11a
100
(K11a
100
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 3 9 5 11 4 7
Solving Sequence
4,10 7,11
1 3 2 6 9 8 5
c
10
c
11
c
3
c
2
c
6
c
9
c
7
c
4
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− u
29
+ ··· + 8b + u, −u
4
+ u
2
+ a − 1, u
31
− u
30
+ ··· + 2u − 1i
I
u
2
= h8.05572 × 10
18
u
45
− 1.78051 × 10
19
u
44
+ ··· + 3.67198 × 10
19
b − 7.81561 × 10
18
,
9.93809 × 10
19
u
45
− 7.04855 × 10
19
u
44
+ ··· + 3.67198 × 10
19
a − 2.19276 × 10
20
, u
46
− u
45
+ ··· − 4u + 1i
I
u
3
= hb
4
+ 4b
3
+ 4b
2
+ 1, a + 1, u + 1i
I
u
4
= hb
3
+ 3b
2
+ 3b + 1, a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 84 representations.
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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hu
30
− u
29
+ · · · + 8b + u, −u
4
+ u
2
+ a − 1, u
31
− u
30
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
u
4
− u
2
+ 1
−
1
8
u
30
+
1
8
u
29
+ ··· −
3
4
u
2
−
1
8
u
a
11
=
1
u
2
a
1
=
−
1
8
u
30
+
1
8
u
29
+ ··· −
1
8
u + 1
u
30
−
9
8
u
29
+ ··· +
3
2
u −
1
8
a
3
=
u
u
a
2
=
−
1
2
u
30
+
1
8
u
29
+ ··· +
1
2
u +
3
8
13
8
u
30
−
27
8
u
29
+ ··· +
79
8
u − 3
a
6
=
−
1
8
u
30
+
1
8
u
29
+ ··· −
1
8
u + 1
−
1
4
u
30
+
1
4
u
29
+ ··· −
3
2
u
2
−
1
4
u
a
9
=
−u
2
+ 1
−u
4
a
8
=
1
−
1
8
u
30
+
1
8
u
29
+ ··· −
3
4
u
2
−
1
8
u
a
5
=
−u
1
8
u
29
−
1
8
u
28
+ ··· +
3
4
u +
1
8
a
5
=
−u
1
8
u
29
−
1
8
u
28
+ ··· +
3
4
u +
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3
2
u
30
−
17
4
u
29
+ ··· +
49
2
u −
69
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
31
− 3u
30
+ ··· − 6u + 2
c
2
u
31
+ 15u
30
+ ··· − 4u − 4
c
3
, c
4
, c
8
c
10
u
31
+ u
30
+ ··· + 2u + 1
c
6
u
31
+ 3u
30
+ ··· + 34u + 2
c
7
, c
9
u
31
+ 13u
30
+ ··· + 8u + 1
c
11
u
31
− 15u
30
+ ··· − 1566u + 158
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
31
+ 15y
30
+ ··· − 4y −4
c
2
y
31
+ 3y
30
+ ··· + 112y −16
c
3
, c
4
, c
8
c
10
y
31
− 13y
30
+ ··· + 8y −1
c
6
y
31
− 9y
30
+ ··· + 92y −4
c
7
, c
9
y
31
+ 19y
30
+ ··· − 4y −1
c
11
y
31
+ 3y
30
+ ··· − 219108y −24964
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.671875 + 0.755704I
a = 0.102801 + 1.258530I
b = 1.26875 + 0.87692I
4.33630 + 2.18000I −1.38223 − 2.85674I
u = −0.671875 − 0.755704I
a = 0.102801 − 1.258530I
b = 1.26875 − 0.87692I
4.33630 − 2.18000I −1.38223 + 2.85674I
u = −0.529243 + 0.781629I
a = 0.75581 + 1.37479I
b = 1.228420 + 0.141119I
3.92659 − 0.20488I −1.21175 − 1.93479I
u = −0.529243 − 0.781629I
a = 0.75581 − 1.37479I
b = 1.228420 − 0.141119I
3.92659 + 0.20488I −1.21175 + 1.93479I
u = 0.473734 + 0.815861I
a = 1.03834 − 1.45511I
b = 1.186120 + 0.184502I
1.98591 + 5.18766I −4.29263 − 2.87164I
u = 0.473734 − 0.815861I
a = 1.03834 + 1.45511I
b = 1.186120 − 0.184502I
1.98591 − 5.18766I −4.29263 + 2.87164I
u = 0.739148 + 0.756876I
a = −0.224684 − 1.178240I
b = 1.18263 − 1.25006I
2.80358 − 7.15169I −4.41360 + 8.13736I
