12a
0924
(K12a
0924
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 2 10 12 1 3 5 8 7
Solving Sequence
2,5
6
3,11
4 1 10 7 9 8 12
c
5
c
2
c
4
c
1
c
10
c
6
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−47905927u
73
+ 611463177u
72
+ ··· + 3439853568b + 11169010901668,
− 4109478614099u
73
+ 27248497195437u
72
+ ··· + 29824677052416a + 129084806711241884,
u
74
− 8u
73
+ ··· − 216611u + 52022i
I
u
2
= hu
3
+ b + 2u, −8u
3
− 3u
2
+ 5a − 17u − 7, u
4
+ 3u
2
+ 1i
I
u
3
= ha
2
+ b − a, a
3
− 2a
2
+ a + 1, u + 1i
I
u
4
= hb
6
a
3
− 3b
5
a
2
+ ··· − a
2
+ 1, u + 1i
I
v
1
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v − 1i
I
v
2
= ha, b
3
+ b
2
+ 2b + 1, v − 1i
* 5 irreducible components of dim
C
= 0, with total 90 representations.
* 1 irreducible components of dim
C
= 1
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−4.79 × 10
7
u
73
+ 6.11 × 10
8
u
72
+ · · · + 3.44 × 10
9
b + 1.12 ×
10
13
, −4.11 × 10
12
u
73
+ 2.72 × 10
13
u
72
+ · · · + 2.98 × 10
13
a + 1.29 ×
10
17
, u
74
− 8u
73
+ · · · − 216611u + 52022i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
0.137788u
73
− 0.913623u
72
+ ··· + 16267.3u − 4328.12
0.0139267u
73
− 0.177758u
72
+ ··· + 9142.14u − 3246.94
a
4
=
−0.00499643u
73
+ 0.0350880u
72
+ ··· − 833.787u + 264.234
0.0000461649u
73
− 0.000532115u
72
+ ··· + 23.8243u − 7.51639
a
1
=
0.00140672u
73
− 0.0127174u
72
+ ··· + 521.516u − 198.382
−0.00563162u
73
+ 0.0396538u
72
+ ··· − 889.693u + 268.556
a
10
=
0.151715u
73
− 1.09138u
72
+ ··· + 25409.5u − 7575.06
0.0139267u
73
− 0.177758u
72
+ ··· + 9142.14u − 3246.94
a
7
=
0.00526992u
73
− 0.0422065u
72
+ ··· + 1460.05u − 545.028
−0.00530723u
73
+ 0.0369747u
72
+ ··· − 859.358u + 270.028
a
9
=
−0.0114518u
73
+ 0.0715137u
72
+ ··· − 1087.20u + 313.766
0.103761u
73
− 0.693948u
72
+ ··· + 13273.7u − 3725.94
a
8
=
−0.0202394u
73
+ 0.0938447u
72
+ ··· + 1301.88u − 735.830
−0.0939198u
73
+ 0.678803u
72
+ ··· − 15904.3u + 4756.89
a
12
=
0.0629844u
73
− 0.398283u
72
+ ··· + 5636.71u − 1251.79
0.0577805u
73
− 0.401753u
72
+ ··· + 8772.09u − 2612.98
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
143175559
644972544
u
73
+
416881405
286654464
u
72
+ ··· −
130085081890987
5159780352
u +
17208542618977
2579890176
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
64(64u
74
− 128u
73
+ ··· − 2725866u + 511569)
c
2
, c
5
u
74
− 8u
73
+ ··· − 216611u + 52022
c
3
, c
9
27(27u
74
− 27u
73
+ ··· − 170u + 61)
c
4
, c
10
27(27u
74
− 27u
73
+ ··· + 208u + 61)
c
6
64(64u
74
+ 128u
73
+ ··· + 1.69976 × 10
7
u + 3434427)
c
7
, c
11
, c
12
u
