.138557 − 0.857281I
c = 0.41356 − 1.98115I
d = −1.00000
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 + 0.986295I
a = 0.422628 − 0.065267I
b = 1.311030 + 0.356898I
c = −1.023380 + 0.710048I
d = −1.00000
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = 0.583232 − 0.580415I
b = −0.138557 + 0.857281I
c = 0.41356 + 1.98115I
d = −1.00000
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = −0.728966 − 0.986295I
a = 0.422628 + 0.065267I
b = 1.311030 − 0.356898I
c = −1.023380 − 0.710048I
d = −1.00000
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 0.777682
b = 0.285873
c = 0.168784
d = −1.00000
−1.19845 −8.65230
u = 0.512358
a = −8.94409
b = −1.11181
c = −8.78753
d = −1.00000
−1.19845 −8.65230
23
IV. I
u
4
= hd + 1, 2u
7
c − u
8
+ · · · + c
2
+ c, −u
7
− u
5
− 2u
3
+ b − u, −u
5
+ a −
u, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
c
−1
a
6
=
u
7
c + u
8
+ 2u
5
c + 2u
3
c + u
4
+ 2cu + 1
u
7
c + u
7
+ u
5
c + 2u
5
+ 2u
3
c + 2u
3
+ cu + 2u
a
2
=
u
5
+ u
−u
5
− u
3
− u
a
1
=
−u
3
−u
5
− u
3
− u
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−u
8
c − u
6
c − u
6
− u
4
c + c
−u
8
c − u
7
c − u
8
− u
6
c − 2u
5
c − u
6
− u
4
c − 2u
3
c − u
4
− 2cu + c − 1
a
7
=
u
2
c + c + 1
u
2
c + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
2
c
2
, c
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
2
c
3
, c
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
2
c
5
, c
6
, c
7
c
10
, c
12
u
18
+ u
17
+ ··· − 2u − 1
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
2
c
11
u
18
+ 13u
17
+ ··· + 12u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
2
c
2
, c
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
2
c
3
, c
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
2
c
5
, c
6
, c
7
c
10
, c
12
y
18
− 13y
17
+ ··· − 12y + 1
c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
2
c
11
y
18
− 17y
17
+ ··· − 156y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.72777 + 1.63562I
b = −0.772920 − 0.510351I
c = 1.76865 + 0.20308I
d = −1.00000
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 + 0.966856I
a = 0.72777 + 1.63562I
b = −0.772920 − 0.510351I
c = 0.48884 + 1.87834I
d = −1.00000
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = 0.72777 − 1.63562I
b = −0.772920 + 0.510351I
c = 1.76865 − 0.20308I
d = −1.00000
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.140343 − 0.966856I
a = 0.72777 − 1.63562I
b = −0.772920 + 0.510351I
c = 0.48884 − 1.87834I
d = −1.00000
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = 0.668544 − 0.575994I
b = −0.141484 + 0.739668I
c = 0.209391 − 0.831348I
d = −1.00000
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 + 0.875112I
a = 0.668544 − 0.575994I
b = −0.141484 + 0.739668I
c = 0.62665 + 2.28784I
d = −1.00000
−0.61694 − 2.45442I −2.32792 + 2.91298I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628449 − 0.875112I
a = 0.668544 + 0.575994I
b = −0.141484 − 0.739668I
c = 0.209391 + 0.831348I
d = −1.00000
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.628449 − 0.875112I
a = 0.668544 + 0.575994I
b = −0.141484 − 0.739668I
c = 0.62665 − 2.28784I
d = −1.00000
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = 0.445546 − 0.080250I
b = 1.173910 + 0.391555I
c = −0.485156 − 0.408132I
d = −1.00000
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 + 0.733148I
a = 0.445546 − 0.080250I
b = 1.173910 + 0.391555I
c = −1.156890 + 0.759007I
d = −1.00000
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = 0.445546 + 0.080250I
b = 1.173910 − 0.391555I
c = −0.485156 + 0.408132I
d = −1.00000
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −0.796005 − 0.733148I
a = 0.445546 + 0.080250I