u = 0.739148 − 0.756876I
a = −0.224684 + 1.178240I
b = 1.18263 + 1.25006I
2.80358 + 7.15169I −4.41360 − 8.13736I
u = −0.998773 + 0.420018I
a = 0.149196 − 0.538864I
b = 1.154630 + 0.334617I
−5.71846 − 1.00535I −12.20049 − 2.17594I
u = −0.998773 − 0.420018I
a = 0.149196 + 0.538864I
b = 1.154630 − 0.334617I
−5.71846 + 1.00535I −12.20049 + 2.17594I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001180 + 0.470735I
a = −0.059625 + 0.529287I
b = 0.707502 − 0.184028I
−2.76836 − 3.54859I −8.60512 + 5.21629I
u = 1.001180 − 0.470735I
a = −0.059625 − 0.529287I
b = 0.707502 + 0.184028I
−2.76836 + 3.54859I −8.60512 − 5.21629I
u = −1.060830 + 0.466616I
a = −0.063939 − 0.807099I
b = 0.799755 − 0.463575I
−6.59629 + 7.25038I −13.7743 − 8.1656I
u = −1.060830 − 0.466616I
a = −0.063939 + 0.807099I
b = 0.799755 + 0.463575I
−6.59629 − 7.25038I −13.7743 + 8.1656I
u = 1.045460 + 0.641230I
a = −1.014590 + 0.487534I
b = −1.013330 − 0.611771I
0.83772 − 3.66094I −6.42863 + 2.29820I
u = 1.045460 − 0.641230I
a = −1.014590 − 0.487534I
b = −1.013330 + 0.611771I
0.83772 + 3.66094I −6.42863 − 2.29820I
u = 0.551309 + 0.517564I
a = 0.639561 − 0.529508I
b = 0.464527 − 0.522513I
−0.67493 − 1.41882I −8.11819 + 4.23209I
u = 0.551309 − 0.517564I
a = 0.639561 + 0.529508I
b = 0.464527 + 0.522513I
−0.67493 + 1.41882I −8.11819 − 4.23209I
u = −1.093950 + 0.638128I
a = −1.115430 − 0.808402I
b = −1.54639 + 0.11518I
1.61779 + 8.62066I −5.39345 − 7.96064I
u = −1.093950 − 0.638128I
a = −1.115430 + 0.808402I
b = −1.54639 − 0.11518I
1.61779 − 8.62066I −5.39345 + 7.96064I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.150290 + 0.579146I
a = −0.78731 + 1.29973I
b = −1.32274 + 1.36596I
−4.83518 − 8.17855I −13.0634 + 5.6311I
u = 1.150290 − 0.579146I
a = −0.78731 − 1.29973I
b = −1.32274 − 1.36596I
−4.83518 + 8.17855I −13.0634 − 5.6311I
u = −1.159090 + 0.618451I
a = −1.09291 − 1.32186I
b = −2.11523 − 1.06499I
−0.06269 + 11.03950I −6.94221 − 7.13356I
u = −1.159090 − 0.618451I
a = −1.09291 + 1.32186I
b = −2.11523 + 1.06499I
−0.06269 − 11.03950I −6.94221 + 7.13356I
u = −0.673147 + 0.057260I
a = 0.746573 + 0.007732I
b = −1.032490 + 0.376155I
−4.34804 + 3.91818I −8.50345 − 5.07903I
u = −0.673147 − 0.057260I
a = 0.746573 − 0.007732I
b = −1.032490 − 0.376155I
−4.34804 − 3.91818I −8.50345 + 5.07903I
u = 1.179340 + 0.616871I
a = −1.10660 + 1.48500I
b = −2.36523 + 1.45569I
−2.4315 − 16.1755I −10.0749 + 10.7687I
u = 1.179340 − 0.616871I
a = −1.10660 − 1.48500I
b = −2.36523 − 1.45569I
−2.4315 + 16.1755I −10.0749 − 10.7687I
u = 0.581693
a = 0.776125
b = −0.645714
−1.33697 −6.39560
u = 0.255598 + 0.492030I
a = 1.144740 − 0.340444I
b = 0.225939 − 0.088212I
−0.56339 − 1.34523I −5.39791 + 4.30982I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.255598 − 0.492030I
a = 1.144740 + 0.340444I
b = 0.225939 + 0.088212I
−0.56339 + 1.34523I −5.39791 − 4.30982I
8
II.