74
− 4u
73
+ ··· − 255u + 62
c
8
u
74
+ 4u
73
+ ··· + 777216u + 285696
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4096
· (4096y
74
− 135168y
73
+ ··· − 338930953884y + 261702841761)
c
2
, c
5
y
74
− 42y
73
+ ··· + 4426533163y + 2706288484
c
3
, c
9
729(729y
74
+ 43011y
73
+ ··· + 40884y + 3721)
c
4
, c
10
729(729y
74
+ 28431y
73
+ ··· + 91668y + 3721)
c
6
4096
· (4096y
74
− 118784y
73
+ ··· − 146351267872524y + 11795288818329)
c
7
, c
11
, c
12
y
74
+ 66y
73
+ ··· + 4787y + 3844
c
8
y
74
− 6y
73
+ ··· + 199138738176y + 81622204416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956855 + 0.323244I
a = 1.58587 − 1.46932I
b = 0.254516 + 0.831849I
−2.11972 − 1.41825I 0
u = 0.956855 − 0.323244I
a = 1.58587 + 1.46932I
b = 0.254516 − 0.831849I
−2.11972 + 1.41825I 0
u = −0.392834 + 0.936221I
a = 0.387039 + 1.005900I
b = −0.481180 − 0.404568I
−1.76313 − 1.05065I 0
u = −0.392834 − 0.936221I
a = 0.387039 − 1.005900I
b = −0.481180 + 0.404568I
−1.76313 + 1.05065I 0
u = 0.349178 + 0.959515I
a = 0.37166 − 1.52102I
b = −0.098677 + 1.279600I
10.04650 − 1.75472I 0
u = 0.349178 − 0.959515I
a = 0.37166 + 1.52102I
b = −0.098677 − 1.279600I
10.04650 + 1.75472I 0
u = −1.039710 + 0.243499I
a = 0.250091 − 0.954693I
b = −0.332462 − 0.537886I
0.82573 + 1.48951I 0
u = −1.039710 − 0.243499I
a = 0.250091 + 0.954693I
b = −0.332462 + 0.537886I
0.82573 − 1.48951I 0
u = 0.853927 + 0.261180I
a = −1.54106 + 2.19678I
b = −0.135462 − 0.805847I
2.19115 + 2.07020I −1.61287 + 2.28344I
u = 0.853927 − 0.261180I
a = −1.54106 − 2.19678I
b = −0.135462 + 0.805847I
2.19115 − 2.07020I −1.61287 − 2.28344I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280504 + 0.832280I
a = −0.514278 − 0.776313I
b = 0.682562 + 0.166619I
−4.77010 + 3.14743I −13.70473 − 3.39156I
u = −0.280504 − 0.832280I
a = −0.514278 + 0.776313I
b = 0.682562 − 0.166619I
−4.77010 − 3.14743I −13.70473 + 3.39156I
u = −1.141320 + 0.128617I
a = −0.208428 + 0.721747I
b = 0.188973 + 0.757335I
−2.36891 − 0.94403I 0
u = −1.141320 − 0.128617I
a = −0.208428 − 0.721747I
b = 0.188973 − 0.757335I
−2.36891 + 0.94403I 0
u = 1.090800 + 0.370077I
a = −1.24076 + 0.89624I
b = −0.514177 − 0.873216I
0.85631 − 4.70807I 0
u = 1.090800 − 0.370077I
a = −1.24076 − 0.89624I
b = −0.514177 + 0.873216I
0.85631 + 4.70807I 0
u = 0.364310 + 0.761476I
a = −0.37557 + 1.45470I
b = 0.204448 − 1.123950I
3.44887 − 0.05340I −0.84658 + 2.45920I
u = 0.364310 − 0.761476I
a = −0.37557 − 1.45470I
b = 0.204448 + 1.123950I
3.44887 + 0.05340I −0.84658 − 2.45920I
u = 0.191646 + 0.815527I
a = −0.59145 + 1.38561I
