12a
0655
(K12a
0655
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 8 2 6 11 1 5 9 4
Solving Sequence
2,6
7
3,10
4 8 1 5 11 9 12
c
6
c
2
c
3
c
7
c
1
c
5
c
10
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.19819 × 10
42
u
79
− 1.59276 × 10
43
u
78
+ ··· + 1.35478 × 10
43
b + 6.72467 × 10
42
,
3.41285 × 10
43
u
79
+ 4.36237 × 10
43
u
78
+ ··· + 5.41912 × 10
43
a − 1.57980 × 10
44
, u
80
+ 2u
79
+ ··· − 3u − 1i
I
u
2
= hb, 2a − 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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−8.20×10
42
u
79
−1.59×10
43
u
78
+· · ·+1.35×10
43
b+6.72×10
42
, 3.41×
10
43
u
79
+4.36×10
43
u
78
+· · ·+5.42×10
43
a−1.58×10
44
, u
80
+2u
79
+· · ·−3u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−0.629779u
79
− 0.804997u
78
+ ··· − 0.236236u + 2.91523
0.605131u
79
+ 1.17566u
78
+ ··· + 0.809601u − 0.496367
a
4
=
0.0169796u
79
+ 0.335459u
78
+ ··· + 5.83903u + 0.475568
0.312645u
79
+ 0.279259u
78
+ ··· − 1.22816u − 0.148293
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
11
=
−1.02827u
79
− 0.503727u
78
+ ··· + 0.572706u + 2.21425
−0.457395u
79
− 0.709552u
78
+ ··· + 3.16267u + 0.625862
a
9
=
−0.897443u
79
− 0.306344u
78
+ ··· + 0.339031u + 3.14474
−0.381766u
79
− 0.537593u
78
+ ··· + 3.60157u + 0.702345
a
12
=
−0.148293u
79
+ 0.0160589u
78
+ ··· + 0.773176u − 0.783280
−0.301500u
79
− 0.639544u
78
+ ··· − 0.526507u − 0.0169796
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.218530u
79
− 4.58968u
78
+ ··· − 13.4585u + 6.15221
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
80
+ 18u
79
+ ··· + 9u + 1
c
2
, c
6
u
80
− 2u
79
+ ··· + 3u − 1
c
3
u
80
+ u
79
+ ··· + 58u + 8
c
4
, c
12
u
80
+ 4u
79
+ ··· + u − 1
c
8
, c
11
u
80
+ 2u
79
+ ··· − 23u − 4
c
9
2(2u
80
+ 41u
79
+ ··· − 792u − 121)
c
10
2(2u
80
+ 23u
79
+ ··· − 1532216u + 259361)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
80
+ 90y
79
+ ··· + 23y + 1
c
2
, c
6
y
80
− 18y
79
+ ··· − 9y + 1
c
3
y
80
− 9y
79
+ ··· + 1228y + 64
c
4
, c
12
y
80
+ 46y
79
+ ··· − 9y + 1
c
8
, c
11
y
80
− 58y
79
+ ··· + 1135y + 16
c
9
4(4y
80
− 1149y
79
+ ··· − 58080y + 14641)
c
10
4(4y
80
+ 1059y
79
+ ··· − 1.70097 × 10
12
y + 6.72681 × 10
10
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908210 + 0.444035I
a = −1.095210 − 0.465911I
b = 0.438874 + 0.850544I
−3.55883 − 7.04654I 0
u = 0.908210 − 0.444035I
a = −1.095210 + 0.465911I
b = 0.438874 − 0.850544I
−3.55883 + 7.04654I 0
u = 0.865717 + 0.552851I
a = 0.875688 − 0.614993I
b = −0.389676 + 0.621158I
−2.62897 − 2.01090I 0
u = 0.865717 − 0.552851I
a = 0.875688 + 0.614993I
b = −0.389676 − 0.621158I
−2.62897 + 2.01090I 0
u = −1.029480 + 0.054908I
a = −0.086104 + 0.140911I
b = −0.611613 − 0.895210I
−3.03805 + 7.01781I 0
u = −1.029480 − 0.054908I
a = −0.086104 − 0.140911I
b = −0.611613 + 0.895210I
−3.03805 − 7.01781I 0
u = −0.862150 + 0.411938I
a = −0.765239 + 0.717847I
b = 0.355988 − 0.594647I
−0.10150 + 3.54359I 0. − 7.68142I
u = −0.862150 − 0.411938I
a = −0.765239 − 0.717847I
b = 0.355988 + 0.594647I
−0.10150 − 3.54359I 0. + 7.68142I