I
u
2
= h8.06 × 10
18
u
45
− 1.78 × 10
19
u
44
+ · · · + 3.67 × 10
19
b − 7.82 × 10
18
, 9.94 ×
10
19
u
45
−7.05×10
19
u
44
+· · ·+3.67×10
19
a−2.19×10
20
, u
46
−u
45
+· · ·−4u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
−2.70647u
45
+ 1.91955u
44
+ ··· − 10.9263u + 5.97160
−0.219384u
45
+ 0.484891u
44
+ ··· − 1.60887u + 0.212845
a
11
=
1
u
2
a
1
=
3.33142u
45
− 2.00063u
44
+ ··· + 10.3559u − 4.02342
1.22417u
45
− 1.02774u
44
+ ··· + 3.03021u − 0.595457
a
3
=
u
u
a
2
=
4.37249u
45
− 1.83378u
44
+ ··· + 15.1410u − 3.15401
2.88125u
45
− 1.87484u
44
+ ··· + 10.2725u − 3.36688
a
6
=
−3.03496u
45
+ 2.13094u
44
+ ··· − 9.20367u + 4.91918
−0.547882u
45
+ 0.696284u
44
+ ··· + 0.113735u − 0.839578
a
9
=
−u
2
+ 1
−u
4
a
8
=
−2.33885u
45
+ 1.49981u
44
+ ··· − 8.74130u + 5.70663
0.536038u
45
− 0.110109u
44
+ ··· − 1.01730u − 0.160962
a
5
=
0.160962u
45
+ 0.375077u
44
+ ··· + 3.35122u − 1.66115
−0.413110u
45
+ 1.85280u
44
+ ··· − 0.665590u + 1.80281
a
5
=
0.160962u
45
+ 0.375077u
44
+ ··· + 3.35122u − 1.66115
−0.413110u
45
+ 1.85280u
44
+ ··· − 0.665590u + 1.80281
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
13372946836041823816
36719786468444867913
u
45
+
53663175405029739464
36719786468444867913
u
44
+ ··· +
374972108042035142776
36719786468444867913
u −
316536124285645900534
36719786468444867913
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
23
+ u
22
+ ··· + 2u + 1)
2
c
2
(u
23
+ 11u
22
+ ··· − 2u
2
− 1)
2
c
3
, c
4
, c
8
c
10
u
46
+ u
45
+ ··· + 4u + 1
c
6
(u
23
− u
22
+ ··· − 8u + 5)
2
c
7
, c
9
u
46
+ 25u
45
+ ··· + 4u + 1
c
11
(u
23
+ 5u
22
+ ··· + 32u + 7)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
23
+ 11y
22
+ ··· − 2y
2
− 1)
2
c
2
(y
23
+ 3y
22
+ ··· − 4y −1)
2
c
3
, c
4
, c
8
c
10
y
46
− 25y
45
+ ··· − 4y + 1
c
6
(y
23
− 5y
22
+ ··· + 264y −25)
2
c
7
, c
9
y
46
− 9y
45
+ ··· − 104y + 1
c
11
(y
23
+ 7y
22
+ ··· − 404y −49)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326451 + 0.907420I
a = −0.77255 + 1.54332I
b = −1.111200 − 0.111182I
0.14155 + 10.59580I −6.96908 − 7.47788I
u = 0.326451 − 0.907420I
a = −0.77255 − 1.54332I
b = −1.111200 + 0.111182I
0.14155 − 10.59580I −6.96908 + 7.47788I
u = 0.539847 + 0.797694I
a = 0.530178 + 0.740332I
b = −0.897400 + 0.896177I
2.35134 − 1.73636I −4.20687 + 2.46590I
u = 0.539847 − 0.797694I
a = 0.530178 − 0.740332I
b = −0.897400 − 0.896177I
2.35134 + 1.73636I −4.20687 − 2.46590I
u = −0.466971 + 0.825572I
a = 0.159069 − 0.983222I
b = −1.088190 − 0.614230I
3.49101 − 3.16234I −2.33540 + 3.46689I
u = −0.466971 − 0.825572I
a = 0.159069 + 0.983222I
