12n
0656
(K12n
0656
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 8 11 2 5 1 7 5 4
Solving Sequence
2,7
8 3
1,11
6 5 10 4 9 12
c
7
c
2
c
1
c
6
c
5
c
10
c
3
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.04974 × 10
93
u
65
9.74388 × 10
92
u
64
+ ··· + 4.92845 × 10
93
b + 3.58696 × 10
95
,
2.17687 × 10
95
u
65
2.86390 × 10
95
u
64
+ ··· + 3.89347 × 10
95
a 3.06729 × 10
97
, u
66
u
65
+ ··· 51u + 79i
I
u
2
= hu
15
4u
13
u
12
+ 8u
11
+ 5u
10
8u
9
13u
8
+ 3u
7
+ 21u
6
+ u
5
19u
4
u
3
+ 7u
2
+ b,
5u
16
+ u
15
+ ··· + a 1,
u
17
4u
15
u
14
+ 9u
13
+ 5u
12
11u
11
14u
10
+ 8u
9
+ 25u
8
2u
7
28u
6
u
5
+ 19u
4
+ u
3
7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 83 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−5.05 × 10
93
u
65
9.74 × 10
92
u
64
+ · · · + 4.93 × 10
93
b + 3.59 ×
10
95
, 2.18 × 10
95
u
65
2.86 × 10
95
u
64
+ · · · + 3.89 × 10
95
a 3.07 ×
10
97
, u
66
u
65
+ · · · 51u + 79i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
0.559109u
65
+ 0.735565u
64
+ ··· + 114.511u + 78.7804
1.02461u
65
+ 0.197707u
64
+ ··· + 26.4996u 72.7807
a
6
=
2.35020u
65
+ 0.204588u
64
+ ··· + 49.0040u + 156.891
2.94625u
65
+ 0.504266u
64
+ ··· + 106.949u + 284.585
a
5
=
1.48828u
65
+ 0.0869445u
64
+ ··· + 18.2941u + 41.8085
2.60902u
65
+ 0.363501u
64
+ ··· + 76.8159u + 225.788
a
10
=
1.58372u
65
+ 0.537858u
64
+ ··· + 88.0118u + 151.561
1.02461u
65
+ 0.197707u
64
+ ··· + 26.4996u 72.7807
a
4
=
0.833366u
65
0.878185u
64
+ ··· 147.529u 89.3505
1.62313u
65
+ 0.338423u
64
+ ··· + 76.6054u + 160.632
a
9
=
1.86117u
65
+ 0.899303u
64
+ ··· + 144.315u + 201.743
0.488512u
65
+ 0.502843u
64
+ ··· + 75.8217u 8.74372
a
12
=
0.606622u
65
0.258104u
64
+ ··· 12.2197u + 16.0020
0.770254u
65
0.0843692u
64
+ ··· 0.510519u + 38.6892
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4.68718u
65
+ 2.07367u
64
+ ··· + 423.125u + 473.176
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 25u
65
+ ··· + 108619u + 6241
c
2
, c
7
u
66
+ u
65
+ ··· + 51u + 79
c
3
u
66
+ u
65
+ ··· 320u 32
c
4
, c
11
, c
12
u
66
+ 2u
65
+ ··· 135u 19
c
5
, c
8
u
66
+ 6u
65
+ ··· + 256u 112
c
6
, c
10
u
66
u
65
+ ··· 22u 1
c
9
u
66
+ u
65
+ ··· + 9183u + 1252
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 35y
65
+ ··· 251925111y + 38950081
c
2
, c
7
y
66
25y
65
+ ··· 108619y + 6241
c
3
y
66
+ 27y
65
+ ··· 115712y + 1024
c
4
, c
11
, c
12
y
66
+ 56y
65
+ ··· 7357y + 361
c
5
, c
8
y
66
50y
65
+ ··· 1254528y + 12544
c
6
, c
10
y
66
+ 11y
65
+ ··· 78y + 1
c
9
y
66
13y
65
+ ··· 59172305y + 1567504
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.257112 + 0.947624I
a = 0.071468 0.219305I
b = 0.934003 0.145624I
0.1053660 + 0.0685567I 6.00000 + 0.I
u = 0.257112 0.947624I
a = 0.071468 + 0.219305I
b = 0.934003 + 0.145624I
0.1053660 0.0685567I 6.00000 + 0.I
u = 0.707502 + 0.680828I
a = 0.510614 + 0.653841I
b = 0.410733 + 0.515754I
0.03346 2.05159I 6.00000 + 4.98115I
u = 0.707502 0.680828I
a = 0.510614 0.653841I
b = 0.410733 0.515754I
0.03346 + 2.05159I 6.00000 4.98115I
u = 0.775544 + 0.661698I
a = 0.65118 + 2.11101I
