10
23
(K10a
57
)
A knot diagram
1
Linearized knot diagam
7 6 9 10 1 2 4 3 8 5
Solving Sequence
1,7
2 6 3 5 10 4 8 9
c
1
c
6
c
2
c
5
c
10
c
4
c
7
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
− u
28
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
− u
28
+ · · · + u − 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
−u
3
− 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
8
=
u
19
+ 8u
17
+ 26u
15
+ 40u
13
+ 19u
11
− 24u
9
− 30u
7
+ 9u
3
−u
19
− 7u
17
− 20u
15
− 27u
13
− 11u
11
+ 13u
9
+ 14u
7
− 3u
3
+ u
a
9
=
−u
25
− 10u
23
+ ··· + 10u
3
− u
u
27
+ 11u
25
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
28
− 4u
27
+ 44u
26
− 40u
25
+ 208u
24
− 172u
23
+ 528u
22
− 396u
21
+ 692u
20
−
468u
19
+ 184u
18
− 112u
17
− 756u
16
+ 404u
15
− 952u
14
+ 460u
13
− 96u
12
+ 92u
11
+
512u
10
− 116u
9
+ 224u
8
− 80u
7
− 92u
6
− 40u
5
− 40u
4
− 4u
3
+ 12u
2
+ 8u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
29
− u
28
+ ··· + u − 1
c
3
, c
8
u
29
− u
28
+ ··· + u − 1
c
4
, c
5
, c
10
u
29
+ u
28
+ ··· − 7u − 1
c
7
u
29
− 3u
28
+ ··· − u + 1
c
9
u
29
+ 13u
28
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
29
+ 23y
28
+ ··· + 3y −1
c
3
, c
8
y
29
− 13y
28
+ ··· + 3y −1
c
4
, c
5
, c
10
y
29
− 29y
28
+ ··· + 19y −1
c
7
y
29
− y
28
+ ··· + 31y −1
c
9
y
29
+ 7y
28
+ ··· − 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.104948 + 1.063430I
−1.50634 + 2.08825I 4.67041 − 4.01921I
u = 0.104948 − 1.063430I
−1.50634 − 2.08825I 4.67041 + 4.01921I
u = 0.867318 + 0.055730I
6.06905 + 6.86231I 7.66791 − 5.15654I
u = 0.867318 − 0.055730I
6.06905 − 6.86231I 7.66791 + 5.15654I
u = −0.865828 + 0.030403I
7.84107 − 1.55857I 10.33093 + 0.38024I
u = −0.865828 − 0.030403I
7.84107 + 1.55857I 10.33093 − 0.38024I
u = 0.802035
2.34920 4.54160
u = 0.144820 + 1.275680I
−3.23997 + 2.39104I 2.27394 − 3.37022I
u = 0.144820 − 1.275680I
−3.23997 − 2.39104I 2.27394 + 3.37022I
u = 0.413631 + 1.222060I
2.47326 − 2.27350I 4.56508 + 1.80235I
u = 0.413631 − 1.222060I
2.47326 + 2.27350I 4.56508 − 1.80235I
u = −0.408190 + 1.247470I
4.07665 − 3.00599I 6.90218 + 3.08222I
u = −0.408190 − 1.247470I
4.07665 + 3.00599I 6.90218 − 3.08222I
u = 0.355449 + 1.278410I
−1.63034 + 4.16530I 0.22706 − 3.16142I
u = 0.355449 − 1.278410I
−1.63034 − 4.16530I 0.22706 + 3.16142I
u = −0.076147 + 1.325550I
−6.70958 + 0.47843I −4.05109 − 0.53373I
u = −0.076147 − 1.325550I
−6.70958 − 0.47843I −4.05109 + 0.53373I
u = −0.164926 + 1.331090I
−5.61619 − 6.65351I −1.43843 + 7.12693I
u = −0.164926 − 1.331090I
−5.61619 + 6.65351I −1.43843 − 7.12693I
u = −0.398344 + 1.297060I
3.70379 − 6.09123I 6.35632 + 3.37420I
u = −0.398344 − 1.297060I
3.70379 + 6.09123I 6.35632 − 3.37420I
u = 0.395776 + 1.314560I
1.78699 + 11.39320I 3.51396 − 7.74456I
u = 0.395776 − 1.314560I
1.78699 − 11.39320I 3.51396 + 7.74456I
u = −0.504557 + 0.291210I
−0.58407 − 4.33232I 4.72516 + 7.80862I
u = −0.504557 − 0.291210I
−0.58407 + 4.33232I 4.72516 − 7.80862I
u = −0.232980 + 0.458467I
−1.44954 + 1.50061I 0.980964 − 0.451451I
u = −0.232980 − 0.458467I
−1.44954 − 1.50061I 0.980964 + 0.451451I
u = 0.468013 + 0.123523I
1.012830 + 0.278366I 10.00481 − 1.83311I
u = 0.468013 − 0.123523I
1.012830 − 0.278366I 10.00481 + 1.83311I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
29
− u
28
+ ··· + u − 1
c
3
, c
8
u
29
− u
28
+ ··· + u − 1
c
4
, c
5
, c
10
u
29
+ u
28
+ ··· − 7u − 1
c
7
u
29
− 3u
28
+ ··· − u + 1
c
9
u
29
+ 13u
28
+ ··· + 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
29
+ 23y
28
+ ··· + 3y −1
c
3
, c
8
y
29
− 13y
28
+ ··· + 3y −1
c
4
, c
5
, c
10
y
29
− 29y
28
+ ··· + 19y −1
c
7
y
29
− y
28
+ ··· + 31y −1
c
9
y
29
+ 7y
28
+ ··· − 17y −1
7
