12a
0032
(K12a
0032
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 11 10 4 8 1 7
Solving Sequence
7,12 1,3
2 6 4 5 11 8 10 9
c
12
c
1
c
6
c
3
c
5
c
11
c
7
c
10
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
72
+ 9u
71
+ ··· + b − 5, 3u
72
+ 6u
71
+ ··· + 2a − 5, u
73
+ 3u
72
+ ··· − 4u − 1i
I
u
2
= hb, a
2
− a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 75 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
= h4u
72
+9u
71
+· · ·+b−5, 3u
72
+6u
71
+· · ·+2a−5, u
73
+3u
72
+· · ·−4u−1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
3
=
−
3
2
u
72
− 3u
71
+ ··· +
9
2
u +
5
2
−4u
72
− 9u
71
+ ··· + 14u + 5
a
2
=
−
1
2
u
72
− u
71
+ ··· −
3
2
u +
1
2
u
29
− 9u
27
+ ··· + 2u
2
+ u
a
6
=
−u
u
a
4
=
2u
72
+ 5u
71
+ ··· − 8u − 2
−
15
2
u
72
− 17u
71
+ ··· +
53
2
u +
19
2
a
5
=
5u
72
+ 11u
71
+ ··· − 18u − 6
3
2
u
72
+ 3u
71
+ ··· −
7
2
u −
3
2
a
11
=
−u
2
+ 1
u
4
a
8
=
−u
5
+ 2u
3
− u
u
7
− u
5
+ u
a
10
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
10
− 2u
8
+ u
6
+ 2u
4
− u
2
a
9
=
−u
11
+ 4u
9
− 6u
7
+ 2u
5
+ 3u
3
− 2u
u
13
− 3u
11
+ 3u
9
+ 2u
7
− 4u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18u
72
− 43u
71
+ ··· + 66u + 25
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 32u
72
+ ··· + 11u − 1
c
2
, c
5
u
73
+ 2u
72
+ ··· − u − 1
c
3
u
73
− 2u
72
+ ··· + 165u − 17
c
4
, c
9
u
73
+ u
72
+ ··· + 4u − 4
c
6
, c
12
u
73
+ 3u
72
+ ··· − 4u − 1
c
7
, c
8
, c
10
u
73
+ 15u
72
+ ··· − 216u − 16
c
11
u
73
− 43u
72
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
+ 20y
72
+ ··· + 275y −1
c
2
, c
5
y
73
+ 32y
72
+ ··· + 11y −1
c
3
y
73
+ 8y
72
+ ··· − 6877y −289
c
4
, c
9
y
73
+ 15y
72
+ ··· − 216y −16
c
6
, c
12
y
73
− 43y
72
+ ··· − 2y −1
c
7
, c
8
, c
10
y
73
+ 83y
72
+ ··· + 4384y −256
c
11
y
73
− 23y
72
+ ··· + 38y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796832 + 0.538347I
a = −2.31129 + 0.06801I
b = 1.70540 − 1.05275I
−4.24142 − 5.70697I 0
u = −0.796832 − 0.538347I
a = −2.31129 − 0.06801I
b = 1.70540 + 1.05275I
−4.24142 + 5.70697I 0
u = 0.899085 + 0.326015I
a = 0.02535 − 2.32970I
b = −0.58316 + 2.15466I
0.082824 + 0.160201I 0
u = 0.899085 − 0.326015I
a = 0.02535 + 2.32970I
b = −0.58316 − 2.15466I
0.082824 − 0.160201I 0
u = −1.030080 + 0.324784I
a = 0.645259 − 0.737289I
b = 0.428910 − 0.037104I
2.50971 + 0.29837I 0
u = −1.030080 − 0.324784I
a = 0.645259 + 0.737289I
b = 0.428910 + 0.037104I
2.50971 − 0.29837I 0
u = −0.060471 + 0.908501I
a = −1.143350 + 0.045300I
b = −0.15329 − 1.46139I
6.24864 + 10.27490I 2.89542 − 7.01845I
u = −0.060471 − 0.908501I
a = −1.143350 − 0.045300I
b = −0.15329 + 1.46139I
6.24864 − 10.27490I 2.89542 + 7.01845I
u = −0.045023 + 0.902001I
a = 1.048390 − 0.026697I
