12a
0025
(K12a
0025
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 12 10 4 8 1 7
Solving Sequence
7,12
8
1,3
2 11 6 4 5 10 9
c
7
c
12
c
1
c
11
c
6
c
3
c
5
c
10
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
19
− u
18
+ ··· − u
2
+ b, u
19
− u
18
+ ··· + a − u, u
22
− u
21
+ ··· − u + 1i
I
u
2
= hu
73
− 3u
72
+ ··· + b − 2, −2u
72
− 30u
70
+ ··· + a − u, u
74
− 2u
73
+ ··· − 3u + 1i
I
u
3
= hb + u + 2, a + 2, u
2
+ u + 1i
I
u
4
= hb − 2u − 1, a − 2u − 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 100 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
19
− u
18
+ · · · − u
2
+ b, u
19
− u
18
+ · · · + a − u, u
22
− u
21
+ · · · − u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
−u
19
+ u
18
+ ··· + u
2
+ u
−u
19
+ u
18
+ ··· − 2u
3
+ u
2
a
2
=
u
21
− u
20
+ ··· − u
3
+ u
u
21
− u
20
+ ··· − u
4
+ u
a
11
=
u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−u
19
+ u
18
+ ··· − 3u
3
+ u
2
−u
19
+ u
18
+ ··· − u
3
+ u
2
a
5
=
−u
20
+ u
19
+ ··· − u
2
+ u
−u
20
+ u
19
+ ··· + u − 1
a
10
=
u
5
+ 2u
3
+ u
−u
7
− u
5
+ u
a
9
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
−u
12
− 2u
10
− 2u
8
+ u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
21
−8u
20
+ 26u
19
−42u
18
+ 82u
17
−116u
16
+ 164u
15
−198u
14
+ 226u
13
−232u
12
+
234u
11
−206u
10
+ 198u
9
−168u
8
+ 152u
7
−132u
6
+ 100u
5
−72u
4
+ 50u
3
−18u
2
+ 14u −6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 11u
21
+ ··· + 3u + 1
c
2
, c
5
, c
7
c
12
u
22
+ u
21
+ ··· + u + 1
c
3
, c
6
u
22
− u
21
+ ··· − 3u + 1
c
4
, c
9
u
22
+ 5u
21
+ ··· + 8u + 4
c
8
, c
10
u
22
+ 5u
21
+ ··· + 56u
2
+ 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
22
+ 3y
21
+ ··· + 11y + 1
c
2
, c
5
, c
7
c
12
y
22
+ 11y
21
+ ··· + 3y + 1
c
3
, c
6
y
22
− 5y
21
+ ··· − 13y + 1
c
4
, c
9
y
22
+ 5y
21
+ ··· + 56y
2
+ 16
c
8
, c
10
y
22
+ 17y
21
+ ··· + 1792y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267420 + 0.934374I
a = 0.866808 + 0.905520I
b = 1.134230 − 0.028854I
−2.03960 − 2.30169I −5.11682 + 3.55862I
u = −0.267420 − 0.934374I
a = 0.866808 − 0.905520I
b = 1.134230 + 0.028854I
−2.03960 + 2.30169I −5.11682 − 3.55862I
u = 0.803411 + 0.448160I
a = 1.64165 − 0.62510I
b = 0.838235 − 1.073260I
6.81231 − 6.24031I 5.35592 + 2.94857I
u = 0.803411 − 0.448160I
a = 1.64165 + 0.62510I
b = 0.838235 + 1.073260I
6.81231 + 6.24031I 5.35592 − 2.94857I
u = −0.773574 + 0.483952I
a = −1.84656 − 0.54883I
b = −1.07298 − 1.03278I
7.30323 − 0.05327I 6.29197 + 2.01808I
u = −0.773574 − 0.483952I
a = −1.84656 + 0.54883I
b = −1.07298 + 1.03278I
7.30323 + 0.05327I 6.29197 − 2.01808I
u = 0.125921 + 1.085150I
a = 0.002278 + 0.829637I
