12a
0500
(K12a
0500
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 11 2 4 1 12 6 5
Solving Sequence
2,8
7 3 4 9 5 1 10 6 12 11
c
7
c
2
c
3
c
8
c
4
c
1
c
9
c
5
c
12
c
11
c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
83
− u
82
+ ··· − u
2
− 1i
* 1 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
= hu
83
− u
82
+ · · · − u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
14
− 3u
12
− 4u
10
− u
8
+ 1
−u
16
− 4u
14
− 8u
12
− 8u
10
− 4u
8
+ 2u
6
+ 4u
4
+ 2u
2
a
6
=
−u
39
− 10u
37
+ ··· + 7u
7
+ 6u
5
−u
41
− 11u
39
+ ··· + 2u
3
+ u
a
12
=
−u
23
− 6u
21
− 16u
19
− 20u
17
− 4u
15
+ 22u
13
+ 26u
11
+ 6u
9
− 9u
7
− 6u
5
u
23
+ 7u
21
+ ··· + 2u
3
+ u
a
11
=
−u
62
− 17u
60
+ ··· + 6u
6
+ 1
u
62
+ 18u
60
+ ··· − 12u
6
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
81
− 4u
80
+ ··· + 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
+ 47u
82
+ ··· − 2u − 1
c
2
, c
7
u
83
+ u
82
+ ··· + u
2
+ 1
c
3
, c
4
, c
8
u
83
− u
82
+ ··· + 124u + 17
c
5
u
83
+ u
82
+ ··· + 450u + 317
c
6
, c
11
u
83
− u
82
+ ··· + u
2
+ 1
c
9
u
83
− 11u
82
+ ··· + 98u − 29
c
10
u
83
− 39u
82
+ ··· − 2u + 1
c
12
u
83
− 5u
82
+ ··· − 2422u + 1767
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
− 21y
82
+ ··· − 6y −1
c
2
, c
7
y
83
+ 47y
82
+ ··· − 2y −1
c
3
, c
4
, c
8
y
83
− 89y
82
+ ··· + 16906y −289
c
5
y
83
− 17y
82
+ ··· + 3479646y −100489
c
6
, c
11
y
83
+ 39y
82
+ ··· − 2y −1
c
9
y
83
− 9y
82
+ ··· − 36274y −841
c
10
y
83
+ 11y
82
+ ··· − 14y −1
c
12
y
83
+ 27y
82
+ ··· − 121693646y −3122289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.133220 + 0.991655I
0.112602 − 1.022790I 0
u = −0.133220 − 0.991655I
0.112602 + 1.022790I 0
u = 0.464485 + 0.901515I
3.37380 + 4.66521I 0
u = 0.464485 − 0.901515I
3.37380 − 4.66521I 0
u = 0.460237 + 0.843965I
2.23760 − 2.68577I − 61.406699 + 0.10I
u = 0.460237 − 0.843965I
2.23760 + 2.68577I − 61.406699 + 0.10I
u = −0.412629 + 0.867916I
−0.09451 − 1.65097I −2.00000 + 3.87536I
u = −0.412629 − 0.867916I
−0.09451 + 1.65097I −2.00000 − 3.87536I
u = 0.180004 + 1.062710I
−4.06382 − 0.99415I 0
u = 0.180004 − 1.062710I
−4.06382 + 0.99415I 0
u = −0.158085 + 1.073960I
−2.03798 + 5.86401I 0
u = −0.158085 − 1.073960I
−2.03798 − 5.86401I 0
u = −0.481262 + 0.976359I
2.43576 − 4.31801I 0
u = −0.481262 − 0.976359I
2.43576 + 4.31801I 0
u = 0.240406 + 1.063530I
−4.57539 + 0.99512I 0
u = 0.240406 − 1.063530I
−4.57539 − 0.99512I 0
u = −0.272320 + 1.076070I
−3.03173 − 5.70325I 0
u = −0.272320 − 1.076070I
−3.03173 + 5.70325I 0
u = 0.442956 + 1.018750I
−3.12620 + 5.10527I 0
u = 0.442956 − 1.018750I
−3.12620 − 5.10527I 0
u = 0.481407 + 1.002460I
−1.91913 + 6.94168I 0
u = 0.481407 − 1.002460I
−1.91913 − 6.94168I 0
u = −0.405689 + 1.036190I
−2.06362 − 0.62641I 0
u = −0.405689 − 1.036190I
−2.06362 + 0.62641I 0
u = −0.493791 + 1.001660I
0.34760 − 11.85990I 0
u = −0.493791 − 1.001660I
0.34760 + 11.85990I 0
u = 0.869469 + 0.062981I
−4.54025 − 10.83720I −2.95711 + 7.16406I
u = 0.869469 − 0.062981I
−4.54025 + 10.83720I −2.95711 − 7.16406I
u = 0.870200 + 0.027576I
−6.76117 + 1.63137I −5.57883 − 2.57822I
u = 0.870200 − 0.027576I
−6.76117 − 1.63137I −5.57883 + 2.57822I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.869280 + 0.038602I
−7.89508 + 3.30997I −7.43042 − 3.23415I
u = −0.869280 − 0.038602I
−7.89508 − 3.30997I −7.43042 + 3.23415I
u = −0.868116 + 0.056802I
−6.74487 + 5.74130I −6.14356 − 3.20858I
u = −0.868116 − 0.056802I
−6.74487 − 5.74130I −6.14356 + 3.20858I
