12a
0193
(K12a
0193
)
A knot diagram
1
Linearized knot diagam
3 5 10 6 2 11 12 1 4 9 7 8
Solving Sequence
3,10 4,5
2 6 1 9 11 7 8 12
c
3
c
2
c
5
c
1
c
9
c
10
c
6
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.76155 × 10
30
u
55
+ 2.38665 × 10
30
u
54
+ ··· + 1.86805 × 10
31
b − 5.18520 × 10
31
,
7.54734 × 10
30
u
55
− 1.06356 × 10
31
u
54
+ ··· + 1.86805 × 10
31
a + 8.01489 × 10
31
, u
56
− u
55
+ ··· − 44u
2
− 16i
I
v
1
= ha, v
3
+ 2v
2
+ 2b + 2v + 1, v
4
+ v
3
+ 2v
2
− v + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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
=
h1.76×10
30
u
55
+2.39×10
30
u
54
+· · ·+1.87×10
31
b−5.19×10
31
, 7.55×10
30
u
55
−
1.06 × 10
31
u
54
+ · · · + 1.87 × 10
31
a + 8.01 × 10
31
, u
56
− u
55
+ · · · − 44u
2
− 16i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
5
=
−0.404023u
55
+ 0.569343u
54
+ ··· + 4.15487u − 4.29052
−0.0942991u
55
− 0.127762u
54
+ ··· + 0.441391u + 2.77573
a
2
=
−0.124417u
55
− 0.0227610u
54
+ ··· + 3.42223u + 3.91486
0.197532u
55
− 0.245618u
54
+ ··· + 1.00380u + 1.74945
a
6
=
−0.124417u
55
− 0.0227610u
54
+ ··· + 3.42223u + 3.91486
−0.148908u
55
+ 0.254056u
54
+ ··· − 2.99446u − 4.10429
a
1
=
0.0731156u
55
− 0.268379u
54
+ ··· + 4.42602u + 5.66431
0.197532u
55
− 0.245618u
54
+ ··· + 1.00380u + 1.74945
a
9
=
u
u
3
+ u
a
11
=
u
3
u
5
+ u
3
+ u
a
7
=
0.113306u
55
+ 0.203193u
54
+ ··· − 3.36863u − 1.54199
−0.262328u
55
+ 0.0564765u
54
+ ··· + 0.999404u + 0.529453
a
8
=
−0.516553u
55
+ 0.486410u
54
+ ··· + 8.01784u − 2.62530
−0.254069u
55
+ 0.475756u
54
+ ··· + 2.22140u − 6.56977
a
12
=
0.330162u
55
+ 0.368862u
54
+ ··· − 9.49132u − 8.58801
−0.363570u
55
+ 0.132323u
54
+ ··· + 7.63673u + 0.248734
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0743933u
55
− 0.650973u
54
+ ··· − 12.4637u + 17.4604
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
56
+ 19u
55
+ ··· − 20u + 1
c
2
, c
5
u
56
+ 3u
55
+ ··· + 2u + 1
c
3
, c
9
u
56
− u
55
+ ··· − 44u
2
− 16
c
6
, c
7
, c
8
c
11
, c
12
u
56
− 3u
55
+ ··· + 2u − 1
c
10
u
56
− 25u
55
+ ··· − 1408u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
56
+ 39y
55
+ ··· − 388y + 1
c
2
, c
5
y
56
+ 19y
55
+ ··· − 20y + 1
c
3
, c
9
y
56
+ 25y
55
+ ··· + 1408y + 256
c
6
, c
7
, c
8
c
11
, c
12
y
56
− 73y
55
+ ··· + 16y + 1
c
10
y
56
+ 5y
55
+ ··· − 925696y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.945963 + 0.329000I
a = 0.700162 + 0.301248I
b = −0.710485 + 0.729480I
3.41470 + 0.08627I 10.40732 − 0.41249I
u = 0.945963 − 0.329000I
a = 0.700162 − 0.301248I
b = −0.710485 − 0.729480I
3.41470 − 0.08627I 10.40732 + 0.41249I
u = 0.625712 + 0.814457I
