10
50
(K10a
82
)
A knot diagram
1
Linearized knot diagam
6 10 7 8 9 1 5 4 2 3
Solving Sequence
5,7
8 4 9
1,3
6 2 10
c
7
c
4
c
8
c
3
c
6
c
1
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
28
2u
27
+ ··· + b + 1, 2u
28
2u
27
+ ··· + a + 2, u
29
2u
28
+ ··· + u 1i
I
u
2
= hb, u
2
+ a + 1, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 32 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
28
2u
27
+· · ·+b +1, 2u
28
2u
27
+· · ·+a +2, u
29
2u
28
+· · ·+u 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
2u
28
+ 2u
27
+ ··· 6u 2
u
28
+ 2u
27
+ ··· + u 1
a
3
=
u
3
+ 2u
u
3
+ u
a
6
=
u
5
2u
3
u
u
7
3u
5
2u
3
+ u
a
2
=
u
16
7u
14
+ ··· 6u 1
u
28
2u
27
+ ··· u
2
+ 1
a
10
=
u
28
+ u
27
+ ··· 5u 1
u
17
+ 7u
15
+ ··· + 6u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
28
2u
27
+ 17u
26
28u
25
+ 121u
24
169u
23
+ 476u
22
572u
21
+
1124u
20
1170u
19
+ 1569u
18
1418u
17
+ 1069u
16
834u
15
98u
14
+ 112u
13
636u
12
+
544u
11
270u
10
+ 426u
9
12u
8
+ 183u
7
90u
6
34u
5
38u
4
76u
3
+ 29u
2
+ 2u 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
29
+ u
28
+ ··· 4u 8
c
2
, c
9
, c
10
u
29
4u
28
+ ··· + 2u 1
c
3
, c
5
u
29
+ 2u
28
+ ··· 15u 9
c
4
, c
7
, c
8
u
29
2u
28
+ ··· + u 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
29
+ 21y
28
+ ··· + 144y 64
c
2
, c
9
, c
10
y
29
30y
28
+ ··· + 18y 1
c
3
, c
5
y
29
24y
28
+ ··· + 621y 81
c
4
, c
7
, c
8
y
29
+ 24y
28
+ ··· + 13y 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.872970 + 0.113870I
a = 0.23209 + 2.29662I
b = 0.56484 + 1.49174I
12.27840 6.66801I 13.30046 + 3.89200I
u = 0.872970 0.113870I
a = 0.23209 2.29662I
b = 0.56484 1.49174I
12.27840 + 6.66801I 13.30046 3.89200I
u = 0.824312
a = 1.01744
b = 1.30242
7.43008 12.5870
u = 0.814174 + 0.046599I
a = 0.17300 2.55555I
b = 0.215027 1.248980I
5.26114 2.70743I 11.83350 + 3.32702I
u = 0.814174 0.046599I
a = 0.17300 + 2.55555I
b = 0.215027 + 1.248980I
5.26114 + 2.70743I 11.83350 3.32702I
u = 0.050561 + 1.224810I
a = 1.179120 0.735696I
b = 0.603790 0.612719I
1.43725 1.10103I 6.03106 0.28755I
u = 0.050561 1.224810I
a = 1.179120 + 0.735696I
b = 0.603790 + 0.612719I
1.43725 + 1.10103I 6.03106 + 0.28755I
u = 0.438893 + 1.153290I
a = 0.614951 + 0.762748I
b = 0.45548 + 1.52023I
9.09072 + 1.97634I 10.56391 0.15391I
u = 0.438893 1.153290I
a = 0.614951 0.762748I
b = 0.45548 1.52023I
9.09072 1.97634I 10.56391 + 0.15391I
u = 0.566873 + 0.506506I
a = 0.914731 + 0.813821I
b = 0.112616 + 1.303260I
6.34917 + 2.02688I 11.64196 3.46616I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.566873 0.506506I
a = 0.914731 0.813821I
b = 0.112616 1.303260I
6.34917 2.02688I 11.64196 + 3.46616I
u = 0.357598 + 1.229040I
a = 0.75023 1.33832I
b = 0.063501 1.233240I
1.62082 1.51334I 8.49380 + 0.41799I
u = 0.357598 1.229040I
a = 0.75023 + 1.33832I
b = 0.063501 + 1.233240I
1.62082 + 1.51334I 8.49380 0.41799I
u = 0.255230 + 1.288030I
a = 0.111769 0.476267I
b = 0.607413 + 0.112242I
2.53302 + 3.25312I 0.46847 3.58405I