u = −0.805506 + 0.494428I
a = −1.054990 + 0.759347I
b = −0.414849 + 0.172313I
1.50560 + 5.11913I 5.17837 − 10.30158I
u = −0.805506 − 0.494428I
a = −1.054990 − 0.759347I
b = −0.414849 − 0.172313I
1.50560 − 5.11913I 5.17837 + 10.30158I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900523 + 0.041367I
a = −0.305993 − 0.178109I
b = 0.720582 − 1.129830I
−5.73822 − 2.28735I −7.12415 + 1.62116I
u = −0.900523 − 0.041367I
a = −0.305993 + 0.178109I
b = 0.720582 + 1.129830I
−5.73822 + 2.28735I −7.12415 − 1.62116I
u = −0.376173 + 0.818414I
a = −0.757603 + 0.029800I
b = 0.455373 − 0.302854I
5.96762 − 1.94537I 12.19550 + 3.06031I
u = −0.376173 − 0.818414I
a = −0.757603 − 0.029800I
b = 0.455373 + 0.302854I
5.96762 + 1.94537I 12.19550 − 3.06031I
u = 0.997813 + 0.498144I
a = 1.059100 + 0.742760I
b = −0.668142 − 0.394736I
0.21830 − 12.90460I 0
u = 0.997813 − 0.498144I
a = 1.059100 − 0.742760I
b = −0.668142 + 0.394736I
0.21830 + 12.90460I 0
u = 0.736410 + 0.485024I
a = −0.962764 − 0.238510I
b = −0.258198 − 1.145200I
2.76606 − 1.97173I 7.71264 + 2.63546I
u = 0.736410 − 0.485024I
a = −0.962764 + 0.238510I
b = −0.258198 + 1.145200I
2.76606 + 1.97173I 7.71264 − 2.63546I
u = 1.065740 + 0.394552I
a = −0.227830 + 0.296596I
b = 0.262901 + 0.085388I
−1.036590 + 0.614054I 0
u = 1.065740 − 0.394552I
a = −0.227830 − 0.296596I
b = 0.262901 − 0.085388I
−1.036590 − 0.614054I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.393317 + 0.768055I
a = −1.219110 − 0.511536I
b = 0.585050 + 0.524028I
2.20503 + 8.30381I 6.33496 − 5.30249I
u = 0.393317 − 0.768055I
a = −1.219110 + 0.511536I
b = 0.585050 − 0.524028I
2.20503 − 8.30381I 6.33496 + 5.30249I
u = −1.024360 + 0.515111I
a = 0.624975 − 0.528092I
b = −0.311319 + 0.219577I
3.83148 + 6.74819I 0
u = −1.024360 − 0.515111I
a = 0.624975 + 0.528092I
b = −0.311319 − 0.219577I
3.83148 − 6.74819I 0
u = 0.687160 + 0.501005I
a = −0.282184 − 0.064378I
b = −0.51019 − 1.36518I
2.92099 − 1.83327I 8.18864 + 5.75972I
u = 0.687160 − 0.501005I
a = −0.282184 + 0.064378I
b = −0.51019 + 1.36518I
2.92099 + 1.83327I 8.18864 − 5.75972I
u = −0.769360 + 0.358403I
a = −2.31120 + 5.45588I
b = 3.99649 − 1.94508I
−0.280690 + 1.300660I 18.3751 − 32.3353I
u = −0.769360 − 0.358403I
a = −2.31120 − 5.45588I
b = 3.99649 + 1.94508I
−0.280690 − 1.300660I 18.3751 + 32.3353I
u = 0.819942 + 0.191250I
a = 0.078129 − 0.134282I
b = 0.356444 + 0.554305I
−1.40523 − 0.61914I −4.60800 + 0.82851I
u = 0.819942 − 0.191250I
a = 0.078129 + 0.134282I
b = 0.356444 − 0.554305I
−1.40523 + 0.61914I −4.60800 − 0.82851I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16108
a = −0.0517082
b = −0.378668
0.324488 0
u = 0.276198 + 0.789141I
a = −0.201775 + 0.641459I
b = 0.394592 − 0.012771I
1.64531 − 4.95419I 7.71109 + 7.25315I
u = 0.276198 − 0.789141I
a = −0.201775 − 0.641459I
b = 0.394592 + 0.012771I
1.64531 + 4.95419I 7.71109 − 7.25315I
u = −0.594052 + 0.518671I
a = 0.926803 + 0.177997I
b = −0.441308 + 1.081290I
2.16348 − 1.21726I 8.19465 + 1.97536I
u = −0.594052 − 0.518671I
a = 0.926803 − 0.177997I
