10
32
(K10a
55
)
A knot diagram
1
Linearized knot diagam
7 5 8 9 10 1 6 4 3 2
Solving Sequence
3,8
4 9 5 10 6 2 7 1
c
3
c
8
c
4
c
9
c
5
c
2
c
7
c
1
c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
2u
32
+ ··· + u
2
+ 1i
I
u
2
= hu + 1i
* 2 irreducible components of dim
C
= 0, with total 34 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
33
2u
32
+ · · · + u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
2u
2
a
10
=
u
3
+ 2u
u
3
+ u
a
6
=
u
10
+ 5u
8
8u
6
+ 3u
4
+ u
2
+ 1
u
10
+ 4u
8
5u
6
+ 2u
4
u
2
a
2
=
u
6
3u
4
+ 2u
2
+ 1
u
8
+ 4u
6
4u
4
a
7
=
u
21
10u
19
+ ··· + 2u
3
+ u
u
21
9u
19
+ 33u
17
62u
15
+ 62u
13
33u
11
+ 13u
9
6u
7
+ u
5
u
3
+ u
a
1
=
u
17
8u
15
+ 25u
13
36u
11
+ 19u
9
+ 4u
7
2u
5
4u
3
+ u
u
19
+ 9u
17
32u
15
+ 55u
13
43u
11
+ 9u
9
+ 4u
5
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
31
56u
29
4u
28
+ 344u
27
+ 52u
26
1204u
25
292u
24
+ 2600u
23
+ 912u
22
3476u
21
1692u
20
+ 2672u
19
+ 1824u
18
912u
17
1016u
16
+ 40u
15
+ 276u
14
156u
13
260u
12
+ 144u
11
+ 276u
10
+ 24u
9
48u
8
16u
7
12u
6
+ 16u
5
8u
4
20u
3
8u
2
4u 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
2u
32
+ ··· 2u + 1
c
2
u
33
6u
32
+ ··· + 128u 23
c
3
, c
4
, c
8
u
33
2u
32
+ ··· + u
2
+ 1
c
5
u
33
+ u
31
+ ··· 8u + 1
c
7
, c
10
u
33
+ 10u
32
+ ··· 2u + 1
c
9
u
33
+ 3u
32
+ ··· + 32u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
10y
32
+ ··· 2y 1
c
2
y
33
+ 14y
32
+ ··· 2062y 529
c
3
, c
4
, c
8
y
33
30y
32
+ ··· 2y 1
c
5
y
33
+ 2y
32
+ ··· 2y 1
c
7
, c
10
y
33
+ 26y
32
+ ··· + 6y 1
c
9
y
33
3y
32
+ ··· + 394y 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.145930 + 0.199234I
2.02163 5.40417I 1.16809 + 6.21521I
u = 1.145930 0.199234I
2.02163 + 5.40417I 1.16809 6.21521I
u = 1.226990 + 0.119877I
2.93624 + 0.57729I 61.088687 + 0.10I
u = 1.226990 0.119877I
2.93624 0.57729I 61.088687 + 0.10I
u = 0.313132 + 0.699748I
1.61043 8.54919I 1.81653 + 8.15424I
u = 0.313132 0.699748I
1.61043 + 8.54919I 1.81653 8.15424I
u = 0.325114 + 0.672913I
2.49948 + 2.85888I 0.03469 3.31371I
u = 0.325114 0.672913I
2.49948 2.85888I 0.03469 + 3.31371I
u = 0.592603 + 0.413344I
2.74796 + 4.66940I 0.86326 2.61989I
u = 0.592603 0.413344I
2.74796 4.66940I 0.86326 + 2.61989I
u = 0.225806 + 0.667717I
3.60419 3.13953I 8.34254 + 5.36114I
u = 0.225806 0.667717I
3.60419 + 3.13953I 8.34254 5.36114I
u = 0.529781 + 0.441659I
3.40197 + 0.91195I 2.34870 3.13722I
u = 0.529781 0.441659I
3.40197 0.91195I 2.34870 + 3.13722I
u = 1.323560 + 0.186117I
3.02759 + 0.73587I 0.673126 + 0.769843I
u = 1.323560 0.186117I
3.02759 0.73587I 0.673126 0.769843I
u = 0.065742 + 0.645142I
1.19428 + 2.21654I 6.16344 2.48417I
u = 0.065742 0.645142I
1.19428 2.21654I 6.16344 + 2.48417I
u = 0.596679
1.73897 4.71290
u = 1.387740 + 0.260179I
1.53217 + 6.51294I 2.89383 5.98872I
u = 1.387740 0.260179I
1.53217 6.51294I 2.89383 + 5.98872I
u = 1.396540 + 0.216616I
5.26725 4.07711I 4.72201 + 3.88410I
u = 1.396540 0.216616I
5.26725 + 4.07711I 4.72201 3.88410I
u = 0.245019 + 0.527971I
0.007405 + 1.282000I 0.00329 5.16805I
u = 0.245019 0.527971I
0.007405 1.282000I 0.00329 + 5.16805I
u = 1.42908 + 0.26025I
8.11565 6.26770I 4.18982 + 3.24511I
u = 1.42908 0.26025I
8.11565 + 6.26770I 4.18982 3.24511I
u = 1.44655 + 0.13460I
9.14238 2.78863I 4.90822 + 2.57820I
u = 1.44655 0.13460I
9.14238 + 2.78863I 4.90822 2.57820I
u = 1.42746 + 0.27209I
7.18048 + 12.09090I 2.43573 8.11579I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.42746 0.27209I
7.18048 12.09090I 2.43573 + 8.11579I
u = 1.44503 + 0.15402I
9.63768 3.04389I 5.82618 + 2.90426I
u = 1.44503 0.15402I
9.63768 + 3.04389I 5.82618 2.90426I
6
II. I
u
2
= hu + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
1
a
4
=
1
1
a
9
=
1
0
a
5
=
0
1
a
10
=
1
0
a
6
=
1
1
a
2
=
1
1
a
7
=
1
0
a
1
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
10
u + 1
c
2
u 1
c
9
u
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
10
y 1
c
9
y
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
1.64493 6.00000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u + 1)(u
33
2u
32
+ ··· 2u + 1)
c
2
(u 1)(u
33
6u
32
+ ··· + 128u 23)
c
3
, c
4
, c
8
(u + 1)(u
33
2u
32
+ ··· + u
2
+ 1)
c
5
(u + 1)(u
33
+ u
31
+ ··· 8u + 1)
c
7
, c
10
(u + 1)(u
33
+ 10u
32
+ ··· 2u + 1)
c
9
u(u
33
+ 3u
32
+ ··· + 32u + 7)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y 1)(y
33
10y
32
+ ··· 2y 1)
c
2
(y 1)(y
33
+ 14y
32
+ ··· 2062y 529)
c
3
, c
4
, c
8
(y 1)(y
33
30y
32
+ ··· 2y 1)
c
5
(y 1)(y
33
+ 2y
32
+ ··· 2y 1)
c
7
, c
10
(y 1)(y
33
+ 26y
32
+ ··· + 6y 1)
c
9
y(y
33
3y
32
+ ··· + 394y 49)
12