b = 0.425897 + 0.828457I
8.09212 + 4.88858I 5.55498 − 2.56495I
u = −0.045023 − 0.902001I
a = 1.048390 + 0.026697I
b = 0.425897 − 0.828457I
8.09212 − 4.88858I 5.55498 + 2.56495I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027830 + 0.411352I
a = −2.75340 − 1.31041I
b = 2.13202 + 2.36044I
1.86319 + 6.29573I 0
u = 1.027830 − 0.411352I
a = −2.75340 + 1.31041I
b = 2.13202 − 2.36044I
1.86319 − 6.29573I 0
u = −0.992153 + 0.494153I
a = −0.13867 + 1.47620I
b = −0.25797 − 1.67319I
−2.09315 − 4.25967I 0
u = −0.992153 − 0.494153I
a = −0.13867 − 1.47620I
b = −0.25797 + 1.67319I
−2.09315 + 4.25967I 0
u = −0.003685 + 0.885221I
a = 1.061200 + 0.001583I
b = 0.448605 − 0.796552I
8.26656 + 1.57314I 5.85573 − 2.28832I
u = −0.003685 − 0.885221I
a = 1.061200 − 0.001583I
b = 0.448605 + 0.796552I
8.26656 − 1.57314I 5.85573 + 2.28832I
u = 1.061310 + 0.358999I
a = 1.73187 + 0.46057I
b = −1.55065 − 1.27425I
3.61712 + 1.77427I 0
u = 1.061310 − 0.358999I
a = 1.73187 − 0.46057I
b = −1.55065 + 1.27425I
3.61712 − 1.77427I 0
u = −1.055210 + 0.377398I
a = 0.143235 + 0.585101I
b = −0.653103 + 0.376649I
3.48602 − 4.64873I 0
u = −1.055210 − 0.377398I
a = 0.143235 − 0.585101I
b = −0.653103 − 0.376649I
3.48602 + 4.64873I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014910 + 0.877594I
a = −1.170160 + 0.036770I
b = −0.15465 + 1.42320I
6.56651 − 3.81304I 3.48761 + 2.37237I
u = 0.014910 − 0.877594I
a = −1.170160 − 0.036770I
b = −0.15465 − 1.42320I
6.56651 + 3.81304I 3.48761 − 2.37237I
u = −0.745666 + 0.449141I
a = 1.241710 − 0.206618I
b = −0.615729 + 0.808004I
−1.60556 − 1.91846I −0.83992 + 4.54593I
u = −0.745666 − 0.449141I
a = 1.241710 + 0.206618I
b = −0.615729 − 0.808004I
−1.60556 + 1.91846I −0.83992 − 4.54593I
u = −0.663356 + 0.548451I
a = −1.09116 + 1.48131I
b = 0.05851 − 1.82675I
−4.60806 + 1.34225I −6.07081 − 0.60893I
u = −0.663356 − 0.548451I
a = −1.09116 − 1.48131I
b = 0.05851 + 1.82675I
−4.60806 − 1.34225I −6.07081 + 0.60893I
u = −0.044946 + 0.858380I
a = −0.926262 − 0.036801I
b = 0.583114 − 0.035791I
2.49214 + 3.07068I −0.36042 − 2.48054I
u = −0.044946 − 0.858380I
a = −0.926262 + 0.036801I
b = 0.583114 + 0.035791I
2.49214 − 3.07068I −0.36042 + 2.48054I
u = 1.148100 + 0.066282I
a = 0.481281 − 0.828556I
b = −0.072635 + 0.333417I
0.94991 + 1.54341I 0
u = 1.148100 − 0.066282I
a = 0.481281 + 0.828556I
b = −0.072635 − 0.333417I
0.94991 − 1.54341I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831297
a = 1.18611
b = −0.878157
1.20245 8.84780
u = −1.067090 + 0.480663I
a = 1.43081 − 0.55418I
b = −1.10301 + 1.47768I
2.23047 − 6.58216I 0
u = −1.067090 − 0.480663I
a = 1.43081 + 0.55418I
b = −1.10301 − 1.47768I
2.23047 + 6.58216I 0
u = 1.143120 + 0.264741I
a = 0.321926 − 0.475229I