b = 1.173910 − 0.391555I
c = −1.156890 − 0.759007I
d = −1.00000
−4.37135 + 1.33617I −7.28409 − 0.70175I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = −0.61569 − 1.78625I
b = −1.172470 + 0.500383I
c = −0.058202 − 0.817156I
d = −1.00000
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 + 0.986295I
a = −0.61569 − 1.78625I
b = −1.172470 + 0.500383I
c = −0.73020 − 2.13952I
d = −1.00000
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = −0.61569 + 1.78625I
b = −1.172470 − 0.500383I
c = −0.058202 + 0.817156I
d = −1.00000
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = −0.728966 − 0.986295I
a = −0.61569 + 1.78625I
b = −1.172470 − 0.500383I
c = −0.73020 + 2.13952I
d = −1.00000
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 0.547665
b = 0.825933
c = −0.316966
d = −1.00000
−1.19845 −8.65230
u = 0.512358
a = 0.547665
b = 0.825933
c = −2.00921
d = −1.00000
−1.19845 −8.65230
29
V. I
u
5
= h2u
8
+ 2u
7
+ · · · + d + 4u, 2u
8
+ 2u
6
+ · · · + c + 1, −u
7
− u
5
− 2u
3
+
b − u, −u
5
+ a − u, u
9
+ u
8
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
−2u
8
− 2u
6
− 4u
4
− 2u
2
− 1
−2u
8
− 2u
7
− 4u
6
− 4u
5
− 6u
4
− 4u
3
− 4u
2
− 4u
a
6
=
u
7
+ 2u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u
2u
8
+ u
7
+ 4u
6
+ u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 2
a
2
=
u
5
+ u
−u
5
− u
3
− u
a
1
=
−u
3
−u
5
− u
3
− u
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−u
8
− u
6
− 3u
4
− 2u
2
− 1
−u
8
− u
7
− 3u
6
− 2u
5
− 5u
4
− 2u
3
− 4u
2
− 2u − 1
a
7
=
2u
6
+ 2u
4
+ 3u
2
+ 1
2u
8
+ 4u
6
+ 6u
4
+ 5u
2
+ 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
5
− 4u
4
− 8u
3
− 4u
2
− 6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
3
, c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
8
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.72777 + 1.63562I
b = −0.772920 − 0.510351I
c = −1.76992 + 1.63785I
d = 0.75135 − 1.48568I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.140343 − 0.966856I
a = 0.72777 − 1.63562I
b = −0.772920 + 0.510351I
c = −1.76992 − 1.63785I
d = 0.75135 + 1.48568I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.628449 + 0.875112I
a = 0.668544 − 0.575994I
b = −0.141484 + 0.739668I
c = 0.472416 − 0.682058I
d = 0.714469 + 0.176194I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.628449 − 0.875112I
a = 0.668544 + 0.575994I
b = −0.141484 − 0.739668I
c = 0.472416 + 0.682058I
d = 0.714469 − 0.176194I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.796005 + 0.733148I
a = 0.445546 − 0.080250I
b = 1.173910 + 0.391555I
c = 1.44301 − 1.09794I
d = 2.50189 − 2.05286I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.796005 − 0.733148I
a = 0.445546 + 0.080250I
b = 1.173910 − 0.391555I
c = 1.44301 + 1.09794I
d = 2.50189 + 2.05286I
−4.37135 + 1.33617I −7.28409 − 0.70175I
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728966 + 0.986295I
a = −0.61569 − 1.78625I
b = −1.172470 + 0.500383I
c = −1.72233 + 3.04233I
d = 2.17857 + 1.68557I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.728966 − 0.986295I
a = −0.61569 + 1.78625I
b = −1.172470 − 0.500383I
c = −1.72233 − 3.04233I
d = 2.17857 − 1.68557I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.512358
a = 0.547665
b = 0.825933
c = −1.84635
d = −4.29257
−1.19845 −8.65230
34
VI. I
v
1
= ha, d + 1, c + a + 1, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
12
=
−1
−1
a
6
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
8
=
−1
0
a
10
=
−1
0
a
11
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
11
u − 1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
u
c
4
, c
12
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
11
, c
12