b = −1.088190 + 0.614230I
3.49101 + 3.16234I −2.33540 − 3.46689I
u = −0.356156 + 0.878751I
a = −0.54445 − 1.35389I
b = −1.126660 − 0.091255I
2.34965 − 5.52406I −3.72778 + 3.52157I
u = −0.356156 − 0.878751I
a = −0.54445 + 1.35389I
b = −1.126660 + 0.091255I
2.34965 + 5.52406I −3.72778 − 3.52157I
u = −1.036260 + 0.200630I
a = −0.031632 + 0.423510I
b = −0.996138 + 0.538101I
−4.31524 + 3.60580I −10.88555 − 4.48858I
u = −1.036260 − 0.200630I
a = −0.031632 − 0.423510I
b = −0.996138 − 0.538101I
−4.31524 − 3.60580I −10.88555 + 4.48858I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.976746 + 0.435286I
a = −0.94989 − 2.08219I
b = −1.89184 − 1.72781I
−3.06946 + 2.29224I −8.17333 − 3.81893I
u = −0.976746 − 0.435286I
a = −0.94989 + 2.08219I
b = −1.89184 + 1.72781I
−3.06946 − 2.29224I −8.17333 + 3.81893I
u = 0.886233 + 0.678199I
a = 1.217710 − 0.695264I
b = 1.155150 + 0.542637I
2.35134 + 1.73636I −4.20687 − 2.46590I
u = 0.886233 − 0.678199I
a = 1.217710 + 0.695264I
b = 1.155150 − 0.542637I
2.35134 − 1.73636I −4.20687 + 2.46590I
u = 1.009630 + 0.482481I
a = −0.74786 + 2.38510I
b = −2.07366 + 2.28227I
−5.29128 − 7.02777I −11.56401 + 7.34039I
u = 1.009630 − 0.482481I
a = −0.74786 − 2.38510I
b = −2.07366 − 2.28227I
−5.29128 + 7.02777I −11.56401 − 7.34039I
u = −0.807547 + 0.331658I
a = −1.81318 − 1.49133I
b = −1.88066 − 0.51355I
−2.27583 + 0.94673I −5.56367 − 4.33310I
u = −0.807547 − 0.331658I
a = −1.81318 + 1.49133I
b = −1.88066 + 0.51355I
−2.27583 − 0.94673I −5.56367 + 4.33310I
u = 0.296950 + 0.801445I
a = −0.872198 + 0.800219I
b = −0.792177 + 0.162915I
−2.33291 + 3.02476I −10.12213 − 2.21609I
u = 0.296950 − 0.801445I
a = −0.872198 − 0.800219I
b = −0.792177 − 0.162915I
−2.33291 − 3.02476I −10.12213 + 2.21609I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.079890 + 0.398169I
a = −0.33037 + 1.80790I
b = −0.88071 + 2.08789I
−7.03235 + 0.30335I −15.4115 + 0.4048I
u = 1.079890 − 0.398169I
a = −0.33037 − 1.80790I
b = −0.88071 − 2.08789I
−7.03235 − 0.30335I −15.4115 − 0.4048I
u = −0.952704 + 0.656540I
a = 1.13459 + 0.99283I
b = 1.52639 + 0.00115I
3.49101 + 3.16234I −2.33540 − 3.46689I
u = −0.952704 − 0.656540I
a = 1.13459 − 0.99283I
b = 1.52639 − 0.00115I
3.49101 − 3.16234I −2.33540 + 3.46689I
u = 1.050590 + 0.549581I
a = 0.568130 − 1.260550I
b = 1.01651 − 1.37602I
−2.33291 − 3.02476I −10.12213 + 2.21609I
u = 1.050590 − 0.549581I
a = 0.568130 + 1.260550I
b = 1.01651 + 1.37602I
−2.33291 + 3.02476I −10.12213 − 2.21609I
u = 1.213100 + 0.082369I
a = −0.285118 + 0.176496I
b = −0.551742 − 0.474744I
−2.27583 + 0.94673I −5.56367 − 4.33310I