b = 1.02196 + 1.17957I
0.84171 1.91050I 6.00000 + 0.I
u = 0.775544 0.661698I
a = 0.65118 2.11101I
b = 1.02196 1.17957I
0.84171 + 1.91050I 6.00000 + 0.I
u = 0.855134 + 0.471238I
a = 0.28210 + 2.12553I
b = 0.203001 + 1.196910I
6.43277 1.93176I 0. + 3.96327I
u = 0.855134 0.471238I
a = 0.28210 2.12553I
b = 0.203001 1.196910I
6.43277 + 1.93176I 0. 3.96327I
u = 0.695152 + 0.756763I
a = 0.285265 + 0.382734I
b = 1.096470 + 0.816570I
2.92421 2.75395I 6.00000 + 0.I
u = 0.695152 0.756763I
a = 0.285265 0.382734I
b = 1.096470 0.816570I
2.92421 + 2.75395I 6.00000 + 0.I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.832084 + 0.479093I
a = 0.964406 0.722252I
b = 0.388483 + 0.305721I
6.35326 + 1.92286I 0.61610 3.80019I
u = 0.832084 0.479093I
a = 0.964406 + 0.722252I
b = 0.388483 0.305721I
6.35326 1.92286I 0.61610 + 3.80019I
u = 0.831367 + 0.696653I
a = 0.595869 0.242192I
b = 1.29532 0.88221I
5.68298 2.17633I 0
u = 0.831367 0.696653I
a = 0.595869 + 0.242192I
b = 1.29532 + 0.88221I
5.68298 + 2.17633I 0
u = 0.887020 + 0.687260I
a = 0.53117 2.06451I
b = 0.94726 1.09875I
5.51025 3.14310I 0
u = 0.887020 0.687260I
a = 0.53117 + 2.06451I
b = 0.94726 + 1.09875I
5.51025 + 3.14310I 0
u = 0.839142 + 0.235261I
a = 0.610217 + 0.679297I
b = 1.303620 + 0.043632I
2.21197 + 2.72682I 0.929885 + 0.873234I
u = 0.839142 0.235261I
a = 0.610217 0.679297I
b = 1.303620 0.043632I
2.21197 2.72682I 0.929885 0.873234I
u = 0.928111 + 0.642178I
a = 0.913757 + 0.186542I
b = 1.43369 + 1.01259I
0.36496 + 6.98411I 0
u = 0.928111 0.642178I
a = 0.913757 0.186542I
b = 1.43369 1.01259I
0.36496 6.98411I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.838382 + 0.213695I
a = 1.40107 2.19862I
b = 0.09948 1.79877I
11.89330 0.93560I 4.33716 3.52776I
u = 0.838382 0.213695I
a = 1.40107 + 2.19862I
b = 0.09948 + 1.79877I
11.89330 + 0.93560I 4.33716 + 3.52776I
u = 0.899982 + 0.708778I
a = 1.09863 0.90483I
b = 0.16265 1.57424I
9.01530 + 2.75120I 0
u = 0.899982 0.708778I
a = 1.09863 + 0.90483I
b = 0.16265 + 1.57424I
9.01530 2.75120I 0
u = 0.526272 + 1.019400I
a = 0.318206 + 0.066951I
b = 1.05853 + 0.95213I
1.45735 + 9.54908I 0
u = 0.526272 1.019400I
a = 0.318206 0.066951I
b = 1.05853 0.95213I
1.45735 9.54908I 0
u = 1.102590 + 0.320589I
a = 0.33068 1.61344I
b = 0.266522 0.929330I
6.22093 + 0.10686I 0
u = 1.102590 0.320589I
a = 0.33068 + 1.61344I
b = 0.266522 + 0.929330I
6.22093 0.10686I 0
u = 0.834282 + 0.117518I
a = 0.44582 2.20169I
b = 0.106930 1.272370I
4.82653 + 0.53157I 0.07384 + 2.64833I
u = 0.834282 0.117518I
a = 0.44582 + 2.20169I
b = 0.106930 + 1.272370I
4.82653 0.53157I 0.07384 2.64833I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.636597 + 1.006470I
a = 0.458947 0.050429I
b = 0.998665 0.921408I
6.05616 4.04965I 0
u = 0.636597 1.006470I
a = 0.458947 + 0.050429I
b = 0.998665 + 0.921408I
6.05616 + 4.04965I 0
u = 0.983398 + 0.684141I
a = 0.51377 + 2.02937I
b = 0.849833 + 1.042050I
2.05072 + 8.22966I 0
u = 0.983398 0.684141I
a = 0.51377 2.02937I
b = 0.849833 1.042050I
2.05072 8.22966I 0
u = 0.977568 + 0.708124I
a = 0.209781 0.209812I