b = −0.123644 − 0.255513I
−3.59209 − 2.19399I −7.43206 + 2.16700I
u = 0.125921 − 1.085150I
a = 0.002278 − 0.829637I
b = −0.123644 + 0.255513I
−3.59209 + 2.19399I −7.43206 − 2.16700I
u = −0.469571 + 1.049440I
a = −0.16005 − 2.27593I
b = 0.30952 − 3.32537I
−2.42559 − 6.55386I −3.45447 + 8.04873I
u = −0.469571 − 1.049440I
a = −0.16005 + 2.27593I
b = 0.30952 + 3.32537I
−2.42559 + 6.55386I −3.45447 − 8.04873I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.361702 + 1.107050I
a = 0.209067 − 0.490062I
b = −0.15263 − 1.59711I
−7.56344 + 3.87204I −10.26851 − 4.35879I
u = 0.361702 − 1.107050I
a = 0.209067 + 0.490062I
b = −0.15263 + 1.59711I
−7.56344 − 3.87204I −10.26851 + 4.35879I
u = 0.510802 + 1.115330I
a = 1.37025 − 1.89407I
b = 0.85945 − 3.00940I
−5.48268 + 11.20780I −5.92791 − 10.64614I
u = 0.510802 − 1.115330I
a = 1.37025 + 1.89407I
b = 0.85945 + 3.00940I
−5.48268 − 11.20780I −5.92791 + 10.64614I
u = −0.611674 + 1.083050I
a = −2.45227 − 2.64694I
b = −1.84060 − 3.72999I
3.70474 − 10.43210I 0.79280 + 7.46958I
u = −0.611674 − 1.083050I
a = −2.45227 + 2.64694I
b = −1.84060 + 3.72999I
3.70474 + 10.43210I 0.79280 − 7.46958I
u = 0.620139 + 1.106350I
a = 2.54875 − 2.41058I
b = 1.92861 − 3.51693I
2.8718 + 16.9388I −0.30393 − 11.38128I
u = 0.620139 − 1.106350I
a = 2.54875 + 2.41058I
b = 1.92861 + 3.51693I
2.8718 − 16.9388I −0.30393 + 11.38128I
u = 0.619109 + 0.241097I
a = 1.096950 + 0.038223I
b = 0.477839 − 0.202874I
−0.59135 − 2.31883I 1.12676 + 3.72876I
u = 0.619109 − 0.241097I
a = 1.096950 − 0.038223I
b = 0.477839 + 0.202874I
−0.59135 + 2.31883I 1.12676 − 3.72876I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.418845 + 0.499289I
a = −1.27687 + 1.05838I
b = −0.858029 + 0.559094I
1.00269 − 1.14066I 4.93625 + 3.17573I
u = −0.418845 − 0.499289I
a = −1.27687 − 1.05838I
b = −0.858029 − 0.559094I
1.00269 + 1.14066I 4.93625 − 3.17573I
7
II.
I
u
2
= hu
73
−3u
72
+· · ·+b−2, −2u
72
−30u
70
+· · ·+a−u, u
74
−2u
73
+· · ·−3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
3
=
2u
72
+ 30u
70
+ ··· + 2u
2
+ u
−u
73
+ 3u
72
+ ··· − 2u + 2
a
2
=
2u
72
− 2u
71
+ ··· − 6u + 3
−u
73
+ 3u
72
+ ··· − 5u + 2
a
11
=
u
3
u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−2u
73
+ 3u
72
+ ··· − u − 1
−u
73
− 13u
71
+ ··· + 3u − 1
a
5
=
−u
72
− u
71
+ ··· − u + 1
u
73
− 2u
72
+ ··· + u − 1
a
10
=
u
5
+ 2u
3
+ u
−u
7
− u
5
+ u
a
9
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
−u
12
− 2u
10
− 2u
8
+ u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
73
+ 8u
72
+ ··· − 7u + 7
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
74
+ 32u
73
+ ··· + 5u + 1
c
2
, c
5
, c
7
c
12
u
74
+ 2u
73
+ ··· + 3u + 1
