12a
0535
(K12a
0535
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 2 1 6 12 5 4 9
Solving Sequence
4,10
5 11 6 12 9 1 8 3 2 7
c
4
c
10
c
5
c
11
c
9
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
87
− u
86
+ ··· + 2u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 87 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
87
− u
86
+ · · · + 2u
3
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
−u
3
+ 2u
−u
3
+ u
a
9
=
u
7
− 4u
5
+ 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
1
=
−u
11
+ 6u
9
− 12u
7
+ 8u
5
− u
3
+ 2u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
8
=
−u
13
+ 6u
11
− 13u
9
+ 12u
7
− 6u
5
+ 4u
3
− u
u
15
− 7u
13
+ 18u
11
− 19u
9
+ 6u
7
− 2u
5
+ 4u
3
+ u
a
3
=
−u
28
+ 13u
26
+ ··· − u
2
+ 1
u
30
− 14u
28
+ ··· + 8u
4
+ u
2
a
2
=
u
69
− 32u
67
+ ··· + 2u
3
+ u
−u
71
+ 33u
69
+ ··· − 3u
5
+ u
a
7
=
−u
37
+ 18u
35
+ ··· − 2u
3
− u
−u
37
+ 17u
35
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
85
+ 160u
83
+ ··· + 4u
2
+ 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
87
+ 41u
86
+ ··· + 2u
2
+ 1
c
2
, c
6
u
87
− u
86
+ ··· + 2u − 1
c
3
u
87
+ u
86
+ ··· + 200u − 676
c
4
, c
5
, c
10
u
87
+ u
86
+ ··· + 2u
3
− 1
c
7
u
87
− 3u
86
+ ··· + 1868u − 369
c
8
u
87
+ 11u
86
+ ··· − 4u + 1
c
9
, c
12
u
87
− 13u
86
+ ··· + 672u − 23
c
11
u
87
− 3u
86
+ ··· − 760u + 1491
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
87
+ 11y
86
+ ··· − 4y −1
c
2
, c
6
y
87
− 41y
86
+ ··· − 2y
2
− 1
c
3
y
87
− 25y
86
+ ··· + 2553368y −456976
c
4
, c
5
, c
10
y
87
− 81y
86
+ ··· + 6y
2
− 1
c
7
y
87
+ 19y
86
+ ··· − 3993896y −136161
c
8
y
87
− y
86
+ ··· + 276y −1
c
9
, c
12
y
87
+ 71y
86
+ ··· − 2068y −529
c
11
y
87
− 29y
86
+ ··· + 72372232y −2223081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.156780 + 0.129439I
−0.70238 − 4.44670I 0
u = 1.156780 − 0.129439I
−0.70238 + 4.44670I 0
u = −1.190410 + 0.114228I
1.68051 − 0.08481I 0
u = −1.190410 − 0.114228I
1.68051 + 0.08481I 0
u = 1.197740 + 0.161716I
−2.06048 + 3.05466I 0
u = 1.197740 − 0.161716I
−2.06048 − 3.05466I 0
u = −0.394345 + 0.684266I
1.51716 − 12.42810I 2.28821 + 10.31032I
u = −0.394345 − 0.684266I
1.51716 + 12.42810I 2.28821 − 10.31032I
u = 0.397280 + 0.677777I
3.75424 + 7.36938I 5.55912 − 6.47433I
u = 0.397280 − 0.677777I
3.75424 − 7.36938I 5.55912 + 6.47433I
u = 0.411947 + 0.661442I
4.96694 + 5.07089I 7.17620 − 6.66777I
u = 0.411947 − 0.661442I
4.96694 − 5.07089I 7.17620 + 6.66777I
