12a
0648
(K12a
0648
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 9 2 12 6 5 4 1 8
Solving Sequence
3,10
4 11
5,7
2 1 12 6 9 8
c
3
c
10
c
4
c
2
c
1
c
11
c
6
c
9
c
8
c
5
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
33
+ u
32
+ ··· + b − 1, u
33
− u
32
+ ··· + 2a + u, u
34
− 3u
33
+ ··· + 7u
2
− 2i
I
u
2
= h40u
23
a + 70u
23
+ ··· + 34a + 57, 2u
23
a + u
23
+ ··· + a
2
+ 2, u
24
+ u
23
+ ··· + 2u
2
+ 1i
I
u
3
= hb − 1, −2u
3
+ 3u
2
+ 3a + 3u − 6, u
4
− 3u
2
+ 3i
I
u
4
= hb + 1, u
2
+ a − u, u
4
− u
2
− 1i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 91 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
= h−u
33
+u
32
+· · ·+b−1, u
33
−u
32
+· · ·+2a+u, u
34
−3u
33
+· · ·+7u
2
−2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−
1
2
u
33
+
1
2
u
32
+ ··· + 2u
2
−
1
2
u
u
33
− u
32
+ ··· + u + 1
a
2
=
7
2
u
33
−
13
2
u
32
+ ··· +
7
2
u + 6
u
33
− 2u
32
+ ··· + 2u + 1
a
1
=
9
2
u
33
−
17
2
u
32
+ ··· +
11
2
u + 7
u
33
− 2u
32
+ ··· + 2u + 1
a
12
=
7
2
u
33
−
13
2
u
32
+ ··· +
5
2
u + 5
u
33
− 2u
32
+ ··· + 3u + 1
a
6
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
9
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
u
11
− 4u
9
+ 6u
7
− 2u
5
− 3u
3
+ 2u
u
13
− 5u
11
+ 9u
9
− 4u
7
− 6u
5
+ 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 16u
33
−30u
32
−176u
31
+ 310u
30
+ 906u
29
−1386u
28
−2824u
27
+
3246u
26
+ 5702u
25
− 3296u
24
− 7040u
23
− 2332u
22
+ 3058u
21
+ 10882u
20
+ 6024u
19
−
10740u
18
− 12104u
17
− 2002u
16
+ 6950u
15
+ 11788u
14
+ 4152u
13
− 6006u
12
− 7292u
11
−
3698u
10
+ 1314u
9
+ 3622u
8
+ 2284u
7
+ 444u
6
−662u
5
−734u
4
−368u
3
−88u
2
+ 8u + 12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
34
+ 13u
33
+ ··· + 18u + 1
c
2
, c
6
, c
7
c
12
u
34
− u
33
+ ··· − 2u − 1
c
3
, c
4
, c
10
u
34
+ 3u
33
+ ··· + 7u
2
− 2
c
5
, c
8
, c
9
u
34
− 9u
33
+ ··· − 104u + 14
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
34
+ 27y
33
+ ··· − 46y + 1
c
2
, c
6
, c
7
c
12
y
34
− 13y
33
+ ··· − 18y + 1
c
3
, c
4
, c
10
y
34
− 27y
33
+ ··· − 28y + 4
c
5
, c
8
, c
9
y
34
+ 33y
33
+ ··· − 540y + 196
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.013520 + 0.242521I
a = 0.355644 + 1.026690I
b = 0.890943 − 0.630816I
−0.60916 + 4.94810I −11.40571 − 6.58430I
u = −1.013520 − 0.242521I
a = 0.355644 − 1.026690I
b = 0.890943 + 0.630816I
−0.60916 − 4.94810I −11.40571 + 6.58430I
u = −0.019993 + 0.886536I
a = −0.99279 − 1.72000I
b = 0.620427 + 0.888173I
10.23300 − 0.57498I −4.93221 + 2.01552I
u = −0.019993 − 0.886536I
a = −0.99279 + 1.72000I
b = 0.620427 − 0.888173I
10.23300 + 0.57498I −4.93221 − 2.01552I
u = −0.068695 + 0.879558I
a = −0.61168 + 2.14998I