b = 0.438339 − 1.274520I
7.47797 + 7.12202I −0.64413 − 4.63750I
u = 0.191646 − 0.815527I
a = −0.59145 − 1.38561I
b = 0.438339 + 1.274520I
7.47797 − 7.12202I −0.64413 + 4.63750I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.216626 + 0.805515I
a = 0.625128 + 0.613776I
b = −0.810740 − 0.031535I
−0.12800 + 7.13488I −8.36711 − 5.76742I
u = −0.216626 − 0.805515I
a = 0.625128 − 0.613776I
b = −0.810740 + 0.031535I
−0.12800 − 7.13488I −8.36711 + 5.76742I
u = −0.019667 + 1.177440I
a = 0.22341 + 1.62438I
b = −0.478486 − 1.241690I
3.47740 − 11.84660I 0
u = −0.019667 − 1.177440I
a = 0.22341 − 1.62438I
b = −0.478486 + 1.241690I
3.47740 + 11.84660I 0
u = 0.220938 + 0.770110I
a = 0.48419 − 1.33432I
b = −0.393339 + 1.167180I
2.19132 + 3.60535I −4.61334 − 4.48567I
u = 0.220938 − 0.770110I
a = 0.48419 + 1.33432I
b = −0.393339 − 1.167180I
2.19132 − 3.60535I −4.61334 + 4.48567I
u = 1.116020 + 0.448323I
a = −1.01041 + 1.01076I
b = −0.551215 − 1.123180I
1.08886 − 4.47773I 0
u = 1.116020 − 0.448323I
a = −1.01041 − 1.01076I
b = −0.551215 + 1.123180I
1.08886 + 4.47773I 0
u = −0.062871 + 1.206620I
a = −0.25251 − 1.53863I
b = 0.474532 + 1.147300I
−1.94478 − 7.53049I 0
u = −0.062871 − 1.206620I
a = −0.25251 + 1.53863I
b = 0.474532 − 1.147300I
−1.94478 + 7.53049I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.128650 + 0.526095I
a = 0.915681 − 1.068180I
b = 0.386717 + 1.327900I
7.55452 − 3.52374I 0
u = 1.128650 − 0.526095I
a = 0.915681 + 1.068180I
b = 0.386717 − 1.327900I
7.55452 + 3.52374I 0
u = 1.163190 + 0.452050I
a = 0.922106 − 0.983293I
b = 0.72737 + 1.24040I
−0.68826 − 8.14483I 0
u = 1.163190 − 0.452050I
a = 0.922106 + 0.983293I
b = 0.72737 − 1.24040I
−0.68826 + 8.14483I 0
u = −1.241260 + 0.141904I
a = 0.296574 − 0.534537I
b = −0.199203 − 0.922535I
2.60736 − 3.89508I 0
u = −1.241260 − 0.141904I
a = 0.296574 + 0.534537I
b = −0.199203 + 0.922535I
2.60736 + 3.89508I 0
u = 1.176930 + 0.463093I
a = −0.902180 + 1.007980I
b = −0.75759 − 1.34685I
4.46422 − 11.80280I 0
u = 1.176930 − 0.463093I
a = −0.902180 − 1.007980I
b = −0.75759 + 1.34685I
4.46422 + 11.80280I 0
u = −0.143657 + 1.278550I
a = 0.24276 + 1.40588I
b = −0.405638 − 1.018490I
−0.08646 − 2.61917I 0
u = −0.143657 − 1.278550I
a = 0.24276 − 1.40588I
b = −0.405638 + 1.018490I
−0.08646 + 2.61917I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.279230 + 0.234772I
a = −0.642765 − 0.276219I
b = −0.580762 − 0.124608I
0.24329 − 4.29843I 0
u = 1.279230 − 0.234772I
a = −0.642765 + 0.276219I
b = −0.580762 + 0.124608I
0.24329 + 4.29843I 0
u = 1.311670 + 0.369854I
a = 0.092483 − 0.294979I