a = 0.889757 + 0.875058I
b = −0.083216 + 1.022700I
−3.46331 − 2.44033I −1.79100 + 4.21493I
u = 0.625712 − 0.814457I
a = 0.889757 − 0.875058I
b = −0.083216 − 1.022700I
−3.46331 + 2.44033I −1.79100 − 4.21493I
u = 0.323104 + 1.005060I
a = 0.642445 − 0.528510I
b = −0.489124 − 1.083120I
10.64430 + 0.45572I 9.98152 − 0.50436I
u = 0.323104 − 1.005060I
a = 0.642445 + 0.528510I
b = −0.489124 + 1.083120I
10.64430 − 0.45572I 9.98152 + 0.50436I
u = 0.371261 + 0.991405I
a = 0.781690 + 0.096007I
b = −0.675087 + 0.237892I
3.78611 − 2.97347I 12.77186 + 5.12067I
u = 0.371261 − 0.991405I
a = 0.781690 − 0.096007I
b = −0.675087 − 0.237892I
3.78611 + 2.97347I 12.77186 − 5.12067I
u = 0.284163 + 1.021260I
a = −1.11146 − 1.51595I
b = 0.733335 + 0.752099I
3.44212 + 1.17546I 10.25427 − 3.27090I
u = 0.284163 − 1.021260I
a = −1.11146 + 1.51595I
b = 0.733335 − 0.752099I
3.44212 − 1.17546I 10.25427 + 3.27090I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.661266 + 0.661352I
a = 1.09003 − 0.94478I
b = −0.000047 − 0.953461I
−1.41938 − 0.49911I 2.60701 + 1.40158I
u = −0.661266 − 0.661352I
a = 1.09003 + 0.94478I
b = −0.000047 + 0.953461I
−1.41938 + 0.49911I 2.60701 − 1.40158I
u = −0.978145 + 0.449475I
a = 0.635866 + 0.398468I
b = −0.681700 + 0.964218I
2.70209 − 5.44166I 8.56320 + 6.09737I
u = −0.978145 − 0.449475I
a = 0.635866 − 0.398468I
b = −0.681700 − 0.964218I
2.70209 + 5.44166I 8.56320 − 6.09737I
u = 0.739636 + 0.543266I
a = 1.27278 + 1.20579I
b = 0.109646 + 0.952563I
6.95218 + 1.78242I 3.71796 − 0.00626I
u = 0.739636 − 0.543266I
a = 1.27278 − 1.20579I
b = 0.109646 − 0.952563I
6.95218 − 1.78242I 3.71796 + 0.00626I
u = −0.423575 + 1.030690I
a = −2.51731 + 0.08098I
b = 0.696401 + 0.959847I
2.80455 + 4.29067I 8.68297 − 2.64204I
u = −0.423575 − 1.030690I
a = −2.51731 − 0.08098I
b = 0.696401 − 0.959847I
2.80455 − 4.29067I 8.68297 + 2.64204I
u = 0.144714 + 0.863875I
a = −3.05379 + 1.22740I
b = 0.662709 − 0.878637I
9.78220 − 2.56986I 13.5531 + 4.3615I
u = 0.144714 − 0.863875I
a = −3.05379 − 1.22740I
b = 0.662709 + 0.878637I
9.78220 + 2.56986I 13.5531 − 4.3615I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588153 + 0.958301I
a = 0.773912 − 0.833223I
b = −0.137469 − 1.083360I
−0.51184 + 5.35586I 4.95676 − 7.14944I
u = −0.588153 − 0.958301I
a = 0.773912 + 0.833223I
b = −0.137469 + 1.083360I
−0.51184 − 5.35586I 4.95676 + 7.14944I
u = −0.473668 + 1.064350I
a = −0.68920 + 1.25309I
b = 0.770337 − 0.690812I
2.37111 + 2.38012I 7.11781 − 3.12902I
u = −0.473668 − 1.064350I
a = −0.68920 − 1.25309I
b = 0.770337 + 0.690812I
2.37111 − 2.38012I 7.11781 + 3.12902I
u = −0.306607 + 0.768934I
a = 0.677930 + 0.501746I
