12a
0499
(K12a
0499
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 2 1 12 11 6 5 4
Solving Sequence
6,10
11 5 12 9 4 1 8 3 2 7
c
10
c
5
c
11
c
9
c
4
c
12
c
8
c
3
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
116
+ u
115
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 116 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
= hu
116
+ u
115
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
−u
u
a
12
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
2
+ 1
u
4
a
4
=
−u
7
+ 2u
5
− 2u
3
u
9
− u
7
+ u
5
+ u
a
1
=
u
20
− 5u
18
+ 13u
16
− 20u
14
+ 20u
12
− 13u
10
+ 7u
8
− 4u
6
+ 3u
4
− u
2
+ 1
−u
22
+ 4u
20
− 9u
18
+ 12u
16
− 12u
14
+ 10u
12
− 9u
10
+ 6u
8
− 3u
6
− u
2
a
8
=
u
12
− 3u
10
+ 5u
8
− 4u
6
+ 2u
4
− u
2
+ 1
−u
12
+ 2u
10
− 2u
8
+ u
4
a
3
=
−u
33
+ 8u
31
+ ··· − 4u
5
− u
u
33
− 7u
31
+ ··· + 2u
13
+ u
a
2
=
u
88
− 21u
86
+ ··· − 2u
2
+ 1
−u
88
+ 20u
86
+ ··· − 5u
8
− 2u
4
a
7
=
−u
54
+ 13u
52
+ ··· − 2u
2
+ 1
u
56
− 12u
54
+ ··· + 5u
8
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
114
+ 108u
112
+ ··· + 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
116
+ 55u
115
+ ··· + 2u + 1
c
2
, c
6
u
116
− u
115
+ ··· − 2u + 1
c
3
u
116
+ u
115
+ ··· − 4460u + 481
c
4
u
116
− u
115
+ ··· + 4460u + 481
c
5
, c
10
u
116
+ u
115
+ ··· + 2u + 1
c
7
u
116
− 3u
115
+ ··· − 3102u + 1491
c
8
u
116
− 13u
115
+ ··· − 28714u + 1493
c
9
u
116
− 55u
115
+ ··· − 2u + 1
c
11
u
116
+ 3u
115
+ ··· + 3102u + 1491
c
12
u
116
+ 13u
115
+ ··· + 28714u + 1493
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
116
+ 13y
115
+ ··· + 10y + 1
c
2
, c
5
, c
6
c
10
y
116
− 55y
115
+ ··· − 2y + 1
c
3
, c
4
y
116
− 23y
115
+ ··· − 20059950y + 231361
c
7
, c
11
y
116
+ 29y
115
+ ··· + 95901630y + 2223081
c
8
, c
12
y
116
+ 25y
115
+ ··· + 93441422y + 2229049
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980916 + 0.187806I
−0.46811 − 4.80626I 0
u = −0.980916 − 0.187806I
−0.46811 + 4.80626I 0
u = 1.038040 + 0.264208I
1.92758 + 0.70552I 0
u = 1.038040 − 0.264208I
1.92758 − 0.70552I 0
u = 0.946091 + 0.512909I
0.924676 + 0.744595I 0
u = 0.946091 − 0.512909I
0.924676 − 0.744595I 0
u = −1.060920 + 0.213508I
−1.38450 + 2.53956I 0
u = −1.060920 − 0.213508I
−1.38450 − 2.53956I 0
u = −0.814804 + 0.409673I
−0.25942 − 4.77611I 0
u = −0.814804 − 0.409673I
−0.25942 + 4.77611I 0
u = −0.628886 + 0.653348I
−3.77819 − 10.54700I 0
u = −0.628886 − 0.653348I
−3.77819 + 10.54700I 0
u = 0.942453 + 0.559925I
−0.504439 − 0.872368I 0
u = 0.942453 − 0.559925I
−0.504439 + 0.872368I 0
u = −0.940053 + 0.570126I
−2.86201 + 5.76865I 0
u = −0.940053 − 0.570126I
−2.86201 − 5.76865I 0
u = 0.625796 + 0.644391I
−1.43505 + 5.59418I 0
u = 0.625796 − 0.644391I
−1.43505 − 5.59418I 0
u = −0.608287 + 0.651469I
−5.84997 − 2.81500I 0
u = −0.608287 − 0.651469I
−5.84997 + 2.81500I 0
u = −0.960180 + 0.566648I
−4.81422 − 1.94454I 0
u = −0.960180 − 0.566648I
−4.81422 + 1.94454I 0
u = 0.625750 + 0.608379I