c
3
, c
6
u
74
− 2u
73
+ ··· − 3u + 1
c
4
, c
9
(u
37
− 2u
36
+ ··· − u − 2)
2
c
8
, c
10
(u
37
+ 10u
36
+ ··· − 39u − 4)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
74
+ 20y
73
+ ··· + 37y + 1
c
2
, c
5
, c
7
c
12
y
74
+ 32y
73
+ ··· + 5y + 1
c
3
, c
6
y
74
+ 8y
73
+ ··· + 101y + 1
c
4
, c
9
(y
37
+ 10y
36
+ ··· − 39y −4)
2
c
8
, c
10
(y
37
+ 34y
36
+ ··· − 159y −16)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.639479 + 0.752607I
a = −2.15983 + 0.09363I
b = −1.93455 − 1.15641I
−0.61107 − 5.41655I 0. + 9.62417I
u = −0.639479 − 0.752607I
a = −2.15983 − 0.09363I
b = −1.93455 + 1.15641I
−0.61107 + 5.41655I 0. − 9.62417I
u = −0.784429 + 0.545941I
a = −2.03595 − 0.33437I
b = −1.91239 − 1.94292I
5.47701 − 8.31264I 3.19623 + 7.51099I
u = −0.784429 − 0.545941I
a = −2.03595 + 0.33437I
b = −1.91239 + 1.94292I
5.47701 + 8.31264I 3.19623 − 7.51099I
u = −0.047209 + 1.049760I
a = 2.14571 − 0.35342I
b = 0.925538 − 1.003280I
0.33366 + 3.54390I 0
u = −0.047209 − 1.049760I
a = 2.14571 + 0.35342I
b = 0.925538 + 1.003280I
0.33366 − 3.54390I 0
u = −0.779819 + 0.528531I
a = 0.740110 + 0.451946I
b = 0.62798 + 1.32561I
7.26569 − 3.05590I 6.03502 + 2.77359I
u = −0.779819 − 0.528531I
a = 0.740110 − 0.451946I
b = 0.62798 − 1.32561I
7.26569 + 3.05590I 6.03502 − 2.77359I
u = 0.009056 + 1.063140I
a = −1.19514 + 0.78248I
b = −0.491540 + 1.031220I
1.91033 − 1.51255I 0
u = 0.009056 − 1.063140I
a = −1.19514 − 0.78248I
b = −0.491540 − 1.031220I
1.91033 + 1.51255I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622852 + 0.865244I
a = 0.79438 + 2.08172I
b = −0.29643 + 1.96964I
−0.936846 + 0.485539I 0
u = −0.622852 − 0.865244I
a = 0.79438 − 2.08172I
b = −0.29643 − 1.96964I
−0.936846 − 0.485539I 0
u = 0.813660 + 0.438643I
a = −2.38959 + 1.49627I
b = −0.90547 + 2.36932I
4.86825 − 11.57530I 2.50814 + 7.25667I
u = 0.813660 − 0.438643I
a = −2.38959 − 1.49627I
b = −0.90547 − 2.36932I
4.86825 + 11.57530I 2.50814 − 7.25667I
u = 0.443091 + 0.986263I
a = −1.38423 + 1.70607I
b = −0.33820 + 1.81029I
−0.936846 + 0.485539I 0
u = 0.443091 − 0.986263I
a = −1.38423 − 1.70607I
b = −0.33820 − 1.81029I
−0.936846 − 0.485539I 0
u = 0.775921 + 0.477218I
a = −0.740766 + 0.505518I
b = −0.57413 + 1.46540I
7.26569 − 3.05590I 6.03502 + 2.77359I
u = 0.775921 − 0.477218I
a = −0.740766 − 0.505518I
b = −0.57413 − 1.46540I
7.26569 + 3.05590I 6.03502 − 2.77359I
u = 0.762103 + 0.491833I
a = 1.87904 − 0.32585I
b = 1.73107 − 1.98585I
5.70204 + 2.27936I 3.88815 − 2.05007I
u = 0.762103 − 0.491833I
a = 1.87904 + 0.32585I
b = 1.73107 + 1.98585I
5.70204 − 2.27936I 3.88815 + 2.05007I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.773218 + 0.464058I