b = −0.495582 + 1.016170I
1.59907 − 1.22012I 10.24669 − 1.76763I
u = −0.306607 − 0.768934I
a = 0.677930 − 0.501746I
b = −0.495582 − 1.016170I
1.59907 + 1.22012I 10.24669 + 1.76763I
u = 0.691853 + 0.442021I
a = 0.666356 − 0.423245I
b = −0.608819 − 0.951542I
−0.47690 + 3.08931I 0.47513 − 3.63327I
u = 0.691853 − 0.442021I
a = 0.666356 + 0.423245I
b = −0.608819 + 0.951542I
−0.47690 − 3.08931I 0.47513 + 3.63327I
u = −1.123100 + 0.376086I
a = 0.673422 − 0.285619I
b = −0.777518 − 0.731848I
12.79390 − 1.04374I 11.13568 + 0.I
u = −1.123100 − 0.376086I
a = 0.673422 + 0.285619I
b = −0.777518 + 0.731848I
12.79390 + 1.04374I 11.13568 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031496 + 1.220130I
a = −1.73190 + 0.77105I
b = 0.769526 − 0.864952I
9.36102 − 2.89044I 13.8461 + 3.0592I
u = 0.031496 − 1.220130I
a = −1.73190 − 0.77105I
b = 0.769526 + 0.864952I
9.36102 + 2.89044I 13.8461 − 3.0592I
u = 0.568066 + 1.084730I
a = −2.24565 − 0.41344I
b = 0.703592 − 0.999172I
1.44085 − 7.97313I 0. + 7.82699I
u = 0.568066 − 1.084730I
a = −2.24565 + 0.41344I
b = 0.703592 + 0.999172I
1.44085 + 7.97313I 0. − 7.82699I
u = 0.591719 + 1.074220I
a = 0.704304 + 0.824413I
b = −0.157829 + 1.132950I
8.62037 − 6.88650I 0
u = 0.591719 − 1.074220I
a = 0.704304 − 0.824413I
b = −0.157829 − 1.132950I
8.62037 + 6.88650I 0
u = −0.422992 + 1.152020I
a = 0.742663 − 0.089155I
b = −0.772781 − 0.231893I
13.22670 + 4.07484I 13.16985 + 0.I
u = −0.422992 − 1.152020I
a = 0.742663 + 0.089155I
b = −0.772781 + 0.231893I
13.22670 − 4.07484I 13.16985 + 0.I
u = 1.127950 + 0.485672I
a = 0.618155 − 0.389809I
b = −0.718412 − 0.980360I
12.03690 + 6.70540I 0
u = 1.127950 − 0.485672I
a = 0.618155 + 0.389809I
b = −0.718412 + 0.980360I
12.03690 − 6.70540I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754125
a = 0.724705
b = 0.455004
9.83456 8.53390
u = −0.256062 + 0.665128I
a = 0.904103 − 0.096717I
b = −0.397261 − 0.233187I
0.338686 + 0.999830I 6.13657 − 6.36197I
u = −0.256062 − 0.665128I
a = 0.904103 + 0.096717I
b = −0.397261 + 0.233187I
0.338686 − 0.999830I 6.13657 + 6.36197I
u = 0.588126 + 1.170640I
a = −0.617779 − 0.984152I
b = 0.824403 + 0.669190I
6.05580 − 5.59891I 0
u = 0.588126 − 1.170640I
a = −0.617779 + 0.984152I
b = 0.824403 − 0.669190I
6.05580 + 5.59891I 0
u = −0.658056 + 1.167570I
a = −1.99266 + 0.49709I
b = 0.720138 + 1.025440I
4.97425 + 11.38970I 0
u = −0.658056 − 1.167570I
a = −1.99266 − 0.49709I
b = 0.720138 − 1.025440I
4.97425 − 11.38970I 0
u = −0.66401 + 1.25051I
a = −0.594793 + 0.840724I
b = 0.862806 − 0.659902I
15.6301 + 7.4127I 0
u = −0.66401 − 1.25051I
a = −0.594793 − 0.840724I
b = 0.862806 + 0.659902I