y −1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
y
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = −1.00000
d = −1.00000
−3.28987 −12.0000
38
VII. I
v
2
= hc, d + 1, b, a − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
1
0
a
4
=
1
0
a
5
=
1
0
a
12
=
0
−1
a
6
=
1
1
a
2
=
1
0
a
1
=
1
0
a
8
=
1
0
a
10
=
1
0
a
11
=
−1
−1
a
7
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
9
u
c
5
, c
6
, c
7
u + 1
c
10
, c
11
, c
12
u − 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
, c
9
y
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y −1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
0 0
42
VIII. I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
1
0
a
4
=
1
0
a
5
=
0
1
a
12
=
0
−1
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
1
0
a
10
=
1
0
a
11
=
0
−1
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
u − 1
c
3
, c
5
, c
8
c
9
, c
11
, c
12
u
c
4
, c
6
, c
7
u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
10
y −1
c
3
, c
5
, c
8
c
9
, c
11
, c
12
y
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
0 0
46
IX. I
v
4
= ha, da − c − 1, dv + v − 1, cv + av − a + v, b − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
12
=
−1
d
a
6
=
−1
d + 1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
10
=
v
0
a
11
=
−1
d + 1
a
7
=
v −1
d + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
+ 2d − 7
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
47
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−1.64493 −9.16360 − 0.46474I
48
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
· (u
18
+ 13u
17
+ ··· + 12u + 1)(u
22
+ 11u
21
+ ··· + 40u + 16)
· (u
25
+ 12u
24
+ ··· + 3u + 1)
c
2
u(u − 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
18
+ u
17
+ ··· − 2u − 1)(u
22
− u
21
+ ··· − 4u + 4)
· (u
25
− 2u
24
+ ··· − u + 1)
c
3
, c
8
u
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
5
· (u
11
+ 3u
10
+ 6u
9
+ 7u
8
+ 7u
7
+ 3u
6
− 2u
5
− 8u
4
− 7u
3
− 5u
2
− 2u − 2)
2
· (u
25
− 2u
24
+ ··· − 16u + 8)
c
4
u(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
18
+ u
17
+ ··· − 2u − 1)(u
22
− u
21
+ ··· − 4u + 4)
· (u
25
− 2u
24
+ ··· − u + 1)
c
5
, c
12
u(u − 1)(u + 1)(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
18
+ u
17
+ ··· − 2u − 1)(u
22
− u
21
+ ··· − 4u + 4)
· (u
25
− 2u
24
+ ··· − u + 1)
c
6
, c
7
u(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 4u
6
− 5u
5
+ 3u
4
− 3u
3
− 5u
2
+ 3u − 1)
2
· ((u
18
+ u
17
+ ··· − 2u − 1)
2
)(u
25
+ 2u
24
+ ··· + 8u + 4)
c
9
u
3
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
5
· ((u
11
− 3u
10
+ ··· − 16u + 4)
2
)(u
25
− 6u
24
+ ··· + 64u + 64)
c
10
u(u − 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 4u
6
− 5u
5
+ 3u
4
− 3u
3
− 5u
2
+ 3u − 1)
2
· ((u
18
+ u
17
+ ··· − 2u − 1)
2
)(u
25
+ 2u
24
+ ··· + 8u + 4)
49
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y(y − 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
3
· (y
18
− 17y
17
+ ··· − 156y + 1)(y
22
− 3y
21
+ ··· − 544y + 256)
· (y
25
+ 8y
24
+ ··· − 13y −1)
c
2
, c
4
, c
5
c
12
y(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
· (y
18
− 13y
17
+ ··· − 12y + 1)(y
22
− 11y
21
+ ··· − 40y + 16)
· (y
25
− 12y
24
+ ··· + 3y −1)
c
3
, c
8
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
5
· ((y
11
+ 3y
10
+ ··· − 16y −4)
2
)(y
25
+ 6y
24
+ ··· + 64y −64)
c
6
, c
7
, c
10
y(y − 1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· ((y
11
− 11y
10
+ ··· − y −1)
2
)(y
18
− 13y
17
+ ··· − 12y + 1)
2
· (y
25
− 22y
24
+ ··· + 88y −16)
c
9
y
3
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
5
· ((y
11
+ 7y
10
+ ··· + 24y −16)
2
)(y
25
+ 14y
24
+ ··· + 43008y −4096)
50