b = 1.162480 − 0.677594I
6.70898 + 11.31000I −9.03751 − 7.13336I
u = −0.068695 − 0.879558I
a = −0.61168 − 2.14998I
b = 1.162480 + 0.677594I
6.70898 − 11.31000I −9.03751 + 7.13336I
u = 1.207750 + 0.187996I
a = −0.308967 + 0.091247I
b = 0.324451 − 0.579872I
−1.55132 − 1.46622I −9.64070 + 0.44653I
u = 1.207750 − 0.187996I
a = −0.308967 − 0.091247I
b = 0.324451 + 0.579872I
−1.55132 + 1.46622I −9.64070 − 0.44653I
u = −1.211280 + 0.430207I
a = 0.282844 + 0.666214I
b = −1.145270 − 0.686416I
3.19057 − 6.62584I −12.00000 + 3.79448I
u = −1.211280 − 0.430207I
a = 0.282844 − 0.666214I
b = −1.145270 + 0.686416I
3.19057 + 6.62584I −12.00000 − 3.79448I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.086828 + 0.686695I
a = 0.675634 + 0.571144I
b = −0.750792 − 0.491169I
2.05021 − 1.49541I −7.38318 + 3.42302I
u = −0.086828 − 0.686695I
a = 0.675634 − 0.571144I
b = −0.750792 + 0.491169I
2.05021 + 1.49541I −7.38318 − 3.42302I
u = −1.31718
a = −1.28254
b = −0.594449
−5.52603 −16.4440
u = −1.281510 + 0.305200I
a = 0.845662 + 0.733598I
b = 0.682471 − 0.253099I
−1.94338 + 5.09853I −12.0000 − 8.2909I
u = −1.281510 − 0.305200I
a = 0.845662 − 0.733598I
b = 0.682471 + 0.253099I
−1.94338 − 5.09853I −12.0000 + 8.2909I
u = −1.260670 + 0.425063I
a = −0.21847 − 1.46519I
b = −0.653525 + 0.878185I
6.38980 + 5.26542I −8.46055 − 5.30635I
u = −1.260670 − 0.425063I
a = −0.21847 + 1.46519I
b = −0.653525 − 0.878185I
6.38980 − 5.26542I −8.46055 + 5.30635I
u = −0.007042 + 0.669070I
a = 0.407696 + 0.768480I
b = −0.636123 − 0.421028I
2.05008 − 1.46908I −6.49670 + 4.60453I
u = −0.007042 − 0.669070I
a = 0.407696 − 0.768480I
b = −0.636123 + 0.421028I
2.05008 + 1.46908I −6.49670 − 4.60453I
u = −0.584426 + 0.322111I
a = 0.0940661 − 0.0123771I
b = 0.998997 + 0.590488I
−1.17138 − 4.75212I −13.33145 + 3.31691I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584426 − 0.322111I
a = 0.0940661 + 0.0123771I
b = 0.998997 − 0.590488I
−1.17138 + 4.75212I −13.33145 − 3.31691I
u = −0.331538 + 0.561990I
a = −0.42743 − 2.05569I
b = −1.071630 + 0.613723I
−0.24987 + 8.13095I −11.3800 − 9.4182I
u = −0.331538 − 0.561990I
a = −0.42743 + 2.05569I
b = −1.071630 − 0.613723I
−0.24987 − 8.13095I −11.3800 + 9.4182I
u = 1.312450 + 0.320860I
a = 0.246500 − 0.701851I
b = 0.854983 − 0.402484I
−2.29444 − 2.26511I −13.59499 − 1.93125I
u = 1.312450 − 0.320860I
a = 0.246500 + 0.701851I
b = 0.854983 + 0.402484I
−2.29444 + 2.26511I −13.59499 + 1.93125I
u = 1.292790 + 0.415380I
a = 1.050280 − 0.475483I
b = −0.587435 + 0.891176I
6.14677 − 4.08463I −8.53251 + 0.I
u = 1.292790 − 0.415380I
a = 1.050280 + 0.475483I
b = −0.587435 − 0.891176I
6.14677 + 4.08463I −8.53251 + 0.I
u = 1.365780 + 0.061291I
