12a
0517
(K12a
0517
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 10 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
6
c
12
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
72
− u
71
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 72 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
72
− u
71
+ · · · + 2u − 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
28
+ 7u
26
+ ··· + u
2
+ 1
u
30
+ 8u
28
+ ··· + 2u
4
+ u
2
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
+ ··· + 8u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
70
− 4u
69
+ ··· + 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
+ 41u
71
+ ··· − 10u
2
+ 1
c
2
, c
7
u
72
+ u
71
+ ··· − 2u − 1
c
3
, c
4
, c
8
u
72
− u
71
+ ··· + 42u − 17
c
5
, c
11
u
72
− u
71
+ ··· + 2u
3
− 1
c
6
, c
12
u
72
− 3u
71
+ ··· − 18u + 3
c
9
u
72
− 11u
71
+ ··· − 18764u + 1889
c
10
u
72
+ 39u
71
+ ··· − 2u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
− 19y
71
+ ··· − 20y + 1
c
2
, c
7
y
72
+ 41y
71
+ ··· − 10y
2
+ 1
c
3
, c
4
, c
8
y
72
− 79y
71
+ ··· − 10740y + 289
c
5
, c
11
y
72
− 39y
71
+ ··· − 2y
2
+ 1
c
6
, c
12
y
72
+ 61y
71
+ ··· − 624y + 9
c
9
y
72
− 31y
71
+ ··· − 2222228y + 3568321
c
10
y
72
− 11y
71
+ ··· − 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439849 + 0.927313I
0.59296 − 2.15388I 0. + 3.34635I
u = −0.439849 − 0.927313I
0.59296 + 2.15388I 0. − 3.34635I
u = 0.127748 + 0.947194I
−2.02452 − 1.35976I −10.77685 + 3.46053I
u = 0.127748 − 0.947194I
−2.02452 + 1.35976I −10.77685 − 3.46053I
u = −0.351185 + 0.866043I
−0.38120 − 1.62589I −2.66925 + 4.11942I
u = −0.351185 − 0.866043I
−0.38120 + 1.62589I −2.66925 − 4.11942I
u = 0.461087 + 0.962460I
0.08467 + 6.28501I 0
u = 0.461087 − 0.962460I
0.08467 − 6.28501I 0
u = 0.344819 + 1.019280I
−3.62015 + 2.92141I 0
u = 0.344819 − 1.019280I
−3.62015 − 2.92141I 0
u = 0.206282 + 1.082360I
−4.82312 − 0.17742I 0
u = 0.206282 − 1.082360I
−4.82312 + 0.17742I 0
u = 0.456210 + 0.765907I
−3.17229 − 2.09595I −5.70344 − 0.42832I
u = 0.456210 − 0.765907I
−3.17229 + 2.09595I −5.70344 + 0.42832I
u = −0.189472 + 1.099100I
−8.15714 + 4.74025I 0
u = −0.189472 − 1.099100I
−8.15714 − 4.74025I 0
u = 0.882022 + 0.044279I
−11.98020 − 0.80891I −10.79930 − 0.35413I
u = 0.882022 − 0.044279I
−11.98020 + 0.80891I −10.79930 + 0.35413I
u = 0.879727 + 0.056445I
−11.1703 − 9.8634I −9.53343 + 5.93137I
u = 0.879727 − 0.056445I
−11.1703 + 9.8634I −9.53343 − 5.93137I
u = −0.875707 + 0.050791I
−7.91972 + 4.99528I −6.55693 − 2.82964I
u = −0.875707 − 0.050791I
−7.91972 − 4.99528I −6.55693 + 2.82964I
u = −0.225561 + 1.101690I
−8.49214 − 4.06217I 0
u = −0.225561 − 1.101690I
−8.49214 + 4.06217I 0
u = 0.474807 + 1.020050I
−2.88869 + 6.40679I 0
u = 0.474807 − 1.020050I
−2.88869 − 6.40679I 0
u = −0.489288 + 1.023920I
−5.98929 − 11.10170I 0
u = −0.489288 − 1.023920I
−5.98929 + 11.10170I 0
u = −0.862003
−7.62273 −11.5620
u = −0.467805 + 1.041330I
−6.73822 − 2.46906I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.467805 − 1.041330I