b = −0.441308 − 1.081290I
2.16348 + 1.21726I 8.19465 − 1.97536I
u = −0.888871 + 0.850062I
a = −1.031000 + 0.156735I
b = 0.81250 + 1.39597I
5.01781 + 2.94177I 0
u = −0.888871 − 0.850062I
a = −1.031000 − 0.156735I
b = 0.81250 − 1.39597I
5.01781 − 2.94177I 0
u = 0.884877 + 0.875922I
a = −1.64030 − 1.54748I
b = 3.03145 − 0.58809I
7.91819 − 0.07865I 0
u = 0.884877 − 0.875922I
a = −1.64030 + 1.54748I
b = 3.03145 + 0.58809I
7.91819 + 0.07865I 0
u = −0.926943 + 0.832833I
a = 0.286660 − 0.815402I
b = −1.52828 + 0.64200I
4.89547 + 3.32207I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926943 − 0.832833I
a = 0.286660 + 0.815402I
b = −1.52828 − 0.64200I
4.89547 − 3.32207I 0
u = −0.875865 + 0.887015I
a = −1.21431 + 2.34469I
b = 3.30413 − 0.59349I
4.89656 − 3.73236I 0
u = −0.875865 − 0.887015I
a = −1.21431 − 2.34469I
b = 3.30413 + 0.59349I
4.89656 + 3.73236I 0
u = 0.913469 + 0.855850I
a = 7.90543 − 5.83238I
b = 2.1500 + 17.7012I
6.83434 − 3.17732I 0
u = 0.913469 − 0.855850I
a = 7.90543 + 5.83238I
b = 2.1500 − 17.7012I
6.83434 + 3.17732I 0
u = −0.858554 + 0.925077I
a = 1.36360 − 1.87978I
b = −3.18932 + 0.02579I
9.7035 − 10.2935I 0
u = −0.858554 − 0.925077I
a = 1.36360 + 1.87978I
b = −3.18932 − 0.02579I
9.7035 + 10.2935I 0
u = 0.905807 + 0.883629I
a = −2.49473 − 0.75276I
b = 3.27476 − 1.66368I
9.90082 + 0.66319I 0
u = 0.905807 − 0.883629I
a = −2.49473 + 0.75276I
b = 3.27476 + 1.66368I
9.90082 − 0.66319I 0
u = 0.723920 + 0.124460I
a = 1.21857 − 1.47110I
b = 0.780068 + 0.970212I
−1.21288 − 2.12033I −2.81970 + 3.07552I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723920 − 0.124460I
a = 1.21857 + 1.47110I
b = 0.780068 − 0.970212I
−1.21288 + 2.12033I −2.81970 − 3.07552I
u = 0.857297 + 0.932255I
a = 1.30613 + 1.32110I
b = −2.54938 + 0.28745I
13.5592 + 4.2838I 0
u = 0.857297 − 0.932255I
a = 1.30613 − 1.32110I
b = −2.54938 − 0.28745I
13.5592 − 4.2838I 0
u = −0.916009 + 0.877875I
a = −1.376650 − 0.243211I
b = 1.47545 + 1.19753I
10.84760 + 2.95253I 0
u = −0.916009 − 0.877875I
a = −1.376650 + 0.243211I
b = 1.47545 − 1.19753I
10.84760 − 2.95253I 0
u = 0.945271 + 0.851052I
a = 1.65910 + 1.44872I
b = −3.28901 + 0.49671I
7.72695 − 6.32210I 0
u = 0.945271 − 0.851052I
a = 1.65910 − 1.44872I
b = −3.28901 − 0.49671I
7.72695 + 6.32210I 0
u = −0.926203 + 0.873253I
a = −0.00593 − 1.47214I
b = −1.146450 + 0.764895I
10.81490 + 3.52603I 0
u = −0.926203 − 0.873253I
a = −0.00593 + 1.47214I
b = −1.146450 − 0.764895I
10.81490 − 3.52603I 0
u = 0.936906 + 0.870026I
a = 1.02403 + 2.45543I
b = −3.30105 − 0.80227I
9.80182 − 7.14932I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936906 − 0.870026I
a = 1.02403 − 2.45543I
b = −3.30105 + 0.80227I
9.80182 + 7.14932I 0
u = −0.847914 + 0.957867I
a = 0.799931 − 0.479515I
b = −1.283290 − 0.364046I
8.58054 + 1.91116I 0
u = −0.847914 − 0.957867I
a = 0.799931 + 0.479515I
b = −1.283290 + 0.364046I
8.58054 − 1.91116I 0
u = −0.957274 + 0.852492I
a = 2.41489 − 0.96433I
b = −3.42506 − 1.60897I
4.63845 + 10.17100I 0
u = −0.957274 − 0.852492I
a = 2.41489 + 0.96433I