u = −0.422450 + 0.650766I
3.87197 − 0.21546I 5.49137 + 0.72436I
u = −0.422450 − 0.650766I
3.87197 + 0.21546I 5.49137 − 0.72436I
u = −0.383227 + 0.669870I
−0.89151 − 4.80723I −0.97957 + 5.10975I
u = −0.383227 − 0.669870I
−0.89151 + 4.80723I −0.97957 − 5.10975I
u = −0.526813 + 0.558841I
2.05288 + 8.27457I 3.75896 − 4.30912I
u = −0.526813 − 0.558841I
2.05288 − 8.27457I 3.75896 + 4.30912I
u = −0.477712 + 0.597005I
4.10203 − 3.89674I 6.13861 + 5.88274I
u = −0.477712 − 0.597005I
4.10203 + 3.89674I 6.13861 − 5.88274I
u = 0.515570 + 0.562335I
4.24183 − 3.23972I 7.01693 + 0.29788I
u = 0.515570 − 0.562335I
4.24183 + 3.23972I 7.01693 − 0.29788I
u = 0.490448 + 0.582937I
5.29751 − 0.95847I 8.28381 + 0.09263I
u = 0.490448 − 0.582937I
5.29751 + 0.95847I 8.28381 − 0.09263I
u = −0.503329 + 0.535550I
−0.358919 + 0.797404I 0.536680 + 1.151908I
u = −0.503329 − 0.535550I
−0.358919 − 0.797404I 0.536680 − 1.151908I
u = −1.255210 + 0.203993I
−1.51650 − 2.92945I 0
u = −1.255210 − 0.203993I
−1.51650 + 2.92945I 0
u = 0.332557 + 0.627242I
−2.65475 + 5.15343I −2.54076 − 7.53067I
u = 0.332557 − 0.627242I
−2.65475 − 5.15343I −2.54076 + 7.53067I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29153
2.70892 0
u = −1.275740 + 0.221412I
0.38686 − 10.53480I 0
u = −1.275740 − 0.221412I
0.38686 + 10.53480I 0
u = 1.279400 + 0.209305I
2.71537 + 5.68459I 0
u = 1.279400 − 0.209305I
2.71537 − 5.68459I 0
u = 1.306270 + 0.174474I
4.06397 + 4.13533I 0
u = 1.306270 − 0.174474I
4.06397 − 4.13533I 0
u = −0.354989 + 0.578954I
0.51266 − 1.71188I 2.60562 + 3.92232I
u = −0.354989 − 0.578954I
0.51266 + 1.71188I 2.60562 − 3.92232I
u = −1.332530 + 0.123240I
3.22730 + 0.03439I 0
u = −1.332530 − 0.123240I
3.22730 − 0.03439I 0
u = 0.079050 + 0.640246I
−3.79331 + 7.39706I −4.18948 − 7.63957I
u = 0.079050 − 0.640246I
−3.79331 − 7.39706I −4.18948 + 7.63957I
u = 0.269882 + 0.583125I
−2.06224 − 2.16472I −1.83071 − 0.20236I
u = 0.269882 − 0.583125I
−2.06224 + 2.16472I −1.83071 + 0.20236I
u = 0.040574 + 0.629744I
−5.47859 − 0.11339I −7.64972 − 0.43755I
u = 0.040574 − 0.629744I
−5.47859 + 0.11339I −7.64972 + 0.43755I
u = −0.078398 + 0.618585I
−1.47306 − 2.66672I −1.11507 + 4.12840I
u = −0.078398 − 0.618585I
−1.47306 + 2.66672I −1.11507 − 4.12840I
u = 1.389750 + 0.020023I
6.81321 + 0.99479I 0
u = 1.389750 − 0.020023I
6.81321 − 0.99479I 0
u = −1.397660 + 0.038212I
5.01700 − 5.77605I 0
u = −1.397660 − 0.038212I
5.01700 + 5.77605I 0
u = −1.42214 + 0.21746I