15.6301 − 7.4127I 0
u = 0.72488 + 1.23003I
a = −1.83482 − 0.53507I
b = 0.732388 − 1.044730I
14.4517 − 13.3499I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.72488 − 1.23003I
a = −1.83482 + 0.53507I
b = 0.732388 + 1.044730I
14.4517 + 13.3499I 0
u = −0.520003 + 0.233894I
a = 0.762531 − 0.369226I
b = −0.544789 − 0.773570I
0.16754 + 1.55102I −0.50728 − 2.39456I
u = −0.520003 − 0.233894I
a = 0.762531 + 0.369226I
b = −0.544789 + 0.773570I
0.16754 − 1.55102I −0.50728 + 2.39456I
u = −0.04885 + 1.43050I
a = −1.47868 − 0.48254I
b = 0.825254 + 0.886448I
−19.6229 + 3.0661I 0
u = −0.04885 − 1.43050I
a = −1.47868 + 0.48254I
b = 0.825254 − 0.886448I
−19.6229 − 3.0661I 0
u = 0.485800
a = 0.939168
b = 0.224170
1.28164 7.41160
10
II. I
v
1
= ha, v
3
+ 2v
2
+ 2b + 2v + 1, v
4
+ v
3
+ 2v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
5
=
0
−
1
2
v
3
− v
2
− v −
1
2
a
2
=
1
1
2
v
3
+ v
2
+ v −
1
2
a
6
=
−
1
2
v
3
− v
2
− v −
1
2
−
1
2
v
3
− v
2
− v +
1
2
a
1
=
1
2
v
3
+ v
2
+ v +
1
2
1
2
v
3
+ v
2
+ v −
1
2
a
9
=
v
0
a
11
=
v
0
a
7
=
−v
−
1
2
v
3
− v
2
− v +
1
2
a
8
=
0
−
1
2
v
3
− v +
1
2
a
12
=
1
2
v
3
+ v
2
+ v +
1
2
1
2
v
3
+ v −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3v
3
− 5v
2
− 7v + 7
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
9
, c
10
u
4
c
6
, c
7
, c
8
(u
2
− u − 1)
2
c
11
, c
12
(u
2
+ u − 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
9
, c
10
y
4
c
6
, c
7
, c
8
c
11
, c
12
(y
2
− 3y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.309017 + 0.535233I
a = 0
b = −0.500000 − 0.866025I
0.98696 + 2.02988I 6.50000 − 5.40059I
v = 0.309017 − 0.535233I
a = 0
b = −0.500000 + 0.866025I
0.98696 − 2.02988I 6.50000 + 5.40059I
v = −0.80902 + 1.40126I
a = 0
b = −0.500000 + 0.866025I
8.88264 − 2.02988I 6.50000 + 1.52761I
v = −0.80902 − 1.40126I
a = 0
b = −0.500000 − 0.866025I
8.88264 + 2.02988I 6.50000 − 1.52761I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
2
)(u
56
+ 19u
55
+ ··· − 20u + 1)
c
2
((u
2
+ u + 1)
2
)(u
56
+ 3u
55
+ ··· + 2u + 1)
c
3
, c
9
u
4
(u
56
− u
55
+ ··· − 44u
2
− 16)
c
5
((u
2
− u + 1)
2
)(u
56
+ 3u
55
+ ··· + 2u + 1)
c
6
, c
7
, c
8
((u
2
− u − 1)
2
)(u
56
− 3u
55
+ ··· + 2u − 1)
c
10
u
4
(u
56
− 25u
55
+ ··· − 1408u + 256)
c
11
, c
12
((u
2
+ u − 1)
2
)(u
56
− 3u
55
+ ··· + 2u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
56
+ 39y
55
+ ··· − 388y + 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
56
+ 19y
55
+ ··· − 20y + 1)
c
3
, c
9
y
4
(y
56
+ 25y
55
+ ··· + 1408y + 256)
c
6
, c
7
, c
8
c
11
, c
12
((y
2
− 3y + 1)
2
)(y
56
− 73y
55
+ ··· + 16y + 1)
c
10
y
4
(y
56
+ 5y
55
+ ··· − 925696y + 65536)
16