b = 0.606595 0.224505I
0.90500 3.33318I 0
u = 0.977568 0.708124I
a = 0.209781 + 0.209812I
b = 0.606595 + 0.224505I
0.90500 + 3.33318I 0
u = 1.096460 + 0.507389I
a = 1.14935 1.39168I
b = 0.501177 0.634307I
4.99940 7.29186I 0
u = 1.096460 0.507389I
a = 1.14935 + 1.39168I
b = 0.501177 + 0.634307I
4.99940 + 7.29186I 0
u = 1.096320 + 0.542363I
a = 0.483047 + 1.273850I
b = 0.710209 + 0.578523I
1.06694 + 5.17758I 0
u = 1.096320 0.542363I
a = 0.483047 1.273850I
b = 0.710209 0.578523I
1.06694 5.17758I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.764652 + 0.955944I
a = 0.586188 + 0.078330I
b = 0.846583 + 0.894829I
2.53161 1.78458I 0
u = 0.764652 0.955944I
a = 0.586188 0.078330I
b = 0.846583 0.894829I
2.53161 + 1.78458I 0
u = 0.393732 + 1.163820I
a = 0.284564 + 0.124345I
b = 0.243672 + 0.002661I
0.89352 2.40317I 0
u = 0.393732 1.163820I
a = 0.284564 0.124345I
b = 0.243672 0.002661I
0.89352 + 2.40317I 0
u = 0.763441 + 0.052004I
a = 2.67743 + 1.41213I
b = 0.283142 + 0.043659I
2.06277 + 3.79226I 1.58367 5.91104I
u = 0.763441 0.052004I
a = 2.67743 1.41213I
b = 0.283142 0.043659I
2.06277 3.79226I 1.58367 + 5.91104I
u = 1.237200 + 0.275538I
a = 0.149817 + 1.097540I
b = 0.115179 + 0.814116I
2.61077 2.63613I 0
u = 1.237200 0.275538I
a = 0.149817 1.097540I
b = 0.115179 0.814116I
2.61077 + 2.63613I 0
u = 0.728667
a = 2.69016
b = 0.228552
1.95571 2.70420
u = 1.211310 + 0.434932I
a = 0.216289 1.388270I
b = 0.908237 0.547503I
4.31364 4.41545I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.211310 0.434932I
a = 0.216289 + 1.388270I
b = 0.908237 + 0.547503I
4.31364 + 4.41545I 0
u = 0.368903 + 0.599292I
a = 0.551631 + 0.006032I
b = 0.543091 + 0.225358I
1.044430 0.587332I 8.98331 + 3.47323I
u = 0.368903 0.599292I
a = 0.551631 0.006032I
b = 0.543091 0.225358I
1.044430 + 0.587332I 8.98331 3.47323I
u = 1.028890 + 0.791131I
a = 0.45447 + 1.39568I
b = 0.90585 + 1.21148I
1.64235 4.60831I 0
u = 1.028890 0.791131I
a = 0.45447 1.39568I
b = 0.90585 1.21148I
1.64235 + 4.60831I 0
u = 0.192509 + 0.631326I
a = 1.095920 0.610070I
b = 0.227382 0.678722I
2.56446 + 2.95191I 1.85269 4.42524I
u = 0.192509 0.631326I
a = 1.095920 + 0.610070I
b = 0.227382 + 0.678722I
2.56446 2.95191I 1.85269 + 4.42524I
u = 1.110370 + 0.768499I
a = 0.37175 1.58877I
b = 1.04037 1.21889I
4.54605 + 10.49520I 0
u = 1.110370 0.768499I
a = 0.37175 + 1.58877I
b = 1.04037 + 1.21889I
4.54605 10.49520I 0
u = 0.639532
a = 0.572453
b = 1.15533
2.36942 1.84080
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.156750 + 0.728414I
a = 0.35107 + 1.71491I
b = 1.10396 + 1.21839I
0.5174 15.8754I 0
u = 1.156750 0.728414I
a = 0.35107 1.71491I
b = 1.10396 1.21839I
0.5174 + 15.8754I 0
u = 1.396300 + 0.095553I
a = 0.539554 0.929625I
b = 0.390433 0.822365I
6.23593 + 6.65763I 0
u = 1.396300 0.095553I
a = 0.539554 + 0.929625I
b = 0.390433 + 0.822365I
6.23593 6.65763I 0
u = 1.206480 + 0.716734I
a = 0.198206 + 0.687413I
b = 0.885867 + 0.292505I
2.62837 + 5.98510I 0
u = 1.206480 0.716734I
a = 0.198206 0.687413I
b = 0.885867 0.292505I
2.62837 5.98510I 0
11
II.