b = −0.765191 − 0.174011I
3.87826 + 0.47986I 0
u = 1.143120 − 0.264741I
a = 0.321926 + 0.475229I
b = −0.765191 + 0.174011I
3.87826 − 0.47986I 0
u = −1.072090 + 0.517956I
a = −2.16667 + 1.15750I
b = 1.50805 − 2.21750I
0.09169 − 11.38030I 0
u = −1.072090 − 0.517956I
a = −2.16667 − 1.15750I
b = 1.50805 + 2.21750I
0.09169 + 11.38030I 0
u = 1.189960 + 0.217721I
a = 0.538138 + 0.733544I
b = 0.386122 − 0.182674I
2.38629 − 3.99102I 0
u = 1.189960 − 0.217721I
a = 0.538138 − 0.733544I
b = 0.386122 + 0.182674I
2.38629 + 3.99102I 0
u = −0.759472 + 0.078072I
a = 0.409671 + 1.121040I
b = −0.025028 + 0.368371I
0.90189 − 2.32067I −2.23029 + 5.61700I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759472 − 0.078072I
a = 0.409671 − 1.121040I
b = −0.025028 − 0.368371I
0.90189 + 2.32067I −2.23029 − 5.61700I
u = −0.294691 + 0.697762I
a = −1.52227 + 0.52821I
b = 0.04655 − 1.54343I
−2.13058 + 6.78357I −1.78763 − 7.49032I
u = −0.294691 − 0.697762I
a = −1.52227 − 0.52821I
b = 0.04655 + 1.54343I
−2.13058 − 6.78357I −1.78763 + 7.49032I
u = −0.411090 + 0.594862I
a = −1.33198 − 0.64422I
b = 1.058470 − 0.183219I
−3.71919 − 0.03530I −5.73582 − 0.13433I
u = −0.411090 − 0.594862I
a = −1.33198 + 0.64422I
b = 1.058470 + 0.183219I
−3.71919 + 0.03530I −5.73582 + 0.13433I
u = 0.638508 + 0.276958I
a = −2.85677 + 1.41704I
b = 2.23207 − 0.27893I
−0.67209 + 2.83977I 0.57232 − 5.77641I
u = 0.638508 − 0.276958I
a = −2.85677 − 1.41704I
b = 2.23207 + 0.27893I
−0.67209 − 2.83977I 0.57232 + 5.77641I
u = 1.245740 + 0.440942I
a = 0.151191 − 1.053990I
b = −0.087474 + 1.281280I
6.38924 + 1.49871I 0
u = 1.245740 − 0.440942I
a = 0.151191 + 1.053990I
b = −0.087474 − 1.281280I
6.38924 − 1.49871I 0
u = −1.237210 + 0.485257I
a = 0.092149 + 1.060120I
b = −0.069199 − 1.349010I
6.06816 − 7.90409I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.237210 − 0.485257I
a = 0.092149 − 1.060120I
b = −0.069199 + 1.349010I
6.06816 + 7.90409I 0
u = −0.247172 + 0.623477I
a = 1.109370 − 0.156214I
b = 0.146837 + 0.686540I
−0.05164 + 2.31958I 1.90774 − 3.63180I
u = −0.247172 − 0.623477I
a = 1.109370 + 0.156214I
b = 0.146837 − 0.686540I
−0.05164 − 2.31958I 1.90774 + 3.63180I
u = −1.254650 + 0.458550I
a = 0.571192 − 0.618053I
b = 0.654999 + 0.111159I
10.41650 − 0.92595I 0
u = −1.254650 − 0.458550I
a = 0.571192 + 0.618053I
b = 0.654999 − 0.111159I
10.41650 + 0.92595I 0
u = 1.250410 + 0.474243I
a = −1.64704 − 1.66951I
b = 0.99899 + 2.81058I
10.30140 + 8.63802I 0
u = 1.250410 − 0.474243I
a = −1.64704 + 1.66951I
b = 0.99899 − 2.81058I
10.30140 − 8.63802I 0
u = 1.257260 + 0.465604I
a = 1.34060 + 0.93797I
b = −1.14852 − 2.06285I
12.09550 + 3.22867I 0
u = 1.257260 − 0.465604I
a = 1.34060 − 0.93797I
b = −1.14852 + 2.06285I