−6.73822 + 2.46906I 0
u = −0.838828 + 0.044532I
−3.98379 + 5.00843I −5.49188 − 6.00077I
u = −0.838828 − 0.044532I
−3.98379 − 5.00843I −5.49188 + 6.00077I
u = 0.474990 + 0.690912I
−2.96171 + 6.03372I −4.87395 − 7.35313I
u = 0.474990 − 0.690912I
−2.96171 − 6.03372I −4.87395 + 7.35313I
u = 0.825126 + 0.022311I
−2.88998 − 0.66859I −2.98851 − 0.14329I
u = 0.825126 − 0.022311I
−2.88998 + 0.66859I −2.98851 + 0.14329I
u = −0.413409 + 0.683683I
0.00742 − 1.75216I −1.16689 + 4.43589I
u = −0.413409 − 0.683683I
0.00742 + 1.75216I −1.16689 − 4.43589I
u = 0.450918 + 1.227690I
−6.60070 + 3.85865I 0
u = 0.450918 − 1.227690I
−6.60070 − 3.85865I 0
u = −0.438765 + 1.234300I
−7.81587 + 0.51539I 0
u = −0.438765 − 1.234300I
−7.81587 − 0.51539I 0
u = 0.470711 + 1.225250I
−6.45782 + 5.32632I 0
u = 0.470711 − 1.225250I
−6.45782 − 5.32632I 0
u = −0.442364 + 0.520924I
1.71123 − 1.63055I 1.63060 + 4.27651I
u = −0.442364 − 0.520924I
1.71123 + 1.63055I 1.63060 − 4.27651I
u = −0.481138 + 1.227880I
−7.51183 − 9.76537I 0
u = −0.481138 − 1.227880I
−7.51183 + 9.76537I 0
u = −0.590261 + 0.336282I
−4.08423 + 6.85269I −6.08983 − 5.98107I
u = −0.590261 − 0.336282I
−4.08423 − 6.85269I −6.08983 + 5.98107I
u = −0.463776 + 1.244240I
−11.37070 − 4.72051I 0
u = −0.463776 − 1.244240I
−11.37070 + 4.72051I 0
u = −0.436607 + 1.257510I
−11.90830 + 0.38192I 0
u = −0.436607 − 1.257510I
−11.90830 − 0.38192I 0
u = 0.433445 + 1.260510I
−15.1956 − 5.2532I 0
u = 0.433445 − 1.260510I
−15.1956 + 5.2532I 0
u = 0.441141 + 1.260650I
−15.9636 + 3.8514I 0
u = 0.441141 − 1.260650I
−15.9636 − 3.8514I 0
u = −0.490825 + 1.242560I
−11.5116 − 9.9029I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.490825 − 1.242560I
−11.5116 + 9.9029I 0
u = 0.494249 + 1.243290I
−14.7502 + 14.8001I 0
u = 0.494249 − 1.243290I
−14.7502 − 14.8001I 0
u = 0.488923 + 1.246820I
−15.6129 + 5.7245I 0
u = 0.488923 − 1.246820I
−15.6129 − 5.7245I 0
u = 0.477316 + 0.439878I
1.50816 − 2.35510I 0.54892 + 4.70586I
u = 0.477316 − 0.439878I
1.50816 + 2.35510I 0.54892 − 4.70586I
u = −0.586128 + 0.275072I
−4.62644 − 1.65735I −7.50243 + 0.63837I
u = −0.586128 − 0.275072I
−4.62644 + 1.65735I −7.50243 − 0.63837I
u = 0.556736 + 0.320665I
−0.97920 − 2.29313I −2.83779 + 3.07654I
u = 0.556736 − 0.320665I
−0.97920 + 2.29313I −2.83779 − 3.07654I
u = 0.411425
−1.15550 −8.76440
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
72
+ 41u
71
+ ··· − 10u
2
+ 1
c
2
, c
7
u
72
+ u
71
+ ··· − 2u − 1
c
3
, c
4
, c
8
u
72
− u
71
+ ··· + 42u − 17
c
5
, c
11
u
72
− u
71
+ ··· + 2u
3
− 1
c
6
, c
12
u
72
− 3u
71
+ ··· − 18u + 3
c
9
u
72
− 11u
71
+ ··· − 18764u + 1889
c
10
u
72
+ 39u
71
+ ··· − 2u
2
+ 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
72
− 19y
71
+ ··· − 20y + 1
c
2
, c
7
y
72
+ 41y
71
+ ··· − 10y
2
+ 1
c
3
, c
4
, c
8
y
72
− 79y
71
+ ··· − 10740y + 289
c
5
, c
11
y
72
− 39y
71
+ ··· − 2y
2
+ 1
c
6
, c
12
y
72
+ 61y
71
+ ··· − 624y + 9
c
9
y
72
− 31y
71
+ ··· − 2222228y + 3568321
c
10
y
72
− 11y
71
+ ··· − 4y + 1
9