a = 2.65308 + 1.45047I
b = 1.16242 + 2.27131I
5.54616 + 5.20107I 3.66602 − 2.81386I
u = −0.773218 − 0.464058I
a = 2.65308 − 1.45047I
b = 1.16242 − 2.27131I
5.54616 − 5.20107I 3.66602 + 2.81386I
u = −0.395925 + 1.024370I
a = −0.444820 − 1.150880I
b = −1.42676 − 1.64270I
−2.95124 0
u = −0.395925 − 1.024370I
a = −0.444820 + 1.150880I
b = −1.42676 + 1.64270I
−2.95124 0
u = −0.480742 + 0.988204I
a = −0.418583 + 1.307900I
b = −0.50569 + 1.47970I
−0.32230 − 2.77484I 0
u = −0.480742 − 0.988204I
a = −0.418583 − 1.307900I
b = −0.50569 − 1.47970I
−0.32230 + 2.77484I 0
u = −0.569891 + 0.939876I
a = −1.55469 + 0.28140I
b = −1.41271 − 0.18656I
0.15880 − 2.93389I 0
u = −0.569891 − 0.939876I
a = −1.55469 − 0.28140I
b = −1.41271 + 0.18656I
0.15880 + 2.93389I 0
u = −0.725089 + 0.517371I
a = −0.05378 + 1.70419I
b = −1.09918 + 0.98483I
1.91033 − 1.51255I 0. + 2.66920I
u = −0.725089 − 0.517371I
a = −0.05378 − 1.70419I
b = −1.09918 − 0.98483I
1.91033 + 1.51255I 0. − 2.66920I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324310 + 1.067530I
a = 0.368103 + 0.746898I
b = 0.134333 + 1.055790I
−4.13208 + 0.49053I 0
u = 0.324310 − 1.067530I
a = 0.368103 − 0.746898I
b = 0.134333 − 1.055790I
−4.13208 − 0.49053I 0
u = 0.771853 + 0.430210I
a = 0.12391 + 1.52352I
b = 1.27111 + 0.67805I
1.41199 − 4.22774I −0.66777 + 2.80088I
u = 0.771853 − 0.430210I
a = 0.12391 − 1.52352I
b = 1.27111 − 0.67805I
1.41199 + 4.22774I −0.66777 − 2.80088I
u = 0.478382 + 1.012710I
a = 1.86046 − 0.41541I
b = 1.14344 − 0.90963I
−0.61107 + 5.41655I 0
u = 0.478382 − 1.012710I
a = 1.86046 + 0.41541I
b = 1.14344 + 0.90963I
−0.61107 − 5.41655I 0
u = 0.071006 + 1.119930I
a = 1.061640 + 0.567159I
b = 0.447863 + 0.894942I
1.41199 − 4.22774I 0
u = 0.071006 − 1.119930I
a = 1.061640 − 0.567159I
b = 0.447863 − 0.894942I
1.41199 + 4.22774I 0
u = −0.552065 + 0.679047I
a = 0.318468 + 0.837668I
b = −0.026831 + 1.040650I
0.94543 − 1.58284I 3.46208 + 5.25506I
u = −0.552065 − 0.679047I
a = 0.318468 − 0.837668I
b = −0.026831 − 1.040650I
0.94543 + 1.58284I 3.46208 − 5.25506I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083389 + 1.139640I
a = −2.01039 − 0.09832I
b = −0.804300 − 0.746868I
−0.56297 − 9.41729I 0
u = 0.083389 − 1.139640I
a = −2.01039 + 0.09832I
b = −0.804300 + 0.746868I
−0.56297 + 9.41729I 0
u = 0.297227 + 1.107630I
a = −0.797728 − 0.282670I
b = 0.300506 − 0.901521I
−6.88031 − 3.64383I 0
u = 0.297227 − 1.107630I
a = −0.797728 + 0.282670I
b = 0.300506 + 0.901521I
−6.88031 + 3.64383I 0
u = 0.501716 + 1.091230I
a = −0.270062 + 1.221430I
b = −0.17916 + 1.65956I
−2.94967 + 6.65921I 0
u = 0.501716 − 1.091230I
a = −0.270062 − 1.221430I