a = −1.52752 + 0.49479I
b = −1.016200 + 0.501862I
−7.06900 + 3.73055I −18.8014 − 4.5700I
u = 1.365780 − 0.061291I
a = −1.52752 − 0.49479I
b = −1.016200 − 0.501862I
−7.06900 − 3.73055I −18.8014 + 4.5700I
u = 1.356100 + 0.180668I
a = 1.87588 − 1.22676I
b = 1.113880 + 0.583314I
−5.54762 − 10.69250I −17.2417 + 9.2859I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.356100 − 0.180668I
a = 1.87588 + 1.22676I
b = 1.113880 − 0.583314I
−5.54762 + 10.69250I −17.2417 − 9.2859I
u = 1.325120 + 0.401209I
a = −0.95387 + 2.20135I
b = −1.173850 − 0.667200I
2.3480 − 15.9016I −12.0000 + 9.6149I
u = 1.325120 − 0.401209I
a = −0.95387 − 2.20135I
b = −1.173850 + 0.667200I
2.3480 + 15.9016I −12.0000 − 9.6149I
u = 0.328225
a = 0.695567
b = 0.366829
−0.582542 −16.9630
8
II. I
u
2
=
h40u
23
a+70u
23
+· · ·+34a+ 57, 2u
23
a+u
23
+· · ·+a
2
+2, u
24
+u
23
+· · ·+2u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
a
−20u
23
a − 35u
23
+ ··· − 17a −
57
2
a
2
=
−35u
23
a −
121
2
u
23
+ ··· −
57
2
a − 50
−
23
2
u
23
a − 21u
23
+ ··· − 9a − 18
a
1
=
−
93
2
u
23
a −
163
2
u
23
+ ··· −
75
2
a − 68
−
23
2
u
23
a − 21u
23
+ ··· − 9a − 18
a
12
=
35u
23
a +
121
2
u
23
+ ··· +
57
2
a + 51
1
a
6
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
9
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
u
11
− 4u
9
+ 6u
7
− 2u
5
− 3u
3
+ 2u
u
13
− 5u
11
+ 9u
9
− 4u
7
− 6u
5
+ 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
21
−32u
19
+ 4u
18
+ 108u
17
−28u
16
−180u
15
+ 80u
14
+ 104u
13
−104u
12
+ 120u
11
+
24u
10
− 216u
9
+ 88u
8
+ 56u
7
− 76u
6
+ 80u
5
− 12u
4
− 36u
3
+ 24u
2
− 8u − 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
48
+ 25u
47
+ ··· + 1100u + 49
c
2
, c
6
, c
7
c
12
u
48
− u
47
+ ··· + 20u − 7
c
3
, c
4
, c
10
(u
24
− u
23
+ ··· + 2u
2
+ 1)
2
c
5
, c
8
, c
9
(u
24
+ 3u
23
+ ··· + 8u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
48
− 5y
47
+ ··· − 196288y + 2401
c
2
, c
6
, c
7
c
12
y
48
− 25y
47
+ ··· − 1100y + 49
c
3
, c
4
, c
10
(y
24
− 19y
23
+ ··· + 4y + 1)
2
c
5
, c
8
, c
9
(y
24
+ 25y
23
+ ··· − 20y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047552 + 0.882738I
a = −0.93385 + 1.58747I
b = 0.435071 − 0.953033I
8.92830 − 5.35992I −6.31714 + 3.17670I
u = 0.047552 + 0.882738I
a = −0.77910 − 2.11672I
b = 1.047250 + 0.722390I
8.92830 − 5.35992I −6.31714 + 3.17670I
u = 0.047552 − 0.882738I
a = −0.93385 − 1.58747I
b = 0.435071 + 0.953033I
8.92830 + 5.35992I −6.31714 − 3.17670I
u = 0.047552 − 0.882738I
a = −0.77910 + 2.11672I
b = 1.047250 − 0.722390I
8.92830 + 5.35992I −6.31714 − 3.17670I
u = −0.023946 + 0.850260I
a = 0.854901 + 0.065619I
b = −1.327570 − 0.116085I
2.61833 + 2.14805I −9.50752 − 3.24690I