3.73398I 0. − 6.64937I
u = 0.625750 − 0.608379I
− 3.73398I 0. + 6.64937I
u = 0.555810 + 0.660598I
−6.69334 + 2.65982I −9.45564 − 3.84348I
u = 0.555810 − 0.660598I
−6.69334 − 2.65982I −9.45564 + 3.84348I
u = 1.118040 + 0.226753I
− 2.33040I 0
u = 1.118040 − 0.226753I
2.33040I 0
u = −1.026760 + 0.500607I
0.25942 − 4.77611I 0
u = −1.026760 − 0.500607I
0.25942 + 4.77611I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.527461 + 0.669939I
−5.43231 − 5.03460I −7.42120 + 3.61295I
u = 0.527461 − 0.669939I
−5.43231 + 5.03460I −7.42120 − 3.61295I
u = 1.000610 + 0.570056I
−5.38292 + 2.13233I 0
u = 1.000610 − 0.570056I
−5.38292 − 2.13233I 0
u = −1.125530 + 0.251630I
5.84997 + 2.81500I 0
u = −1.125530 − 0.251630I
5.84997 − 2.81500I 0
u = −1.129690 + 0.233561I
4.55451 + 4.96937I 0
u = −1.129690 − 0.233561I
4.55451 − 4.96937I 0
u = 1.123830 + 0.264580I
4.81422 + 1.94454I 0
u = 1.123830 − 0.264580I
4.81422 − 1.94454I 0
u = −0.629046 + 0.562950I
−0.924676 + 0.744595I −1.70283 + 0.47785I
u = −0.629046 − 0.562950I
−0.924676 − 0.744595I −1.70283 − 0.47785I
u = 1.133100 + 0.228599I
2.27795 − 9.98895I 0
u = 1.133100 − 0.228599I
2.27795 + 9.98895I 0
u = −1.015750 + 0.562708I
−1.48579 − 5.23203I 0
u = −1.015750 − 0.562708I
−1.48579 + 5.23203I 0
u = −0.337603 + 0.767769I
−2.32174 + 12.72840I −3.20740 − 8.63317I
u = −0.337603 − 0.767769I
−2.32174 − 12.72840I −3.20740 + 8.63317I
u = −0.529452 + 0.649722I
−2.91594 + 0.49250I −4.26845 + 0.I
u = −0.529452 − 0.649722I
−2.91594 − 0.49250I −4.26845 + 0.I
u = 1.105330 + 0.361373I
1.38450 + 2.53956I 0
u = 1.105330 − 0.361373I
1.38450 − 2.53956I 0
u = −0.346326 + 0.757864I
−4.55451 + 4.96937I −6.51117 − 3.10487I
u = −0.346326 − 0.757864I
−4.55451 − 4.96937I −6.51117 + 3.10487I
u = 0.335567 + 0.762518I
− 7.70624I 0. + 4.97280I
u = 0.335567 − 0.762518I
7.70624I 0. − 4.97280I
u = 1.018400 + 0.573095I
−3.98793 + 9.86085I 0
u = 1.018400 − 0.573095I
−3.98793 − 9.86085I 0
u = 1.125490 + 0.318238I
5.38292 − 2.13233I 0
u = 1.125490 − 0.318238I
5.38292 + 2.13233I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123770 + 0.330636I
6.69334 − 2.65982I 0
u = −1.123770 − 0.330636I
6.69334 + 2.65982I 0
u = 0.377708 + 0.733138I
−5.83527 − 4.81659I −8.08076 + 4.42676I
u = 0.377708 − 0.733138I
−5.83527 + 4.81659I −8.08076 − 4.42676I
u = −1.125560 + 0.351844I
5.83527 − 4.81659I 0
u = −1.125560 − 0.351844I
5.83527 + 4.81659I 0
u = 0.399874 + 0.716677I
−4.83551 + 2.87101I −6.77334 − 2.97281I
u = 0.399874 − 0.716677I
−4.83551 − 2.87101I −6.77334 + 2.97281I
u = 1.129480 + 0.358841I
3.70499 + 9.78092I 0
u = 1.129480 − 0.358841I
3.70499 − 9.78092I 0
u = 0.323517 + 0.747692I
1.43505 − 5.59418I 1.64640 + 5.68591I
u = 0.323517 − 0.747692I
1.43505 + 5.59418I 1.64640 − 5.68591I
u = −0.379511 + 0.708479I
−2.23541 + 1.50273I −3.25161 − 1.05729I
u = −0.379511 − 0.708479I
−2.23541 − 1.50273I −3.25161 + 1.05729I
u = −1.089270 + 0.503562I
0.46811 − 4.80626I 0
u = −1.089270 − 0.503562I
0.46811 + 4.80626I 0