b = −0.17916 − 1.65956I
−2.94967 − 6.65921I 0
u = 0.465718 + 1.108500I
a = 0.766414 + 0.253446I
b = 1.63805 − 0.40742I
−6.88031 + 3.64383I 0
u = 0.465718 − 1.108500I
a = 0.766414 − 0.253446I
b = 1.63805 + 0.40742I
−6.88031 − 3.64383I 0
u = −0.597031 + 1.047020I
a = −1.74633 + 0.73819I
b = −2.26975 − 0.01372I
0.33366 − 3.54390I 0
u = −0.597031 − 1.047020I
a = −1.74633 − 0.73819I
b = −2.26975 + 0.01372I
0.33366 + 3.54390I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644880 + 1.043780I
a = 1.37188 + 2.45763I
b = 0.13735 + 2.49129I
3.99070 + 2.93314I 0
u = −0.644880 − 1.043780I
a = 1.37188 − 2.45763I
b = 0.13735 − 2.49129I
3.99070 − 2.93314I 0
u = −0.635594 + 1.052450I
a = −1.140050 − 0.824434I
b = −0.475615 − 0.903685I
5.70204 − 2.27936I 0
u = −0.635594 − 1.052450I
a = −1.140050 + 0.824434I
b = −0.475615 + 0.903685I
5.70204 + 2.27936I 0
u = 0.614101 + 1.066830I
a = −1.50588 + 2.36698I
b = −0.28505 + 2.43832I
3.99070 + 2.93314I 0
u = 0.614101 − 1.066830I
a = −1.50588 − 2.36698I
b = −0.28505 − 2.43832I
3.99070 − 2.93314I 0
u = −0.617616 + 1.073840I
a = 1.01978 + 1.95064I
b = 0.67156 + 2.50713I
5.54616 − 5.20107I 0
u = −0.617616 − 1.073840I
a = 1.01978 − 1.95064I
b = 0.67156 − 2.50713I
5.54616 + 5.20107I 0
u = 0.616680 + 1.077750I
a = 1.30539 − 0.90429I
b = 0.579788 − 1.025090I
5.47701 + 8.31264I 0
u = 0.616680 − 1.077750I
a = 1.30539 + 0.90429I
b = 0.579788 + 1.025090I
5.47701 − 8.31264I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.602127 + 1.096470I
a = 1.58976 + 0.92372I
b = 2.22003 + 0.09167I
−0.56297 + 9.41729I 0
u = 0.602127 − 1.096470I
a = 1.58976 − 0.92372I
b = 2.22003 − 0.09167I
−0.56297 − 9.41729I 0
u = 0.619282 + 1.099150I
a = −1.12877 + 1.73008I
b = −0.81856 + 2.33214I
4.86825 + 11.57530I 0
u = 0.619282 − 1.099150I
a = −1.12877 − 1.73008I
b = −0.81856 − 2.33214I
4.86825 − 11.57530I 0
u = 0.298836 + 0.669488I
a = 2.36525 + 0.12741I
b = 1.34154 − 1.16389I
0.15880 + 2.93389I 0.1334486 + 0.0017874I
u = 0.298836 − 0.669488I
a = 2.36525 − 0.12741I
b = 1.34154 + 1.16389I
0.15880 − 2.93389I 0.1334486 − 0.0017874I
u = 0.696387 + 0.229050I
a = −2.03826 + 0.21361I
b = −0.354754 + 1.232240I
−2.94967 − 6.65921I −2.58619 + 7.25641I
u = 0.696387 − 0.229050I
a = −2.03826 − 0.21361I
b = −0.354754 − 1.232240I
−2.94967 + 6.65921I −2.58619 − 7.25641I
u = 0.647209 + 0.115404I
a = −0.845624 + 1.132210I
b = 0.518554 − 0.180895I
−4.13208 + 0.49053I −5.63239 − 0.25281I
u = 0.647209 − 0.115404I
a = −0.845624 − 1.132210I
b = 0.518554 + 0.180895I
−4.13208 − 0.49053I −5.63239 + 0.25281I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.385834 + 0.449069I
a = −1.135030 + 0.682969I
b = −0.002429 + 1.307960I
