10
25
(K10a
61
)
A knot diagram
1
Linearized knot diagam
6 8 7 10 1 3 4 2 5 9
Solving Sequence
4,8
7 3 2 9 6 1 5 10
c
7
c
3
c
2
c
8
c
6
c
1
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
32
+ u
31
+ ··· − 2u − 1i
* 1 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
32
+ u
31
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
3
=
u
−u
3
+ u
a
2
=
−u
3
+ 2u
−u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
9
+ 4u
7
− 5u
5
+ 3u
u
11
− 5u
9
+ 8u
7
− 3u
5
− 3u
3
+ u
a
5
=
u
16
− 7u
14
+ 19u
12
− 22u
10
+ 3u
8
+ 14u
6
− 6u
4
− 4u
2
+ 1
−u
18
+ 8u
16
− 25u
14
+ 36u
12
− 17u
10
− 12u
8
+ 12u
6
+ 2u
4
− 3u
2
a
10
=
u
23
− 10u
21
+ ··· − 2u
3
+ 4u
u
23
− 9u
21
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
29
+ 48u
27
− 4u
26
− 252u
25
+ 44u
24
+ 740u
23
− 208u
22
− 1264u
21
+ 536u
20
+
1080u
19
− 768u
18
+ 64u
17
+ 480u
16
− 1008u
15
+ 176u
14
+ 612u
13
− 436u
12
+ 320u
11
+
120u
10
− 424u
9
+ 128u
8
− 4u
7
− 60u
6
+ 108u
5
− 12u
4
− 4u
3
+ 4u
2
− 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
− u
31
+ ··· + 14u − 5
c
2
, c
8
u
32
− 3u
31
+ ··· − 4u
4
+ 1
c
3
, c
6
, c
7
u
32
+ u
31
+ ··· − 2u − 1
c
4
, c
9
u
32
+ u
31
+ ··· − 2u − 1
c
10
u
32
+ 17u
31
+ ··· − 8u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
− 23y
31
+ ··· − 296y + 25
c
2
, c
8
y
32
+ 17y
31
+ ··· − 8y
2
+ 1
c
3
, c
6
, c
7
y
32
− 27y
31
+ ··· + 16y
2
+ 1
c
4
, c
9
y
32
+ 17y
31
+ ··· − 8y
2
+ 1
c
10
y
32
− 3y
31
+ ··· − 16y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.029010 + 0.281289I
−3.89830 + 3.89503I −9.35061 − 2.90091I
u = 1.029010 − 0.281289I
−3.89830 − 3.89503I −9.35061 + 2.90091I
u = −1.134230 + 0.236397I
−1.32933 + 0.52783I −5.59448 − 0.64788I
u = −1.134230 − 0.236397I
−1.32933 − 0.52783I −5.59448 + 0.64788I
u = 0.166316 + 0.775774I
−1.27472 − 7.88151I −6.19556 + 6.68910I
u = 0.166316 − 0.775774I
−1.27472 + 7.88151I −6.19556 − 6.68910I
u = 0.729645 + 0.240963I
−4.28206 − 3.88889I −10.89128 + 4.90467I
u = 0.729645 − 0.240963I
−4.28206 + 3.88889I −10.89128 − 4.90467I
u = −0.028912 + 0.764004I
4.01456 + 2.24194I −0.65690 − 3.79727I
u = −0.028912 − 0.764004I
4.01456 − 2.24194I −0.65690 + 3.79727I
u = −0.140851 + 0.748200I
1.56622 + 3.15266I −2.67728 − 3.41480I
u = −0.140851 − 0.748200I
1.56622 − 3.15266I −2.67728 + 3.41480I
u = 0.191682 + 0.700576I
−2.34434 + 0.39737I −7.83598 + 0.58140I
u = 0.191682 − 0.700576I
−2.34434 − 0.39737I −7.83598 − 0.58140I
u = −1.237710 + 0.313650I
0.29651 + 1.65231I −4.59303 − 0.15309I
u = −1.237710 − 0.313650I
0.29651 − 1.65231I −4.59303 + 0.15309I
u = 1.288430 + 0.161328I
−5.00599 − 2.81562I −13.51638 + 3.82546I
u = 1.288430 − 0.161328I
−5.00599 + 2.81562I −13.51638 − 3.82546I
u = 1.281200 + 0.325415I
−0.06115 − 6.17510I −5.73067 + 6.90538I
u = 1.281200 − 0.325415I
−0.06115 + 6.17510I −5.73067 − 6.90538I
u = 1.350330 + 0.317347I
−3.13584 − 7.01747I −7.66223 + 4.88322I
u = 1.350330 − 0.317347I
−3.13584 + 7.01747I −7.66223 − 4.88322I
u = 1.39424
−7.31963 −11.4830
u = −1.364340 + 0.293820I
−7.25067 + 3.23058I −12.64791 − 1.85611I
u = −1.364340 − 0.293820I
−7.25067 − 3.23058I −12.64791 + 1.85611I
u = −0.599844
−1.22821 −8.26170
u = −1.364190 + 0.328069I
−6.10646 + 11.87580I −10.77954 − 7.99531I
u = −1.364190 − 0.328069I
−6.10646 − 11.87580I −10.77954 + 7.99531I
u = −1.41547 + 0.02215I
−10.82670 + 4.39858I −14.8085 − 3.5355I
u = −1.41547 − 0.02215I
−10.82670 − 4.39858I −14.8085 + 3.5355I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.248101 + 0.323031I
−0.501058 + 1.034980I −7.18759 − 6.41402I
u = −0.248101 − 0.323031I
−0.501058 − 1.034980I −7.18759 + 6.41402I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
− u
31
+ ··· + 14u − 5
c
2
, c
8
u
32
− 3u
31
+ ··· − 4u
4
+ 1
c
3
, c
6
, c
7
u
32
+ u
31
+ ··· − 2u − 1
c
4
, c
9
u
32
+ u
31
+ ··· − 2u − 1
c
10
u
32
+ 17u
31
+ ··· − 8u
2
+ 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
− 23y
31
+ ··· − 296y + 25
c
2
, c
8
y
32
+ 17y
31
+ ··· − 8y
2
+ 1
c
3
, c
6
, c
7
y
32
− 27y
31
+ ··· + 16y
2
+ 1
c
4
, c
9
y
32
+ 17y
31
+ ··· − 8y
2
+ 1
c
10
y
32
− 3y
31
+ ··· − 16y + 1
8