u = −0.023946 + 0.850260I
a = −1.26227 + 2.30944I
b = 0.859183 − 0.533480I
2.61833 + 2.14805I −9.50752 − 3.24690I
u = −0.023946 − 0.850260I
a = 0.854901 − 0.065619I
b = −1.327570 + 0.116085I
2.61833 − 2.14805I −9.50752 + 3.24690I
u = −0.023946 − 0.850260I
a = −1.26227 − 2.30944I
b = 0.859183 + 0.533480I
2.61833 − 2.14805I −9.50752 + 3.24690I
u = 0.832524
a = 0.131221 + 0.555408I
b = 0.682430 − 0.630183I
−0.0807297 −10.4750
u = 0.832524
a = 0.131221 − 0.555408I
b = 0.682430 + 0.630183I
−0.0807297 −10.4750
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20293
a = −1.73587
b = −1.15462
−5.82330 −13.8910
u = −1.20293
a = −1.78357
b = 0.588840
−5.82330 −13.8910
u = 1.293390 + 0.128068I
a = −1.91095 + 0.30080I
b = −1.204290 + 0.245726I
−7.93370 − 2.66216I −20.0752 + 4.8307I
u = 1.293390 + 0.128068I
a = 1.66650 − 2.23253I
b = 1.051290 + 0.371289I
−7.93370 − 2.66216I −20.0752 + 4.8307I
u = 1.293390 − 0.128068I
a = −1.91095 − 0.30080I
b = −1.204290 − 0.245726I
−7.93370 + 2.66216I −20.0752 − 4.8307I
u = 1.293390 − 0.128068I
a = 1.66650 + 2.23253I
b = 1.051290 − 0.371289I
−7.93370 + 2.66216I −20.0752 − 4.8307I
u = 1.234200 + 0.427679I
a = 0.533072 − 0.692246I
b = −1.021630 + 0.732505I
5.26485 + 0.67393I −9.45928 + 0.18139I
u = 1.234200 + 0.427679I
a = −0.175482 + 1.183140I
b = −0.464333 − 0.941817I
5.26485 + 0.67393I −9.45928 + 0.18139I
u = 1.234200 − 0.427679I
a = 0.533072 + 0.692246I
b = −1.021630 − 0.732505I
5.26485 − 0.67393I −9.45928 − 0.18139I
u = 1.234200 − 0.427679I
a = −0.175482 − 1.183140I
b = −0.464333 + 0.941817I
5.26485 − 0.67393I −9.45928 − 0.18139I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691969
a = 0.274874 + 0.414868I
b = 0.670746 − 0.591354I
−0.0763260 −11.1940
u = 0.691969
a = 0.274874 − 0.414868I
b = 0.670746 + 0.591354I
−0.0763260 −11.1940
u = −1.30821
a = −1.11879
b = −0.332716
−5.51913 −16.7540
u = −1.30821
a = −1.43447
b = −0.791230
−5.51913 −16.7540
u = −1.252440 + 0.391136I
a = 0.449607 + 1.024250I
b = 1.319610 − 0.087540I
−1.18429 + 2.30642I −12.92509 − 0.09891I
u = −1.252440 + 0.391136I
a = 1.03328 + 1.08909I
b = −0.812135 − 0.524983I
−1.18429 + 2.30642I −12.92509 − 0.09891I
u = −1.252440 − 0.391136I
a = 0.449607 − 1.024250I
b = 1.319610 + 0.087540I
−1.18429 − 2.30642I −12.92509 + 0.09891I
u = −1.252440 − 0.391136I
a = 1.03328 − 1.08909I
b = −0.812135 + 0.524983I
−1.18429 − 2.30642I −12.92509 + 0.09891I
u = −1.317160 + 0.196052I
a = −0.353419 + 0.369938I
b = 0.324849 + 0.740601I
−3.30467 + 5.67994I −14.0544 − 5.8984I
u = −1.317160 + 0.196052I
a = 1.52240 + 1.35145I
b = 1.002150 − 0.525239I
−3.30467 + 5.67994I −14.0544 − 5.8984I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.317160 − 0.196052I