0.94543 − 1.58284I 3.46208 + 5.25506I
u = 0.385834 − 0.449069I
a = −1.135030 − 0.682969I
b = −0.002429 − 1.307960I
0.94543 + 1.58284I 3.46208 − 5.25506I
u = −0.412050 + 0.204676I
a = 3.13214 − 0.97399I
b = 0.762365 + 0.154767I
−0.32230 + 2.77484I 2.03391 − 3.58176I
u = −0.412050 − 0.204676I
a = 3.13214 + 0.97399I
b = 0.762365 − 0.154767I
−0.32230 − 2.77484I 2.03391 + 3.58176I
18
III. I
u
3
= hb + u + 2, a + 2, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u + 1
a
1
=
u
u
a
3
=
−2
−u − 2
a
2
=
−u − 2
−u − 1
a
11
=
1
u + 1
a
6
=
−u
−u
a
4
=
−1
−u − 1
a
5
=
−1
−u − 1
a
10
=
1
u + 1
a
9
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
11
, c
12
u
2
− u + 1
c
2
, c
7
u
2
+ u + 1
c
4
, c
8
, c
9
c
10
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
11
, c
12
y
2
+ y + 1
c
4
, c
8
, c
9
c
10
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −2.00000
b = −1.50000 − 0.86603I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −2.00000
b = −1.50000 + 0.86603I
4.05977I 0. − 6.92820I
22
IV. I
u
4
= hb − 2u − 1, a − 2u − 2, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u + 1
a
1
=
u
u
a
3
=
2u + 2
2u + 1
a
2
=
u + 2
2u + 2
a
11
=
1
u + 1
a
6
=
−u
−u
a
4
=
u + 1
u
a
5
=
u + 1
u
a
10
=
1
u + 1
a
9
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
11
, c
12
u
2
− u + 1
c
2
, c
7
u
2
+ u + 1
c
4
, c
8
, c
9
c
10
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
11
, c
12
y
2
+ y + 1
c
4
, c
8
, c
9
c
10
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000 + 1.73205I
b = 1.73205I
0 3.00000
u = −0.500000 − 0.866025I
a = 1.00000 − 1.73205I
b = − 1.73205I
0 3.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u
2
− u + 1)
2
)(u
22
+ 11u
21
+ ··· + 3u + 1)(u
74
+ 32u
73
+ ··· + 5u + 1)
c
2
, c
7
((u
2
+ u + 1)
2
)(u
22
+ u
21
+ ··· + u + 1)(u
74
+ 2u
73
+ ··· + 3u + 1)
c
3
, c
6
((u
2
− u + 1)
2
)(u
22
− u
21
+ ··· − 3u + 1)(u
74
− 2u
73
+ ··· − 3u + 1)
c
4
, c
9
u
4
(u
22
+ 5u
21
+ ··· + 8u + 4)(u
37
− 2u
36
+ ··· − u − 2)
2
c
5
, c
12
((u
2
− u + 1)
2
)(u
22
+ u
21
+ ··· + u + 1)(u
74
+ 2u
73
+ ··· + 3u + 1)
c
8
, c
10
u
4
(u
22
+ 5u
21
+ ··· + 56u
2
+ 16)(u
37
+ 10u
36
+ ··· − 39u − 4)
2
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y
2
+ y + 1)
2
)(y
22
+ 3y
21
+ ··· + 11y + 1)(y
74
+ 20y
73
+ ··· + 37y + 1)
c
2
, c
5
, c
7
c
12
((y
2
+ y + 1)
2
)(y
22
+ 11y
21
+ ··· + 3y + 1)(y
74
+ 32y
73
+ ··· + 5y + 1)
c
3
, c
6
((y
2
+ y + 1)
2
)(y
22
− 5y
21
+ ··· − 13y + 1)(y
74
+ 8y
73
+ ··· + 101y + 1)
c
4
, c
9
y
4
(y
22
+ 5y
21
+ ··· + 56y
2
+ 16)(y
37
+ 10y
36
+ ··· − 39y −4)
2
c
8
, c
10
y
4
(y
22
+ 17y
21
+ ··· + 1792y + 256)
· (y
37
+ 34y
36
+ ··· − 159y −16)
2
28