12.09550 − 3.22867I 0
u = −1.256050 + 0.469575I
a = 0.076133 + 0.366803I
b = −0.925574 + 0.435365I
12.06620 − 6.39600I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.256050 − 0.469575I
a = 0.076133 − 0.366803I
b = −0.925574 − 0.435365I
12.06620 + 6.39600I 0
u = 1.273530 + 0.443626I
a = 0.096224 − 0.351788I
b = −0.940708 − 0.404721I
12.14430 − 0.14495I 0
u = 1.273530 − 0.443626I
a = 0.096224 + 0.351788I
b = −0.940708 + 0.404721I
12.14430 + 0.14495I 0
u = −1.256320 + 0.493887I
a = 1.29631 − 0.89917I
b = −1.07374 + 2.03687I
11.7702 − 9.8863I 0
u = −1.256320 − 0.493887I
a = 1.29631 + 0.89917I
b = −1.07374 − 2.03687I
11.7702 + 9.8863I 0
u = 1.279930 + 0.434233I
a = 0.556079 + 0.623274I
b = 0.648052 − 0.146041I
10.39010 − 5.55528I 0
u = 1.279930 − 0.434233I
a = 0.556079 − 0.623274I
b = 0.648052 + 0.146041I
10.39010 + 5.55528I 0
u = −1.255820 + 0.502698I
a = −1.60562 + 1.57330I
b = 0.94296 − 2.71614I
9.8802 − 15.3350I 0
u = −1.255820 − 0.502698I
a = −1.60562 − 1.57330I
b = 0.94296 + 2.71614I
9.8802 + 15.3350I 0
u = −0.014084 + 0.462153I
a = 1.42124 + 0.30256I
b = 0.409463 − 0.530113I
0.89929 + 1.38203I 4.27247 − 4.11780I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014084 − 0.462153I
a = 1.42124 − 0.30256I
b = 0.409463 + 0.530113I
0.89929 − 1.38203I 4.27247 + 4.11780I
u = 0.217836 + 0.395971I
a = −2.71775 − 0.62754I
b = 0.30369 + 1.39444I
−0.21204 − 2.78157I 2.07158 + 2.47908I
u = 0.217836 − 0.395971I
a = −2.71775 + 0.62754I
b = 0.30369 − 1.39444I
−0.21204 + 2.78157I 2.07158 − 2.47908I
12
II. I
u
2
= hb, a
2
− a + 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
12
=
1
0
a
1
=
1
−1
a
3
=
a
0
a
2
=
a
−1
a
6
=
−1
1
a
4
=
0
a
a
5
=
0
a
a
11
=
0
1
a
8
=
0
1
a
10
=
0
1
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I 9.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I 9.00000 − 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
73
+ 32u
72
+ ··· + 11u − 1)
c
2
(u
2
+ u + 1)(u
73
+ 2u
72
+ ··· − u − 1)
c
3
(u
2
− u + 1)(u
73
− 2u
72
+ ··· + 165u − 17)
c
4
, c
9
u
2
(u
73
+ u
72
+ ··· + 4u − 4)
c
5
(u
2
− u + 1)(u
73
+ 2u
72
+ ··· − u − 1)
c
6
((u + 1)
2
)(u
73
+ 3u
72
+ ··· − 4u − 1)
c
7
, c
8
, c
10
u
2
(u
73
+ 15u
72
+ ··· − 216u − 16)
c
11
((u + 1)
2
)(u
73
− 43u
72
+ ··· − 2u − 1)
c
12
((u − 1)
2
)(u
73
+ 3u
72
+ ··· − 4u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
73
+ 20y
72
+ ··· + 275y − 1)
c
2
, c
5
(y
2
+ y + 1)(y
73
+ 32y
72
+ ··· + 11y − 1)
c
3
(y
2
+ y + 1)(y
73
+ 8y
72
+ ··· − 6877y − 289)
c
4
, c
9
y
2
(y
73
+ 15y
72
+ ··· − 216y − 16)
c
6
, c
12
((y − 1)
2
)(y
73
− 43y
72
+ ··· − 2y − 1)
c
7
, c
8
, c
10
y
2
(y
73
+ 83y
72
+ ··· + 4384y − 256)
c
11
((y − 1)
2
)(y
73
− 23y
72
+ ··· + 38y − 1)
18