u = 1.213100 − 0.082369I
a = −0.285118 − 0.176496I
b = −0.551742 + 0.474744I
−2.27583 − 0.94673I −5.56367 + 4.33310I
u = −1.219100 + 0.005734I
a = −0.379506 + 0.077327I
b = −1.217710 − 0.486619I
−3.90982 − 3.26242I −8.80376 + 2.26815I
u = −1.219100 − 0.005734I
a = −0.379506 − 0.077327I
b = −1.217710 + 0.486619I
−3.90982 + 3.26242I −8.80376 − 2.26815I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.054910 + 0.629750I
a = 0.89707 + 1.44259I
b = 1.92867 + 1.14714I
2.34965 + 5.52406I −3.72778 − 3.52157I
u = −1.054910 − 0.629750I
a = 0.89707 − 1.44259I
b = 1.92867 − 1.14714I
2.34965 − 5.52406I −3.72778 + 3.52157I
u = −1.223310 + 0.272825I
a = 0.227490 − 0.807258I
b = 0.791557 − 0.749493I
−7.03235 + 0.30335I −15.4115 + 0.I
u = −1.223310 − 0.272825I
a = 0.227490 + 0.807258I
b = 0.791557 + 0.749493I
−7.03235 − 0.30335I −15.4115 + 0.I
u = 1.089410 + 0.631074I
a = 0.82929 − 1.61402I
b = 2.12255 − 1.58531I
0.14155 − 10.59580I −7.00000 + 7.47788I
u = 1.089410 − 0.631074I
a = 0.82929 + 1.61402I
b = 2.12255 + 1.58531I
0.14155 + 10.59580I −7.00000 − 7.47788I
u = 1.260980 + 0.195080I
a = 0.136063 + 0.360918I
b = 0.638559 − 0.316478I
−3.06946 + 2.29224I −7.00000 − 3.81893I
u = 1.260980 − 0.195080I
a = 0.136063 − 0.360918I
b = 0.638559 + 0.316478I
−3.06946 − 2.29224I −7.00000 + 3.81893I
u = −1.294740 + 0.221264I
a = 0.355915 − 0.330975I
b = 1.227850 + 0.392277I
−5.29128 − 7.02777I −11.56401 + 7.34039I
u = −1.294740 − 0.221264I
a = 0.355915 + 0.330975I
b = 1.227850 − 0.392277I
−5.29128 + 7.02777I −11.56401 − 7.34039I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594081 + 0.341794I
a = −2.68688 + 1.47263I
b = −1.88722 − 0.13661I
−3.90982 + 3.26242I −8.80376 − 2.26815I
u = 0.594081 − 0.341794I
a = −2.68688 − 1.47263I
b = −1.88722 + 0.13661I
−3.90982 − 3.26242I −8.80376 + 2.26815I
u = 0.663527
a = 0.600867
b = −0.631190
−1.33670 −6.47390
u = 0.486649
a = 1.02746
b = −0.652402
−1.33670 −6.47390
u = −0.033796 + 0.382833I
a = −1.45604 + 2.22878I
b = −0.870135 − 0.373642I
−4.31524 − 3.60580I −10.88555 + 4.48858I
u = −0.033796 − 0.382833I
a = −1.45604 − 2.22878I
b = −0.870135 + 0.373642I
−4.31524 + 3.60580I −10.88555 − 4.48858I
16
III. I
u
3
= hb
4
+ 4b
3
+ 4b
2
+ 1, a + 1, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
10
=
1
0
a
7
=
−1
b
a
11
=
1
1
a
1
=
−b
b
2
+ b + 1
a
3
=
−1
−1
a
2
=
−b
3
− 2b
2
− b − 1
−b
3
+ 3b − 1
a
6
=
b
2b + 1
a
9
=
0
−1
a
8
=
−1
b − 1
a
5
=
1
−b
a
5
=
1
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
2
+ 8b − 16
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
4
+ 2u
2
+ 2