I
u
2
= hu
15
4u
13
+· · ·+7u
2
+b, 5u
16
+u
15
+· · ·+a1, u
17
4u
15
+· · ·−7u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
5u
16
u
15
+ ··· 6u + 1
u
15
+ 4u
13
+ ··· + u
3
7u
2
a
6
=
u
15
u
14
+ ··· 27u
2
+ 4
2u
15
u
14
+ ··· u + 2
a
5
=
u
16
u
15
+ ··· + u + 3
u
16
+ 2u
15
+ ··· 4u
2
+ 2
a
10
=
5u
16
16u
14
+ ··· 6u + 1
u
15
+ 4u
13
+ ··· + u
3
7u
2
a
4
=
7u
15
25u
13
+ ··· + 66u
2
12
u
14
3u
12
u
11
+ 5u
10
+ 4u
9
3u
8
9u
7
+ 12u
5
+ u
4
8u
3
+ u
a
9
=
7u
16
u
15
+ ··· 9u + 2
2u
16
u
15
+ ··· 5u
2
3u
a
12
=
4u
16
+ 17u
14
+ ··· + 13u + 4
2u
16
+ 2u
15
+ ··· + 3u 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16u
16
15u
15
53u
14
+ 38u
13
+ 120u
12
41u
11
166u
10
61u
9
+ 228u
8
+ 210u
7
284u
6
240u
5
+ 269u
4
+ 129u
3
141u
2
24u + 36
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
8u
16
+ ··· + 14u 1
c
2
u
17
4u
15
+ ··· + 7u
2
1
c
3
u
17
+ 8u
15
+ ··· 6u
2
1
c
4
u
17
u
16
+ ··· 10u
2
1
c
5
u
17
+ u
16
+ ··· + 6u
2
+ 1
c
6
u
17
+ 6u
15
+ ··· + u + 1
c
7
u
17
4u
15
+ ··· 7u
2
+ 1
c
8
u
17
u
16
+ ··· 6u
2
1
c
9
u
17
2u
15
+ ··· + 4u + 13
c
10
u
17
+ 6u
15
+ ··· + u 1
c
11
, c
12
u
17
+ u
16
+ ··· + 10u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 4y
16
+ ··· + 22y 1
c
2
, c
7
y
17
8y
16
+ ··· + 14y 1
c
3
y
17
+ 16y
16
+ ··· 12y 1
c
4
, c
11
, c
12
y
17
+ 21y
16
+ ··· 20y 1
c
5
, c
8
y
17
5y
16
+ ··· 12y 1
c
6
, c
10
y
17
+ 12y
16
+ ··· + 5y 1
c
9
y
17
4y
16
+ ··· + 276y 169
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.935454 + 0.285621I
a = 0.74965 2.16184I
b = 0.134278 0.894052I
7.54669 + 1.17742I 6.67270 0.38814I
u = 0.935454 0.285621I
a = 0.74965 + 2.16184I
b = 0.134278 + 0.894052I
7.54669 1.17742I 6.67270 + 0.38814I
u = 0.912131 + 0.328638I
a = 0.30968 + 2.00614I
b = 0.147743 + 1.270230I
4.60840 1.36971I 3.49419 + 5.08345I
u = 0.912131 0.328638I
a = 0.30968 2.00614I
b = 0.147743 1.270230I
4.60840 + 1.36971I 3.49419 5.08345I
u = 0.889395 + 0.372697I
a = 1.29749 2.05795I
b = 0.11611 1.91684I
11.58440 + 1.56045I 1.25948 6.47821I
u = 0.889395 0.372697I
a = 1.29749 + 2.05795I
b = 0.11611 + 1.91684I
11.58440 1.56045I 1.25948 + 6.47821I
u = 0.938625 + 0.706892I
a = 1.030120 0.743145I
b = 0.181857 1.388630I
9.53882 2.78092I 6.42091 + 3.83492I
u = 0.938625 0.706892I
a = 1.030120 + 0.743145I
b = 0.181857 + 1.388630I