b = 1.288210 − 0.094940I
−4.77612 − 11.28530I 0
u = 1.311670 − 0.369854I
a = 0.092483 + 0.294979I
b = 1.288210 + 0.094940I
−4.77612 + 11.28530I 0
u = 1.324880 + 0.364823I
a = −0.060136 + 0.199915I
b = −1.207270 + 0.187553I
−9.63709 − 7.30911I 0
u = 1.324880 − 0.364823I
a = −0.060136 − 0.199915I
b = −1.207270 − 0.187553I
−9.63709 + 7.30911I 0
u = −1.147840 + 0.773330I
a = 0.232086 + 1.254660I
b = 0.436399 − 0.614895I
−2.33044 − 1.74529I 0
u = −1.147840 − 0.773330I
a = 0.232086 − 1.254660I
b = 0.436399 + 0.614895I
−2.33044 + 1.74529I 0
u = 1.348690 + 0.354551I
a = 0.0290628 − 0.0464895I
b = 1.057490 − 0.302589I
−7.05936 − 3.20770I 0
u = 1.348690 − 0.354551I
a = 0.0290628 + 0.0464895I
b = 1.057490 + 0.302589I
−7.05936 + 3.20770I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.011995 + 0.576995I
a = −0.030862 + 0.532816I
b = 0.490221 − 0.663405I
3.82003 + 1.44123I −2.42911 − 4.15844I
u = 0.011995 − 0.576995I
a = −0.030862 − 0.532816I
b = 0.490221 + 0.663405I
3.82003 − 1.44123I −2.42911 + 4.15844I
u = 1.41066 + 0.30363I
a = 0.054757 + 0.271556I
b = 0.689456 − 0.390814I
−6.22916 − 2.87126I 0
u = 1.41066 − 0.30363I
a = 0.054757 − 0.271556I
b = 0.689456 + 0.390814I
−6.22916 + 2.87126I 0
u = −1.27089 + 0.74232I
a = −0.359829 − 1.266690I
b = −0.511628 + 0.814875I
−7.10664 + 2.78984I 0
u = −1.27089 − 0.74232I
a = −0.359829 + 1.266690I
b = −0.511628 − 0.814875I
−7.10664 − 2.78984I 0
u = −1.37156 + 0.56271I
a = 0.88834 + 1.25590I
b = 0.63563 − 1.37097I
−0.7782 + 17.9224I 0
u = −1.37156 − 0.56271I
a = 0.88834 − 1.25590I
b = 0.63563 + 1.37097I
−0.7782 − 17.9224I 0
u = −1.36978 + 0.57557I
a = −0.82799 − 1.26798I
b = −0.63976 + 1.31414I
−6.1011 + 13.7362I 0
u = −1.36978 − 0.57557I
a = −0.82799 + 1.26798I
b = −0.63976 − 1.31414I
−6.1011 − 13.7362I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37394 + 0.59852I
a = 0.73720 + 1.24846I
b = 0.607699 − 1.232080I
−4.11337 + 9.11039I 0
u = −1.37394 − 0.59852I
a = 0.73720 − 1.24846I
b = 0.607699 + 1.232080I
−4.11337 − 9.11039I 0
u = −1.34574 + 0.68489I
a = 0.502680 + 1.250270I
b = 0.549270 − 0.995359I
−4.54187 + 7.58769I 0
u = −1.34574 − 0.68489I
a = 0.502680 − 1.250270I
b = 0.549270 + 0.995359I
−4.54187 − 7.58769I 0
u = 1.51230 + 0.35184I
a = 0.130676 − 0.429581I
b = −0.537934 + 0.676409I
−7.49574 + 1.47115I 0
u = 1.51230 − 0.35184I
a = 0.130676 + 0.429581I
b = −0.537934 − 0.676409I
−7.49574 − 1.47115I 0
u = −1.44576 + 0.60502I
a = −0.683032 − 1.047140I
b = −0.417484 + 1.229110I
4.06899 + 8.19584I 0
u = −1.44576 − 0.60502I
a = −0.683032 + 1.047140I
b = −0.417484 − 1.229110I