u = 0.255230 1.288030I
a = 0.111769 + 0.476267I
b = 0.607413 0.112242I
2.53302 3.25312I 0.46847 + 3.58405I
u = 0.075468 + 1.316000I
a = 0.969152 + 0.088875I
b = 0.538894 + 0.689414I
4.46963 + 2.10537I 0.57633 3.98592I
u = 0.075468 1.316000I
a = 0.969152 0.088875I
b = 0.538894 0.689414I
4.46963 2.10537I 0.57633 + 3.98592I
u = 0.369778 + 1.269420I
a = 0.182052 + 0.874747I
b = 1.298970 0.143296I
3.48935 + 4.29283I 8.53955 3.19264I
u = 0.369778 1.269420I
a = 0.182052 0.874747I
b = 1.298970 + 0.143296I
3.48935 4.29283I 8.53955 + 3.19264I
u = 0.361886 + 1.302780I
a = 1.27373 + 1.39712I
b = 0.338315 + 1.255880I
1.04610 6.94187I 7.09973 + 6.05967I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.361886 1.302780I
a = 1.27373 1.39712I
b = 0.338315 1.255880I
1.04610 + 6.94187I 7.09973 6.05967I
u = 0.645651
a = 0.563691
b = 0.525371
1.50367 5.88400
u = 0.389029 + 1.350370I
a = 1.50604 1.16997I
b = 0.63881 1.44580I
7.67865 11.19890I 9.19156 + 6.17598I
u = 0.389029 1.350370I
a = 1.50604 + 1.16997I
b = 0.63881 + 1.44580I
7.67865 + 11.19890I 9.19156 6.17598I
u = 0.14677 + 1.42338I
a = 0.845011 + 0.480671I
b = 0.257766 1.113060I
0.14603 + 4.37313I 7.64888 4.01970I
u = 0.14677 1.42338I
a = 0.845011 0.480671I
b = 0.257766 + 1.113060I
0.14603 4.37313I 7.64888 + 4.01970I
u = 0.274649 + 0.285133I
a = 0.844421 1.049180I
b = 0.175226 0.644435I
0.389560 + 0.938777I 6.80996 7.32576I
u = 0.274649 0.285133I
a = 0.844421 + 1.049180I
b = 0.175226 + 0.644435I
0.389560 0.938777I 6.80996 + 7.32576I
u = 0.277276
a = 2.75803
b = 0.479164
2.07267 2.13090
7
II. I
u
2
= hb, u
2
+ a + 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
u
u
2
u 1
a
9
=
u
2
+ 1
u
2
+ u + 1
a
1
=
u
2
1
0
a
3
=
u
2
1
u
2
u 1
a
6
=
1
0
a
2
=
u
2
1
0
a
10
=
0
u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
2
4u 16
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
3
c
2
(u + 1)
3
c
3
, c
5
u
3
+ u
2
1
c
4
u
3
u
2
+ 2u 1
c
7
, c
8
u
3
+ u
2
+ 2u + 1
c
9
, c
10
(u 1)
3
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
3
c
2
, c
9
, c
10
(y 1)
3
c
3
, c
5
y
3
y
2
+ 2y 1
c
4
, c
7
, c
8
y
3
+ 3y
2
+ 2y 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.662359 + 0.562280I
b = 0
1.37919 + 2.82812I 6.82789 2.41717I
u = 0.215080 1.307140I
a = 0.662359 0.562280I
b = 0
1.37919 2.82812I 6.82789 + 2.41717I
u = 0.569840
a = 1.32472
b = 0
2.75839 15.3440
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
3
(u
29
+ u
28
+ ··· 4u 8)
c
2
((u + 1)
3
)(u
29
4u
28
+ ··· + 2u 1)
c
3
, c
5
(u
3
+ u
2
1)(u
29
+ 2u
28
+ ··· 15u 9)
c
4
(u
3
u
2
+ 2u 1)(u
29
2u
28
+ ··· + u 1)
c
7
, c
8
(u
3
+ u
2
+ 2u + 1)(u
29
2u
28
+ ··· + u 1)
c
9
, c
10
((u 1)
3
)(u
29
4u
28
+ ··· + 2u 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
3
(y
29
+ 21y
28
+ ··· + 144y 64)
c
2
, c
9
, c
10
((y 1)
3
)(y
29
30y
28
+ ··· + 18y 1)
c
3
, c
5
(y
3
y
2
+ 2y 1)(y
29
24y
28
+ ··· + 621y 81)
c
4
, c
7
, c
8
(y
3
+ 3y
2
+ 2y 1)(y
29
+ 24y
28
+ ··· + 13y 1)
13