9.53882 + 2.78092I 6.42091 3.83492I
u = 0.430993 + 1.143370I
a = 0.247474 0.064001I
b = 0.515702 + 0.275227I
0.99848 + 2.09379I 7.49851 + 6.90388I
u = 0.430993 1.143370I
a = 0.247474 + 0.064001I
b = 0.515702 0.275227I
0.99848 2.09379I 7.49851 6.90388I
15
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.193420 + 0.475980I
a = 0.017645 1.033010I
b = 0.711571 0.148908I
4.07323 6.22059I 1.13082 + 6.76795I
u = 1.193420 0.475980I
a = 0.017645 + 1.033010I
b = 0.711571 + 0.148908I
4.07323 + 6.22059I 1.13082 6.76795I
u = 1.151330 + 0.648836I
a = 0.250827 + 0.900595I
b = 0.603765 + 0.579563I
1.51682 + 4.20012I 2.90139 4.71038I
u = 1.151330 0.648836I
a = 0.250827 0.900595I
b = 0.603765 0.579563I
1.51682 4.20012I 2.90139 + 4.71038I
u = 0.611850 + 0.172842I
a = 2.15280 + 1.56179I
b = 0.917330 + 0.207226I
1.40459 + 3.27513I 7.35874 1.79494I
u = 0.611850 0.172842I
a = 2.15280 1.56179I
b = 0.917330 0.207226I
1.40459 3.27513I 7.35874 + 1.79494I
u = 0.497718
a = 2.07149
b = 0.924578
2.88191 15.9010
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
8u
16
+ ··· + 14u 1)(u
66
+ 25u
65
+ ··· + 108619u + 6241)
c
2
(u
17
4u
15
+ ··· + 7u
2
1)(u
66
+ u
65
+ ··· + 51u + 79)
c
3
(u
17
+ 8u
15
+ ··· 6u
2
1)(u
66
+ u
65
+ ··· 320u 32)
c
4
(u
17
u
16
+ ··· 10u
2
1)(u
66
+ 2u
65
+ ··· 135u 19)
c
5
(u
17
+ u
16
+ ··· + 6u
2
+ 1)(u
66
+ 6u
65
+ ··· + 256u 112)
c
6
(u
17
+ 6u
15
+ ··· + u + 1)(u
66
u
65
+ ··· 22u 1)
c
7
(u
17
4u
15
+ ··· 7u
2
+ 1)(u
66
+ u
65
+ ··· + 51u + 79)
c
8
(u
17
u
16
+ ··· 6u
2
1)(u
66
+ 6u
65
+ ··· + 256u 112)
c
9
(u
17
2u
15
+ ··· + 4u + 13)(u
66
+ u
65
+ ··· + 9183u + 1252)
c
10
(u
17
+ 6u
15
+ ··· + u 1)(u
66
u
65
+ ··· 22u 1)
c
11
, c
12
(u
17
+ u
16
+ ··· + 10u
2
+ 1)(u
66
+ 2u
65
+ ··· 135u 19)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 4y
16
+ ··· + 22y 1)
· (y
66
+ 35y
65
+ ··· 251925111y + 38950081)
c
2
, c
7
(y
17
8y
16
+ ··· + 14y 1)(y
66
25y
65
+ ··· 108619y + 6241)
c
3
(y
17
+ 16y
16
+ ··· 12y 1)(y
66
+ 27y
65
+ ··· 115712y + 1024)
c
4
, c
11
, c
12
(y
17
+ 21y
16
+ ··· 20y 1)(y
66
+ 56y
65
+ ··· 7357y + 361)
c
5
, c
8
(y
17
5y
16
+ ··· 12y 1)(y
66
50y
65
+ ··· 1254528y + 12544)
c
6
, c
10
(y
17
+ 12y
16
+ ··· + 5y 1)(y
66
+ 11y
65
+ ··· 78y + 1)
c
9
(y
17
4y
16
+ ··· + 276y 169)
· (y
66
13y
65
+ ··· 59172305y + 1567504)
18