u = 0.853560 + 0.057638I
−2.00681 − 3.24204I 0.21808 + 1.91880I
u = 0.853560 − 0.057638I
−2.00681 + 3.24204I 0.21808 − 1.91880I
u = 0.809740
−2.84497 −3.18540
u = 0.485858 + 0.628329I
2.83112 + 6.65892I 2.83091 − 7.70358I
u = 0.485858 − 0.628329I
2.83112 − 6.65892I 2.83091 + 7.70358I
u = −0.274315 + 0.744403I
−0.270932 − 1.367880I −2.47570 + 5.35724I
u = −0.274315 − 0.744403I
−0.270932 + 1.367880I −2.47570 − 5.35724I
u = −0.788512 + 0.033384I
0.20844 + 3.73783I 1.09851 − 4.05017I
u = −0.788512 − 0.033384I
0.20844 − 3.73783I 1.09851 + 4.05017I
u = −0.443590 + 0.624580I
0.55457 − 2.06035I −0.38344 + 4.13562I
u = −0.443590 − 0.624580I
0.55457 + 2.06035I −0.38344 − 4.13562I
u = 0.480548 + 0.557812I
4.32394 − 0.70252I 6.01189 − 0.11159I
u = 0.480548 − 0.557812I
4.32394 + 0.70252I 6.01189 + 0.11159I
u = −0.448739 + 1.209870I
−3.40183 − 0.64725I 0
u = −0.448739 − 1.209870I
−3.40183 + 0.64725I 0
u = −0.470662 + 1.211330I
−3.24116 − 8.31020I 0
u = −0.470662 − 1.211330I
−3.24116 + 8.31020I 0
u = 0.460140 + 1.220060I
−6.43985 + 4.54605I 0
u = 0.460140 − 1.220060I
−6.43985 − 4.54605I 0
u = −0.570994 + 0.382917I
2.05864 + 7.62104I 1.38296 − 6.80721I
u = −0.570994 − 0.382917I
2.05864 − 7.62104I 1.38296 + 6.80721I
u = 0.431215 + 1.244170I
−5.94329 + 1.26047I 0
u = 0.431215 − 1.244170I
−5.94329 − 1.26047I 0
u = −0.524837 + 0.426422I
3.94874 + 0.21511I 5.20374 − 0.31901I
u = −0.524837 − 0.426422I
3.94874 − 0.21511I 5.20374 + 0.31901I
u = 0.489637 + 1.231500I
−5.52049 + 8.08364I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489637 − 1.231500I
−5.52049 − 8.08364I 0
u = 0.428440 + 1.254520I
−8.55613 − 6.29178I 0
u = 0.428440 − 1.254520I
−8.55613 + 6.29178I 0
u = −0.432241 + 1.253290I
−10.73130 + 1.17929I 0
u = −0.432241 − 1.253290I
−10.73130 − 1.17929I 0
u = −0.443165 + 1.252520I
−11.81410 − 1.31817I 0
u = −0.443165 − 1.252520I
−11.81410 + 1.31817I 0
u = 0.449371 + 1.252030I
−10.64110 + 6.29820I 0
u = 0.449371 − 1.252030I
−10.64110 − 6.29820I 0
u = −0.492052 + 1.237880I
−10.2955 − 10.6345I 0
u = −0.492052 − 1.237880I
−10.2955 + 10.6345I 0
u = 0.495073 + 1.237260I
−8.0709 + 15.7500I 0
u = 0.495073 − 1.237260I
−8.0709 − 15.7500I 0
u = −0.483809 + 1.241760I
−11.51720 − 8.16214I 0
u = −0.483809 − 1.241760I
−11.51720 + 8.16214I 0
u = 0.478597 + 1.243910I
−10.42700 + 3.19484I 0
u = 0.478597 − 1.243910I
−10.42700 − 3.19484I 0
u = 0.546008 + 0.366004I
−0.17694 − 2.80834I −1.96326 + 3.21508I
u = 0.546008 − 0.366004I
−0.17694 + 2.80834I −1.96326 − 3.21508I
u = −0.545383 + 0.148864I
0.31558 − 3.00332I −1.47850 + 2.74614I
u = −0.545383 − 0.148864I
0.31558 + 3.00332I −1.47850 − 2.74614I
u = 0.500212 + 0.257889I
−1.12463 − 1.27478I −4.20587 + 3.81637I
u = 0.500212 − 0.257889I
−1.12463 + 1.27478I −4.20587 − 3.81637I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
83
+ 47u
82
+ ··· − 2u − 1
c
2
, c
7
u
83
+ u
82
+ ··· + u
2
+ 1
c
3
, c
4
, c
8
u
83
− u
82
+ ··· + 124u + 17
c
5
u
83
+ u
82
+ ··· + 450u + 317
c
6
, c
11
u
83
− u
82
+ ··· + u
2
+ 1
c
9
u
83
− 11u
82
+ ··· + 98u − 29
c
10
u
83
− 39u
82
+ ··· − 2u + 1
c
12
u
83
− 5u
82
+ ··· − 2422u + 1767
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
83
− 21y
82
+ ··· − 6y −1
c
2
, c
7
y
83
+ 47y
82
+ ··· − 2y −1
c
3
, c
4
, c
8
y
83
− 89y
82
+ ··· + 16906y −289
c
5
y
83
− 17y
82
+ ··· + 3479646y −100489
c
6
, c
11
y
83
+ 39y
82
+ ··· − 2y −1
c
9
y
83
− 9y
82
+ ··· − 36274y −841
c
10
y
83
+ 11y
82
+ ··· − 14y −1
c
12
y
83
+ 27y
82
+ ··· − 121693646y −3122289
9