4.06899 − 8.19584I 0
u = −0.274408 + 0.263174I
a = −0.697845 + 0.975456I
b = −0.135972 + 0.391654I
−0.560147 + 0.862728I −9.95266 − 7.82530I
u = −0.274408 − 0.263174I
a = −0.697845 − 0.975456I
b = −0.135972 − 0.391654I
−0.560147 − 0.862728I −9.95266 + 7.82530I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58981 + 0.44139I
a = −0.230102 + 0.549729I
b = 0.422808 − 0.863129I
−1.65458 + 5.47067I 0
u = 1.58981 − 0.44139I
a = −0.230102 − 0.549729I
b = 0.422808 + 0.863129I
−1.65458 − 5.47067I 0
u = −0.26331 + 1.73526I
a = −0.098629 − 1.231090I
b = 0.154343 + 0.965654I
8.73121 − 0.63574I 0
u = −0.26331 − 1.73526I
a = −0.098629 + 1.231090I
b = 0.154343 − 0.965654I
8.73121 + 0.63574I 0
12
II. I
u
2
= hu
3
+ b + 2u, −8u
3
− 3u
2
+ 5a − 17u − 7, u
4
+ 3u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
8
5
u
3
+
3
5
u
2
+
17
5
u +
7
5
−u
3
− 2u
a
4
=
4
5
u
3
−
1
5
u
2
+
11
5
u −
4
5
1
a
1
=
−
2
5
u
3
+
2
5
u
2
− u +
6
5
−
1
5
u
3
−
1
5
u
2
+
1
5
u −
4
5
a
10
=
3
5
u
3
+
3
5
u
2
+
7
5
u +
7
5
−u
3
− 2u
a
7
=
−
2
5
u
3
+
2
5
u
2
− u +
11
5
−
1
5
u
3
+
4
5
u
2
−
4
5
u −
4
5
a
9
=
3
5
u
3
+
8
5
u
2
+
7
5
u +
12
5
−u
3
− 3u
2
− 2u − 2
a
8
=
1
5
u
3
+
8
5
u
2
+
3
5
u +
11
5
−
3
5
u
3
−
8
5
u
2
−
7
5
u −
7
5
a
12
=
3
5
u
2
+
6
5
u +
8
5
3
5
u
3
−
2
5
u
2
−
3
5
u −
3
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
4
− 10u
3
+ 9u
2
− 4u + 1)
c
2
, c
5
, c
7
c
11
, c
12
u
4
+ 3u
2
+ 1
c
3
, c
4
, c
9
c
10
(u
2
+ 1)
2
c
6
5(5u
4
+ u
2
+ 2u + 1)
c
8
u
4
+ 7u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
4
− 10y
3
+ 11y
2
+ 2y + 1)
c
2
, c
5
, c
7
c
11
, c
12
(y
2
+ 3y + 1)
2
c
3
, c
4
, c
9
c
10
(y + 1)
4
c
6
25(25y
4
+ 10y
3
+ 11y
2
− 2y + 1)
c
8
(y
2
+ 7y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034I
a = 1.17082 + 1.72361I
b = − 1.000000I
0.986960 −4.00000
u = − 0.618034I
a = 1.17082 − 1.72361I
b = 1.000000I
0.986960 −4.00000
u = 1.61803I
a = −0.170820 − 1.276390I
b = 1.000000I
8.88264 −4.00000
u = − 1.61803I
a = −0.170820 + 1.276390I
b = − 1.000000I
8.88264 −4.00000
16
III. I
u
3
= ha
2
+ b − a, a
3
− 2a
2
+ a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
11
=
a
−a
2
+ a
a
4
=
a
2
− a
a
a
1
=
a
−a
2
+ a
a
10
=
−a
2
+ 2a
−a
2
+ a
a
7
=
−a
a
2
− a
a
9
=
a
−a
2
+ a
a
8
=
a
−a
2
+ a
a
12
=
a
−a
2
+ a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
u
3
+ u + 1
c
2
, c
5
(u + 1)
3
c
6
u
3
+ 2u
2
+ u − 1
c
7
, c
8
, c
11
c
12
u
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
9
, c
10
y
3
+ 2y
2
+ y − 1
c
2
, c
5
(y − 1)
3
c
6
y
3
− 2y
2
+ 5y − 1
c
7
, c
8
, c
11
c
12
y
