11a
230
(K11a
230
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 8 2 11 5 4 3 7
Solving Sequence
2,7
6 1 3 11 8 5 10 4 9
c
6
c
1
c
2
c
11
c
7
c
5
c
10
c
3
c
9
c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
25
+ u
24
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 25 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
25
+ u
24
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
5
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
14
− 4u
12
+ 7u
10
− 6u
8
+ 2u
6
− u
2
a
10
=
u
11
− 2u
9
+ 2u
7
+ u
3
−u
13
+ 3u
11
− 5u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
4
=
−u
19
+ 4u
17
− 8u
15
+ 8u
13
− 5u
11
+ 2u
9
− 2u
7
− u
3
u
21
− 5u
19
+ 13u
17
− 20u
15
+ 20u
13
− 11u
11
+ u
9
+ 4u
7
− u
5
− u
3
+ u
a
9
=
u
22
− 5u
20
+ 12u
18
− 15u
16
+ 8u
14
+ 4u
12
− 8u
10
+ 3u
8
+ 3u
6
− 3u
4
+ 1
−u
22
+ 6u
20
+ ··· + 2u
4
− u
2
a
9
=
u
22
− 5u
20
+ 12u
18
− 15u
16
+ 8u
14
+ 4u
12
− 8u
10
+ 3u
8
+ 3u
6
− 3u
4
+ 1
−u
22
+ 6u
20
+ ··· + 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
+ 24u
21
+ 4u
20
− 72u
19
− 20u
18
+ 124u
17
+ 48u
16
− 128u
15
− 60u
14
+ 64u
13
+
36u
12
− 16u
9
− 4u
8
− 8u
7
− 8u
6
+ 16u
5
+ 12u
4
− 16u
3
− 4u
2
− 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
25
− u
24
+ ··· − u + 1
c
2
u
25
+ 13u
24
+ ··· + u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
25
− u
24
+ ··· + u + 1
c
7
, c
11
u
25
− 3u
24
+ ··· − 7u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
25
− 13y
24
+ ··· + y −1
c
2
y
25
− y
24
+ ··· + 13y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
25
+ 35y
24
+ ··· + y −1
c
7
, c
11
y
25
+ 15y
24
+ ··· + 241y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779045 + 0.639863I
17.3947 + 2.4684I 0.82696 − 3.09489I
u = −0.779045 − 0.639863I
17.3947 − 2.4684I 0.82696 + 3.09489I
u = 0.763751 + 0.563111I
6.42429 − 2.24483I 0.87739 + 3.73001I
u = 0.763751 − 0.563111I
6.42429 + 2.24483I 0.87739 − 3.73001I
u = −0.245615 + 0.802005I
14.6751 − 4.2594I −0.24448 + 2.05504I
u = −0.245615 − 0.802005I
14.6751 + 4.2594I −0.24448 − 2.05504I
u = −0.738513 + 0.360257I
0.77592 + 1.63253I −1.50081 − 6.32590I
u = −0.738513 − 0.360257I
0.77592 − 1.63253I −1.50081 + 6.32590I
u = −1.143530 + 0.340046I
0.133925 + 0.085472I −5.86002 + 0.34875I
u = −1.143530 − 0.340046I
0.133925 − 0.085472I −5.86002 − 0.34875I
u = 1.140980 + 0.421501I
−3.95366 − 2.40561I −10.55936 + 0.02824I
u = 1.140980 − 0.421501I
−3.95366 + 2.40561I −10.55936 − 0.02824I
u = 1.189550 + 0.291950I
10.21240 + 0.84057I −5.43221 + 0.40339I
u = 1.189550 − 0.291950I
10.21240 − 0.84057I −5.43221 − 0.40339I
u = 0.212747 + 0.739529I
4.10003 + 3.28234I −0.69331 − 3.26169I
u = 0.212747 − 0.739529I
4.10003 − 3.28234I −0.69331 + 3.26169I
u = −1.147100 + 0.473379I
−3.57874 + 5.59583I −8.74632 − 7.67577I
u = −1.147100 − 0.473379I
−3.57874 − 5.59583I −8.74632 + 7.67577I
u = 1.153710 + 0.519862I
1.36392 − 8.01588I −4.14152 + 6.75012I
u = 1.153710 − 0.519862I
1.36392 + 8.01588I −4.14152 − 6.75012I
u = −1.164700 + 0.548434I
11.9587 + 9.2744I −3.33794 − 5.54787I
u = −1.164700 − 0.548434I
11.9587 − 9.2744I −3.33794 + 5.54787I
u = 0.712530
−0.882258 −12.9060
u = −0.098501 + 0.642338I
−0.67035 − 1.33734I −5.73536 + 4.96479I
u = −0.098501 − 0.642338I
−0.67035 + 1.33734I −5.73536 − 4.96479I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
25
− u
24
+ ··· − u + 1
c
2
u
25
+ 13u
24
+ ··· + u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
25
− u
24
+ ··· + u + 1
c
7
, c
11
u
25
− 3u
24
+ ··· − 7u + 8
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
25
− 13y
24
+ ··· + y −1
c
2
y
25
− y
24
+ ··· + 13y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
25
+ 35y
24
+ ··· + y −1
c
7
, c
11
y
25
+ 15y
24
+ ··· + 241y −64
7