c
2
(u
2
+ 2u + 2)
2
c
3
, c
7
, c
8
c
9
(u − 1)
4
c
4
, c
10
(u + 1)
4
c
6
, c
11
u
4
− 2u
2
+ 2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ 2y + 2)
2
c
2
(y
2
+ 4)
2
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
4
c
6
, c
11
(y
2
− 2y + 2)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.098684 + 0.455090I
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −1.00000
a = −1.00000
b = 0.098684 − 0.455090I
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = −1.00000
a = −1.00000
b = −2.09868 + 0.45509I
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = −1.00000
a = −1.00000
b = −2.09868 − 0.45509I
−5.75727 − 3.66386I −16.0000 + 4.0000I
20
IV. I
u
4
= hb
3
+ 3b
2
+ 3b + 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
10
=
1
0
a
7
=
−1
b
a
11
=
1
1
a
1
=
−b
b
2
+ b + 1
a
3
=
1
1
a
2
=
−b
2
− 2b
−b
2
− 2b
a
6
=
b
2b + 1
a
9
=
0
−1
a
8
=
−1
b − 1
a
5
=
−1
b
a
5
=
−1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
2
+ 8b − 8
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
u
3
c
3
, c
8
(u + 1)
3
c
4
, c
7
, c
9
c
10
(u − 1)
3
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
y
3
c
3
, c
4
, c
7
c
8
, c
9
, c
10
(y −1)
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
u = 1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
u = 1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
3
(u
4
+ 2u
2
+ 2)(u
23
+ u
22
+ ··· + 2u + 1)
2
(u
31
− 3u
30
+ ··· − 6u + 2)
c
2
u
3
(u
2
+ 2u + 2)
2
(u
23
+ 11u
22
+ ··· − 2u
2
− 1)
2
· (u
31
+ 15u
30
+ ··· − 4u − 4)
c
3
, c
8
((u − 1)
4
)(u + 1)
3
(u
31
+ u
30
+ ··· + 2u + 1)(u
46
+ u
45
+ ··· + 4u + 1)
c
4
, c
10
((u − 1)
3
)(u + 1)
4
(u
31
+ u
30
+ ··· + 2u + 1)(u
46
+ u
45
+ ··· + 4u + 1)
c
6
u
3
(u
4
− 2u
2
+ 2)(u
23
− u
22
+ ··· − 8u + 5)
2
(u
31
+ 3u
30
+ ··· + 34u + 2)
c
7
, c
9
((u − 1)
7
)(u
31
+ 13u
30
+ ··· + 8u + 1)(u
46
+ 25u
45
+ ··· + 4u + 1)
c
11
u
3
(u
4
− 2u
2
+ 2)(u
23
+ 5u
22
+ ··· + 32u + 7)
2
· (u
31
− 15u
30
+ ··· − 1566u + 158)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
(y
2
+ 2y + 2)
2
(y
23
+ 11y
22
+ ··· − 2y
2
− 1)
2
· (y
31
+ 15y
30
+ ··· − 4y −4)
c
2
y
3
(y
2
+ 4)
2
(y
23
+ 3y
22
+ ··· − 4y −1)
2
(y
31
+ 3y
30
+ ··· + 112y −16)
c
3
, c
4
, c
8
c
10
((y −1)
7
)(y
31
− 13y
30
+ ··· + 8y −1)(y
46
− 25y
45
+ ··· − 4y + 1)
c
6
y
3
(y
2
− 2y + 2)
2
(y
23
− 5y
22
+ ··· + 264y −25)
2
· (y
31
− 9y
30
+ ··· + 92y −4)
c
7
, c
9
((y −1)
7
)(y
31
+ 19y
30
+ ··· − 4y −1)(y
46
− 9y
45
+ ··· − 104y + 1)
c
11
y
3
(y
2
− 2y + 2)
2
(y
23
+ 7y
22
+ ··· − 404y −49)
2
· (y
31
+ 3y
30
+ ··· − 219108y −24964)
26