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.23279 + 0.79255I
b = 0.341164 − 1.161540I
−1.64493 −6.00000
u = −1.00000
a = 1.23279 − 0.79255I
b = 0.341164 + 1.161540I
−1.64493 −6.00000
u = −1.00000
a = −0.465571
b = −0.682328
−1.64493 −6.00000
20
IV. I
u
4
= hb
6
a
3
− 3b
5
a
2
+ · · · − a
2
+ 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
11
=
a
b
a
4
=
−ba + 1
−b
2
a
1
=
−b
2
a
2
+ 2ba − 1
−b
3
a + b
2
− 1
a
10
=
b + a
b
a
7
=
−ba − a
2
+ 1
−ba + 1
a
9
=
a
b
a
8
=
−b
4
a
3
+ 3b
3
a
2
− a
3
b
2
− 3b
2
a + 2a
2
b + b
−b
5
a
2
+ 2b
4
a − b
3
a
2
− b
3
+ 2b − a
a
12
=
−b
5
a
3
− b
4
a
4
+ 3b
4
a
2
− 2a
4
b
2
− 3b
3
a + 2b
2
a
2
+ a
3
b − a
4
+ b
2
+ a
2
− 1
−b
5
a
3
+ 3b
4
a
2
− 2b
3
a
3
− 4b
3
a + 4b
2
a
2
− a
3
b + 2b
2
− 2ba + a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
2
a − 4b + 4a − 12
(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.
21
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
1.37919 − 2.82812I −15.0195 + 0.I
22
V. I
v
1
= ha, b
6
− b
5
+ 2b
4
− 2b
3
+ 2b
2
− 2b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
3
=
1
0
a
11
=
0
b
a
4
=
1
−b
2
a
1
=
b
2
+ 1
−b
4
a
10
=
b
b
a
7
=
b
2
+ 1
b
2
a
9
=
0
b
a
8
=
b
5
+ 2b
3
+ b
1
a
12
=
−2b
5
+ b
4
− 4b
3
+ 3b
2
− 3b + 3
−b
5
− 2b
3
+ b
2
− b + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b
3
+ 4b − 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
2
, c
5
u
6
c
3
, c
4
, c
6
c
9
, c
10
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
7
, c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
c
8
(u
3
− u
2
+ 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
5
y
6
c
3
, c
4
, c
6
c
9
, c
10
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
8
(y
3
− y
2
+ 2y − 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.498832 + 1.001300I
3.02413 − 2.82812I −2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.498832 − 1.001300I
3.02413 + 2.82812I −2.49024 − 2.97945I
v = 1.00000
a = 0
b = 0.284920 + 1.115140I
−1.11345 −9.01951 + 0.I
v = 1.00000
a = 0
b = 0.284920 − 1.115140I
−1.11345 −9.01951 + 0.I
v = 1.00000
a = 0
b = 0.713912 + 0.305839I
3.02413 − 2.82812I −2.49024 + 2.97945I
v = 1.00000
a = 0
b = 0.713912 − 0.305839I
3.02413 + 2.82812I −2.49024 − 2.97945I
26
VI. I
v
2
= ha, b
3
+ b
2
+ 2b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
3
=
1
0
a
11
=
0
b
a
4
=
1
−b
2
a
1
=
b
2
+ 1
b
2
− b − 1
a
10
=
b
b
a
7
=
b
2
+ 1
b
2
a
9
=
0
b
a
8
=
−1
2b
2
+ 2b
a
12
=
−b
−3b − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b
2
− 4b − 10
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 3u
2
+ 2u − 1
c
2
