12a
0204
(K12a
0204
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 10 2 1 12 11 5 9 4
Solving Sequence
2,7
6 3 4 1 8 5 12 9 11 10
c
6
c
2
c
3
c
1
c
7
c
4
c
12
c
8
c
11
c
10
c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
86
+ u
85
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 86 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
86
+ u
85
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
5
=
u
21
+ 4u
19
+ 9u
17
+ 12u
15
+ 12u
13
+ 10u
11
+ 9u
9
+ 6u
7
+ 3u
5
+ u
u
23
+ 5u
21
+ ··· + 2u
3
+ u
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
9
=
u
32
+ 7u
30
+ ··· + 2u
12
+ 1
−u
32
− 8u
30
+ ··· − 12u
8
− 4u
6
a
11
=
−u
53
− 12u
51
+ ··· − 3u
5
− u
u
53
+ 13u
51
+ ··· + u
3
+ u
a
10
=
u
74
+ 17u
72
+ ··· + u
2
+ 1
−u
74
− 18u
72
+ ··· − 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
85
+ 4u
84
+ ··· + 24u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
+ 41u
85
+ ··· + 3u + 1
c
2
, c
6
u
86
− u
85
+ ··· − 3u + 1
c
3
u
86
+ u
85
+ ··· + 471u + 65
c
4
u
86
− u
85
+ ··· − 149u + 137
c
5
, c
10
u
86
− u
85
+ ··· + u + 1
c
7
u
86
− 5u
85
+ ··· − 623u + 111
c
8
, c
9
, c
11
u
86
− 21u
85
+ ··· − 3u + 1
c
12
u
86
+ 9u
85
+ ··· + 6433u + 797
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
86
+ 9y
85
+ ··· + 19y + 1
c
2
, c
6
y
86
+ 41y
85
+ ··· + 3y + 1
c
3
y
86
− 23y
85
+ ··· + 399819y + 4225
c
4
y
86
+ 9y
85
+ ··· + 312079y + 18769
c
5
, c
10
y
86
+ 21y
85
+ ··· + 3y + 1
c
7
y
86
+ 13y
85
+ ··· + 865727y + 12321
c
8
, c
9
, c
11
y
86
+ 89y
85
+ ··· + 11y + 1
c
12
y
86
+ 29y
85
+ ··· + 40057159y + 635209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552073 + 0.903867I
−4.89234 − 1.96034I 0
u = −0.552073 − 0.903867I
−4.89234 + 1.96034I 0
u = −0.022062 + 0.940386I
−5.66854 − 3.02612I −3.62148 + 2.70851I
u = −0.022062 − 0.940386I
−5.66854 + 3.02612I −3.62148 − 2.70851I
u = 0.561963 + 0.912758I
−4.52045 − 4.21833I 0
u = 0.561963 − 0.912758I
−4.52045 + 4.21833I 0
u = 0.642242 + 0.650491I
−3.74752 + 8.94433I 2.00000 − 7.87615I
u = 0.642242 − 0.650491I
−3.74752 − 8.94433I 2.00000 + 7.87615I
u = −0.257669 + 1.056490I
−0.670480 − 0.639201I 0
u = −0.257669 − 1.056490I
−0.670480 + 0.639201I 0
u = −0.633408 + 0.654906I
−4.15827 − 2.71284I 1.31273 + 3.00115I
u = −0.633408 − 0.654906I
−4.15827 + 2.71284I 1.31273 − 3.00115I
u = 0.550086 + 0.961327I
2.46470 − 0.37994I 0
u = 0.550086 − 0.961327I
2.46470 + 0.37994I 0
u = −0.517375 + 0.987111I
0.07166 − 2.62578I 0
u = −0.517375 − 0.987111I
0.07166 + 2.62578I 0
u = 0.633756 + 0.606008I
3.50780 + 5.03732I 7.81344 − 8.08967I
u = 0.633756 − 0.606008I
3.50780 − 5.03732I 7.81344 + 8.08967I
u = −0.238562 + 1.113670I
−2.23970 + 4.39842I 0
u = −0.238562 − 1.113670I
−2.23970 − 4.39842I 0
u = 0.264448 + 1.111100I
−4.27295 − 0.76354I 0
u = 0.264448 − 1.111100I
−4.27295 + 0.76354I 0
u = 0.554348 + 1.004930I
3.01740 + 4.89814I 0
u = 0.554348 − 1.004930I
3.01740 − 4.89814I 0
u = 0.311549 + 1.107070I
−4.74848 + 0.89916I 0
u = 0.311549 − 1.107070I
−4.74848 − 0.89916I 0
u = −0.347956 + 1.100820I
−3.34095 − 4.64653I 0
u = −0.347956 − 1.100820I
−3.34095 + 4.64653I 0
u = 0.635644 + 0.546117I
4.36758 − 0.22453I 10.66536 + 0.55787I
u = 0.635644 − 0.546117I
4.36758 + 0.22453I 10.66536 − 0.55787I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.770174 + 0.323215I
−5.37084 + 11.03650I 0.76608 − 7.01041I
u = −0.770174 − 0.323215I
−5.37084 − 11.03650I 0.76608 + 7.01041I
u = −0.588398 + 0.591566I
1.23725 − 1.78468I 1.82852 + 3.46758I
u = −0.588398 − 0.591566I
1.23725 + 1.78468I 1.82852 − 3.46758I
u = −0.239868 + 1.142870I
−9.93808 + 8.18745I 0