u = −0.313605 + 0.734979I
0.504439 + 0.872368I 0.174078 + 0.321368I
u = −0.313605 − 0.734979I
0.504439 − 0.872368I 0.174078 − 0.321368I
u = 0.773108 + 0.149912I
1.52280 + 0.57753I 5.07994 − 0.95902I
u = 0.773108 − 0.149912I
1.52280 − 0.57753I 5.07994 + 0.95902I
u = −1.120070 + 0.492819I
2.80572 + 2.04914I 0
u = −1.120070 − 0.492819I
2.80572 − 2.04914I 0
u = 1.118000 + 0.500533I
4.83551 + 2.87101I 0
u = 1.118000 − 0.500533I
4.83551 − 2.87101I 0
u = 1.091560 + 0.568564I
−2.80572 + 2.04914I 0
u = 1.091560 − 0.568564I
−2.80572 − 2.04914I 0
u = −1.098380 + 0.561847I
−0.13230 − 6.37734I 0
u = −1.098380 − 0.561847I
−0.13230 + 6.37734I 0
u = 1.120950 + 0.517112I
5.43231 + 5.03460I 0
u = 1.120950 − 0.517112I
5.43231 − 5.03460I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123940 + 0.524552I
3.98793 − 9.86085I 0
u = −1.123940 − 0.524552I
3.98793 + 9.86085I 0
u = 1.103770 + 0.570351I
−3.70499 + 9.78092I 0
u = 1.103770 − 0.570351I
−3.70499 − 9.78092I 0
u = −1.123670 + 0.555323I
2.86201 − 5.76865I 0
u = −1.123670 − 0.555323I
2.86201 + 5.76865I 0
u = 1.124810 + 0.561210I
3.77819 + 10.54700I 0
u = 1.124810 − 0.561210I
3.77819 − 10.54700I 0
u = −1.121090 + 0.570554I
−2.27795 − 9.98895I 0
u = −1.121090 − 0.570554I
−2.27795 + 9.98895I 0
u = 1.125750 + 0.568932I
2.32174 + 12.72840I 0
u = 1.125750 − 0.568932I
2.32174 − 12.72840I 0
u = −1.126700 + 0.571118I
− 17.7724I 0
u = −1.126700 − 0.571118I
17.7724I 0
u = −0.242875 + 0.687753I
1.48579 + 5.23203I 1.33742 − 5.64057I
u = −0.242875 − 0.687753I
1.48579 − 5.23203I 1.33742 + 5.64057I
u = 0.224332 + 0.667829I
2.91594 − 0.49250I 4.26845 − 0.19979I
u = 0.224332 − 0.667829I
2.91594 + 0.49250I 4.26845 + 0.19979I
u = −0.412080 + 0.554449I
−1.52280 + 0.57753I −5.07994 − 0.95902I
u = −0.412080 − 0.554449I
−1.52280 − 0.57753I −5.07994 + 0.95902I
u = −0.147126 + 0.653714I
0.13230 − 6.37734I −0.27591 + 5.27854I
u = −0.147126 − 0.653714I
0.13230 + 6.37734I −0.27591 − 5.27854I
u = 0.170503 + 0.646191I
2.23541 + 1.50273I 3.25161 − 1.05729I
u = 0.170503 − 0.646191I
2.23541 − 1.50273I 3.25161 + 1.05729I
u = −0.123289 + 0.568855I
−1.92758 + 0.70552I −3.67143 − 0.70779I
u = −0.123289 − 0.568855I
−1.92758 − 0.70552I −3.67143 + 0.70779I
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
116
+ 55u
115
+ ··· + 2u + 1
c
2
, c
6
u
116
− u
115
+ ··· − 2u + 1
c
3
u
116
+ u
115
+ ··· − 4460u + 481
c
4
u
116
− u
115
+ ··· + 4460u + 481
c
5
, c
10
u
116
+ u
115
+ ··· + 2u + 1
c
7
u
116
− 3u
115
+ ··· − 3102u + 1491
c
8
u
116
− 13u
115
+ ··· − 28714u + 1493
c
9
u
116
− 55u
115
+ ··· − 2u + 1
c
11
u
116
+ 3u
115
+ ··· + 3102u + 1491
c
12
u
116
+ 13u
115
+ ··· + 28714u + 1493
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
116
+ 13y
115
+ ··· + 10y + 1
c
2
, c
5
, c
6
c
10
y
116
− 55y
115
+ ··· − 2y + 1
c
3
, c
4
y
116
− 23y
115
+ ··· − 20059950y + 231361
c
7
, c
11
y
116
+ 29y
115
+ ··· + 95901630y + 2223081
c
8
, c
12
y
116
+ 25y
115
+ ··· + 93441422y + 2229049
10