b = −3.42506 + 1.60897I
4.63845 − 10.17100I 0
u = 0.484225 + 0.490550I
a = 0.85564 − 1.37009I
b = −0.190985 + 0.748669I
−1.75610 − 2.02511I 1.63204 + 3.32753I
u = 0.484225 − 0.490550I
a = 0.85564 + 1.37009I
b = −0.190985 − 0.748669I
−1.75610 + 2.02511I 1.63204 − 3.32753I
u = −0.989525 + 0.860769I
a = −1.97327 + 1.20741I
b = 3.46394 + 1.15460I
9.2811 + 16.8739I 0
u = −0.989525 − 0.860769I
a = −1.97327 − 1.20741I
b = 3.46394 − 1.15460I
9.2811 − 16.8739I 0
u = 0.994452 + 0.863666I
a = −1.45453 − 1.16136I
b = 2.82195 − 0.59826I
13.1160 − 10.8953I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994452 − 0.863666I
a = −1.45453 + 1.16136I
b = 2.82195 + 0.59826I
13.1160 + 10.8953I 0
u = 0.379240 + 0.558264I
a = 1.51378 + 0.48363I
b = 0.013302 − 0.381211I
−1.97201 + 3.24293I 2.89878 − 3.45469I
u = 0.379240 − 0.558264I
a = 1.51378 − 0.48363I
b = 0.013302 + 0.381211I
−1.97201 − 3.24293I 2.89878 + 3.45469I
u = −1.013580 + 0.875810I
a = −0.681351 + 0.629833I
b = 1.370530 + 0.267728I
8.04920 + 4.81399I 0
u = −1.013580 − 0.875810I
a = −0.681351 − 0.629833I
b = 1.370530 − 0.267728I
8.04920 − 4.81399I 0
u = −0.449816 + 0.406846I
a = 1.48792 − 0.04382I
b = −0.402780 + 0.191398I
1.139930 − 0.176228I 8.91211 + 0.28630I
u = −0.449816 − 0.406846I
a = 1.48792 + 0.04382I
b = −0.402780 − 0.191398I
1.139930 + 0.176228I 8.91211 − 0.28630I
u = −0.436460
a = 2.21751
b = −0.515297
1.05778 11.1780
u = −0.126130 + 0.299152I
a = 3.40879 + 0.64147I
b = −1.206450 − 0.292678I
0.958209 + 1.026080I 4.35377 + 0.66475I
u = −0.126130 − 0.299152I
a = 3.40879 − 0.64147I
b = −1.206450 + 0.292678I
0.958209 − 1.026080I 4.35377 − 0.66475I
12
II. I
u
2
= hb, 2a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
10
=
0.5
0
a
4
=
1
0
a
8
=
0
1
a
1
=
−1
−1
a
5
=
1
−1
a
11
=
1
−0.5
a
9
=
1
0.5
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2.25
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
11
, c
12
u − 1
c
3
u
c
4
, c
6
, c
7
c
8
u + 1
c
9
, c
10
2(2u + 1)
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
11
, c
12
y −1
c
3
y
c
9
, c
10
4(4y −1)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000
b = 0
0 −2.25000
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
80
+ 18u
79
+ ··· + 9u + 1)
c
2
(u − 1)(u
80
− 2u
79
+ ··· + 3u − 1)
c
3
u(u
80
+ u
79
+ ··· + 58u + 8)
c
4
(u + 1)(u
80
+ 4u
79
+ ··· + u − 1)
c
6
(u + 1)(u
80
− 2u
79
+ ··· + 3u − 1)
c
7
(u + 1)(u
80
+ 18u
79
+ ··· + 9u + 1)
c
8
(u + 1)(u
80
+ 2u
79
+ ··· − 23u − 4)
c
9
4(2u + 1)(2u
80
+ 41u
79
+ ··· − 792u − 121)
c
10
4(2u + 1)(2u
80
+ 23u
79
+ ··· − 1532216u + 259361)
c
11
(u − 1)(u
80
+ 2u
79
+ ··· − 23u − 4)
c
12
(u − 1)(u
80
+ 4u
79
+ ··· + u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y −1)(y
80
+ 90y
79
+ ··· + 23y + 1)
c
2
, c
6
(y −1)(y
80
− 18y
79
+ ··· − 9y + 1)
c
3
y(y
80
− 9y
79
+ ··· + 1228y + 64)
c
4
, c
12
(y −1)(y
80
+ 46y
79
+ ··· − 9y + 1)
c
8
, c
11
(y −1)(y
80
− 58y
79
+ ··· + 1135y + 16)
c
9
16(4y −1)(4y
80
− 1149y
79
+ ··· − 58080y + 14641)
c
10
16(4y −1)
· (4y
80
+ 1059y
79
+ ··· − 1700965067380y + 67268128321)
18