a = −0.353419 − 0.369938I
b = 0.324849 − 0.740601I
−3.30467 − 5.67994I −14.0544 + 5.8984I
u = −1.317160 − 0.196052I
a = 1.52240 − 1.35145I
b = 1.002150 + 0.525239I
−3.30467 − 5.67994I −14.0544 + 5.8984I
u = 1.291330 + 0.388939I
a = 0.364047 − 0.995039I
b = 1.331980 − 0.141793I
−1.47874 − 6.59660I −13.7438 + 6.1593I
u = 1.291330 + 0.388939I
a = −0.10197 + 2.46547I
b = −0.898920 − 0.537221I
−1.47874 − 6.59660I −13.7438 + 6.1593I
u = 1.291330 − 0.388939I
a = 0.364047 + 0.995039I
b = 1.331980 + 0.141793I
−1.47874 + 6.59660I −13.7438 − 6.1593I
u = 1.291330 − 0.388939I
a = −0.10197 − 2.46547I
b = −0.898920 + 0.537221I
−1.47874 + 6.59660I −13.7438 − 6.1593I
u = −1.311950 + 0.407404I
a = 1.135480 + 0.399929I
b = −0.408439 − 0.956875I
4.68376 + 9.98187I −10.26847 − 5.91019I
u = −1.311950 + 0.407404I
a = −0.71217 − 2.12659I
b = −1.066530 + 0.709104I
4.68376 + 9.98187I −10.26847 − 5.91019I
u = −1.311950 − 0.407404I
a = 1.135480 − 0.399929I
b = −0.408439 + 0.956875I
4.68376 − 9.98187I −10.26847 + 5.91019I
u = −1.311950 − 0.407404I
a = −0.71217 + 2.12659I
b = −1.066530 − 0.709104I
4.68376 − 9.98187I −10.26847 + 5.91019I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.240904 + 0.566295I
a = 0.923905 − 0.605650I
b = −0.456331 + 0.723385I
1.52510 − 3.00632I −7.78842 + 5.20782I
u = 0.240904 + 0.566295I
a = −0.07657 + 2.00277I
b = −0.904982 − 0.580179I
1.52510 − 3.00632I −7.78842 + 5.20782I
u = 0.240904 − 0.566295I
a = 0.923905 + 0.605650I
b = −0.456331 − 0.723385I
1.52510 + 3.00632I −7.78842 − 5.20782I
u = 0.240904 − 0.566295I
a = −0.07657 − 2.00277I
b = −0.904982 + 0.580179I
1.52510 + 3.00632I −7.78842 − 5.20782I
u = −0.208545 + 0.356460I
a = 0.503731 + 0.170872I
b = 1.145940 + 0.154341I
−3.36920 + 0.91014I −13.7041 − 7.5969I
u = −0.208545 + 0.356460I
a = 0.44912 − 3.83789I
b = −0.960477 + 0.265141I
−3.36920 + 0.91014I −13.7041 − 7.5969I
u = −0.208545 − 0.356460I
a = 0.503731 − 0.170872I
b = 1.145940 − 0.154341I
−3.36920 − 0.91014I −13.7041 + 7.5969I
u = −0.208545 − 0.356460I
a = 0.44912 + 3.83789I
b = −0.960477 − 0.265141I
−3.36920 − 0.91014I −13.7041 + 7.5969I
16
III. I
u
3
= hb − 1, −2u
3
+ 3u
2
+ 3a + 3u − 6, u
4
− 3u
2
+ 3i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
2
+ 3
a
7
=
2
3
u
3
− u
2
− u + 2
1
a
2
=
−
2
3
u
3
+ u
2
+ u − 1
−1
a
1
=
−
2
3
u
3
+ u
2
+ u − 2
−1
a
12
=
−
2
3
u
3
+ u
2
− 2
−u
3
+ u − 1
a
6
=
1
0
a
9
=
u
3
− 2u
−u
3
+ u
a
8
=
−u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 24
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
(u − 1)
4
c
3
, c
4
, c
10
u
4
− 3u
2
+ 3
c
5
, c
8
, c
9
u
4
+ 3u
2
+ 3
c
6
, c
12