3.41028 − 0.73286I 0
u = −1.42214 − 0.21746I
3.41028 + 0.73286I 0
u = 0.522256 + 0.193380I
−0.79956 + 5.07877I 3.26255 − 6.36328I
u = 0.522256 − 0.193380I
−0.79956 − 5.07877I 3.26255 + 6.36328I
u = 0.425921 + 0.358005I
−1.94719 − 1.77409I 0.090741 + 0.339279I
u = 0.425921 − 0.358005I
−1.94719 + 1.77409I 0.090741 − 0.339279I
u = −1.43304 + 0.23763I
3.01862 − 8.32049I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43304 − 0.23763I
3.01862 + 8.32049I 0
u = −0.121744 + 0.530430I
−0.35102 − 1.54409I 0.33199 + 6.05743I
u = −0.121744 − 0.530430I
−0.35102 + 1.54409I 0.33199 − 6.05743I
u = 1.43839 + 0.22451I
6.28029 + 4.69366I 0
u = 1.43839 − 0.22451I
6.28029 − 4.69366I 0
u = 1.45419 + 0.25130I
5.02090 + 8.17446I 0
u = 1.45419 − 0.25130I
5.02090 − 8.17446I 0
u = 1.46400 + 0.18941I
5.93361 + 1.83428I 0
u = 1.46400 − 0.18941I
5.93361 − 1.83428I 0
u = −1.46040 + 0.25270I
9.7370 − 10.7689I 0
u = −1.46040 − 0.25270I
9.7370 + 10.7689I 0
u = 1.46013 + 0.25560I
7.4888 + 15.8607I 0
u = 1.46013 − 0.25560I
7.4888 − 15.8607I 0
u = −1.46342 + 0.24445I
11.01010 − 8.38279I 0
u = −1.46342 − 0.24445I
11.01010 + 8.38279I 0
u = 1.46517 + 0.23900I
9.95560 + 3.46864I 0
u = 1.46517 − 0.23900I
9.95560 − 3.46864I 0
u = −1.47478 + 0.19157I
10.64660 + 0.51731I 0
u = −1.47478 − 0.19157I
10.64660 − 0.51731I 0
u = −1.47348 + 0.20336I
11.62440 − 1.89999I 0
u = −1.47348 − 0.20336I
11.62440 + 1.89999I 0
u = 1.47312 + 0.20995I
10.39210 + 6.83566I 0
u = 1.47312 − 0.20995I
10.39210 − 6.83566I 0
u = 1.47653 + 0.18742I
8.50190 − 5.59085I 0
u = 1.47653 − 0.18742I
8.50190 + 5.59085I 0
u = −0.459395 + 0.110558I
1.200510 − 0.610350I 7.99355 + 1.68998I
u = −0.459395 − 0.110558I
1.200510 + 0.610350I 7.99355 − 1.68998I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
87
+ 41u
86
+ ··· + 2u
2
+ 1
c
2
, c
6
u
87
− u
86
+ ··· + 2u − 1
c
3
u
87
+ u
86
+ ··· + 200u − 676
c
4
, c
5
, c
10
u
87
+ u
86
+ ··· + 2u
3
− 1
c
7
u
87
− 3u
86
+ ··· + 1868u − 369
c
8
u
87
+ 11u
86
+ ··· − 4u + 1
c
9
, c
12
u
87
− 13u
86
+ ··· + 672u − 23
c
11
u
87
− 3u
86
+ ··· − 760u + 1491
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
87
+ 11y
86
+ ··· − 4y −1
c
2
, c
6
y
87
− 41y
86
+ ··· − 2y
2
− 1
c
3
y
87
− 25y
86
+ ··· + 2553368y −456976
c
4
, c
5
, c
10
y
87
− 81y
86
+ ··· + 6y
2
− 1
c
7
y
87
+ 19y
86
+ ··· − 3993896y −136161
c
8
y
87
− y
86
+ ··· + 276y −1
c
9
, c
12
y
87
+ 71y
86
+ ··· − 2068y −529
c
11
y
87
− 29y
86
+ ··· + 72372232y −2223081
9