u = −0.239868 − 1.142870I
−9.93808 − 8.18745I 0
u = 0.245139 + 1.142850I
−10.34130 − 1.86383I 0
u = 0.245139 − 1.142850I
−10.34130 + 1.86383I 0
u = 0.767277 + 0.318425I
−5.80930 − 4.73542I −0.13133 + 2.18376I
u = 0.767277 − 0.318425I
−5.80930 + 4.73542I −0.13133 − 2.18376I
u = 0.676444 + 0.477199I
−1.06723 − 3.95000I 4.49030 + 3.18305I
u = 0.676444 − 0.477199I
−1.06723 + 3.95000I 4.49030 − 3.18305I
u = −0.748230 + 0.339955I
2.22223 + 7.05409I 5.75869 − 7.62186I
u = −0.748230 − 0.339955I
2.22223 − 7.05409I 5.75869 + 7.62186I
u = −0.680511 + 0.452157I
−1.17586 − 1.85794I 4.15708 + 2.29378I
u = −0.680511 − 0.452157I
−1.17586 + 1.85794I 4.15708 − 2.29378I
u = 0.567898 + 1.043900I
−2.72701 + 8.77066I 0
u = 0.567898 − 1.043900I
−2.72701 − 8.77066I 0
u = 0.339044 + 1.142000I
−11.40330 + 1.33625I 0
u = 0.339044 − 1.142000I
−11.40330 − 1.33625I 0
u = −0.344970 + 1.141800I
−11.12770 − 7.68084I 0
u = −0.344970 − 1.141800I
−11.12770 + 7.68084I 0
u = −0.562524 + 1.055970I
−2.94385 − 2.95008I 0
u = −0.562524 − 1.055970I
−2.94385 + 2.95008I 0
u = −0.713316 + 0.364912I
3.53763 + 1.70720I 9.34373 − 0.47522I
u = −0.713316 − 0.364912I
3.53763 − 1.70720I 9.34373 + 0.47522I
u = 0.727927 + 0.324780I
0.00076 − 3.48701I −0.10685 + 2.81460I
u = 0.727927 − 0.324780I
0.00076 + 3.48701I −0.10685 − 2.81460I
u = −0.509299 + 1.093680I
−2.26558 − 2.69665I 0
u = −0.509299 − 1.093680I
−2.26558 + 2.69665I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532946 + 1.112480I
−3.24505 + 6.62506I 0
u = 0.532946 − 1.112480I
−3.24505 − 6.62506I 0
u = −0.560287 + 1.103940I
1.37872 − 6.58460I 0
u = −0.560287 − 1.103940I
1.37872 + 6.58460I 0
u = −0.504237 + 1.132970I
−10.05170 − 0.22011I 0
u = −0.504237 − 1.132970I
−10.05170 + 0.22011I 0
u = 0.509014 + 1.133500I
−10.25420 + 6.56885I 0
u = 0.509014 − 1.133500I
−10.25420 − 6.56885I 0
u = 0.556014 + 1.119300I
−2.31255 + 8.37360I 0
u = 0.556014 − 1.119300I
−2.31255 − 8.37360I 0
u = −0.565704 + 1.120250I
−0.06439 − 12.03000I 0
u = −0.565704 − 1.120250I
−0.06439 + 12.03000I 0
u = 0.565065 + 1.132160I
−8.19937 + 9.74957I 0
u = 0.565065 − 1.132160I
−8.19937 − 9.74957I 0
u = −0.567396 + 1.131720I
−7.7482 − 16.0682I 0
u = −0.567396 − 1.131720I
−7.7482 + 16.0682I 0
u = 0.665867 + 0.284233I
−0.89403 − 1.98382I −1.24074 + 3.64496I
u = 0.665867 − 0.284233I
−0.89403 + 1.98382I −1.24074 − 3.64496I
u = 0.696778 + 0.188590I
−7.58004 − 2.02263I −2.18699 + 2.22834I
u = 0.696778 − 0.188590I
−7.58004 + 2.02263I −2.18699 − 2.22834I
u = −0.692184 + 0.175922I
−7.35283 − 4.28364I −1.74327 + 2.87228I
u = −0.692184 − 0.175922I
−7.35283 + 4.28364I −1.74327 − 2.87228I
u = −0.325865 + 0.553283I
0.082965 − 1.264650I 0.85289 + 5.85230I
u = −0.325865 − 0.553283I
0.082965 + 1.264650I 0.85289 − 5.85230I
u = −0.561379 + 0.192622I
0.06888 − 1.56934I 2.04853 + 4.27715I
u = −0.561379 − 0.192622I
0.06888 + 1.56934I 2.04853 − 4.27715I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
86
+ 41u
85
+ ··· + 3u + 1
c
2
, c
6
u
86
− u
85
+ ··· − 3u + 1
c
3
u
86
+ u
85
+ ··· + 471u + 65
c
4
u
86
− u
85
+ ··· − 149u + 137
c
5
, c
10
u
86
− u
85
+ ··· + u + 1
c
7
u
86
− 5u
85
+ ··· − 623u + 111
c
8
, c
9
, c
11
u
86
− 21u
85
+ ··· − 3u + 1
c
12
u
86
+ 9u
85
+ ··· + 6433u + 797
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
86
+ 9y
85
+ ··· + 19y + 1
c
2
, c
6
y
86
+ 41y
85
+ ··· + 3y + 1
c
3
y
86
− 23y
85
+ ··· + 399819y + 4225
c
4
y
86
+ 9y
85
+ ··· + 312079y + 18769
c
5
, c
10
y
86
+ 21y
85
+ ··· + 3y + 1
c
7
y
86
+ 13y
85
+ ··· + 865727y + 12321
c
8
, c
9
, c
11
y
86
+ 89y
85
+ ··· + 11y + 1
c
12
y
86
+ 29y
85
+ ··· + 40057159y + 635209
9