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
10
(y
2
− 3y + 3)
2
c
5
, c
8
, c
9
(y
2
+ 3y + 3)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.271230 + 0.340625I
a = 0.303340 − 0.132080I
b = 1.00000
−3.28987 − 4.05977I −18.0000 + 3.4641I
u = 1.271230 − 0.340625I
a = 0.303340 + 0.132080I
b = 1.00000
−3.28987 + 4.05977I −18.0000 − 3.4641I
u = −1.271230 + 0.340625I
a = 0.69666 + 1.59997I
b = 1.00000
−3.28987 + 4.05977I −18.0000 − 3.4641I
u = −1.271230 − 0.340625I
a = 0.69666 − 1.59997I
b = 1.00000
−3.28987 − 4.05977I −18.0000 + 3.4641I
20
IV. I
u
4
= hb + 1, u
2
+ a − u, u
4
− u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
u
2
− 1
a
7
=
−u
2
+ u
−1
a
2
=
−u
2
+ u + 1
−1
a
1
=
−u
2
+ u
−1
a
12
=
−u
2
−u
3
+ u − 1
a
6
=
−1
0
a
9
=
−u
3
+ 2u
u
3
− u
a
8
=
u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 16
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
c
12
(u − 1)
4
c
2
, c
7
(u + 1)
4
c
3
, c
4
, c
10
u
4
− u
2
− 1
c
5
, c
8
, c
9
u
4
+ u
2
− 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
10
(y
2
− y −1)
2
c
5
, c
8
, c
9
(y
2
+ y −1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786151I
a = 0.618034 + 0.786151I
b = −1.00000
0.657974 −13.5280
u = − 0.786151I
a = 0.618034 − 0.786151I
b = −1.00000
0.657974 −13.5280
u = 1.27202
a = −0.346014
b = −1.00000
−7.23771 −22.4720
u = −1.27202
a = −2.89005
b = −1.00000
−7.23771 −22.4720
24
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
−1
0
a
4
=
1
0
a
11
=
−1
0
a
5
=
1
0
a
7
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
12
=
−1
−1
a
6
=
1
0
a
9
=
−1
0
a
8
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
12
u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
9
)(u
34
+ 13u
33
+ ··· + 18u + 1)(u
48
+ 25u
47
+ ··· + 1100u + 49)
c
2
, c
7
((u − 1)
5
)(u + 1)
4
(u
34
− u
33
+ ··· − 2u − 1)(u
48
− u
47
+ ··· + 20u − 7)
c
3
, c
4
, c
10
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
24
− u
23
+ ··· + 2u
2
+ 1)
2
· (u
34
+ 3u
33
+ ··· + 7u
2
− 2)
c
5
, c
8
, c
9
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)(u
24
+ 3u
23
+ ··· + 8u + 1)
2
· (u
34
− 9u
33
+ ··· − 104u + 14)
c
6
, c
12
((u − 1)
4
)(u + 1)
5
(u
34
− u
33
+ ··· − 2u − 1)(u
48
− u
47
+ ··· + 20u − 7)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
9
)(y
34
+ 27y
33
+ ··· − 46y + 1)
· (y
48
− 5y
47
+ ··· − 196288y + 2401)
c
2
, c
6
, c
7
c
12
((y −1)
9
)(y
34
− 13y
33
+ ··· − 18y + 1)(y
48
− 25y
47
+ ··· − 1100y + 49)
c
3
, c
4
, c
10
y(y
2
− 3y + 3)
2
(y
2
− y −1)
2
(y
24
− 19y
23
+ ··· + 4y + 1)
2
· (y
34
− 27y
33
+ ··· − 28y + 4)
c
5
, c
8
, c
9
y(y
2
+ y −1)
2
(y
2
+ 3y + 3)
2
(y
24
+ 25y
23
+ ··· − 20y + 1)
2
· (y
34
+ 33y
33
+ ··· − 540y + 196)
30