, c
5
u
3
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
11
, c
12
u
3
+ u
2
+ 2u + 1
c
8
u
3
− u
2
+ 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 5y
2
+ 10y − 1
c
2
, c
5
y
3
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
11
, c
12
y
3
+ 3y
2
+ 2y − 1
c
8
y
3
− y
2
+ 2y − 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.215080 + 1.307140I
3.02413 + 2.82812I −2.49024 − 2.97945I
v = 1.00000
a = 0
b = −0.215080 − 1.307140I
3.02413 − 2.82812I −2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.569840
−1.11345 −9.01950
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
320(u
3
+ u + 1)(u
3
+ 3u
2
+ 2u − 1)(5u
4
− 10u
3
+ 9u
2
− 4u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (64u
74
− 128u
73
+ ··· − 2725866u + 511569)
c
2
, c
5
u
9
(u + 1)
3
(u
4
+ 3u
2
+ 1)(u
74
− 8u
73
+ ··· − 216611u + 52022)
c
3
, c
9
27(u
2
+ 1)
2
(u
3
+ u + 1)(u
3
+ u
2
+ 2u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)(27u
74
− 27u
73
+ ··· − 170u + 61)
c
4
, c
10
27(u
2
+ 1)
2
(u
3
+ u + 1)(u
3
+ u
2
+ 2u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)(27u
74
− 27u
73
+ ··· + 208u + 61)
c
6
320(u
3
+ u
2
+ 2u + 1)(u
3
+ 2u
2
+ u − 1)(5u
4
+ u
2
+ 2u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (64u
74
+ 128u
73
+ ··· + 16997580u + 3434427)
c
7
, c
11
, c
12
u
3
(u
3
+ u
2
+ 2u + 1)
3
(u
4
+ 3u
2
+ 1)(u
74
− 4u
73
+ ··· − 255u + 62)
c
8
u
3
(u
3
− u
2
+ 1)
3
(u
4
+ 7u
2
+ 1)(u
74
+ 4u
73
+ ··· + 777216u + 285696)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
102400(y
3
− 5y
2
+ 10y − 1)(y
3
+ 2y
2
+ y − 1)
· (25y
4
− 10y
3
+ 11y
2
+ 2y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (4096y
74
− 135168y
73
+ ··· − 338930953884y + 261702841761)
c
2
, c
5
y
9
(y − 1)
3
(y
2
+ 3y + 1)
2
· (y
74
− 42y
73
+ ··· + 4426533163y + 2706288484)
c
3
, c
9
729(y + 1)
4
(y
3
+ 2y
2
+ y − 1)(y
3
+ 3y
2
+ 2y − 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(729y
74
+ 43011y
73
+ ··· + 40884y + 3721)
c
4
, c
10
729(y + 1)
4
(y
3
+ 2y
2
+ y − 1)(y
3
+ 3y
2
+ 2y − 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(729y
74
+ 28431y
73
+ ··· + 91668y + 3721)
c
6
102400(y
3
− 2y
2
+ 5y − 1)(y
3
+ 3y
2
+ 2y − 1)
· (25y
4
+ 10y
3
+ 11y
2
− 2y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (4096y
74
− 118784y
73
+ ··· − 146351267872524y + 11795288818329)
c
7
, c
11
, c
12
y
3
(y
2
+ 3y + 1)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
74
+ 66y
73
+ ··· + 4787y + 3844)
c
8
y
3
(y
2
+ 7y + 1)
2
(y
3
− y
2
+ 2y − 1)
3
· (y
74
− 6y
73
+ ··· + 199138738176y + 81622204416)
32
