11a
90
(K11a
90
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 11 4 5 8 7
Solving Sequence
4,8
9 5 10 11 3 7 1 2 6
c
8
c
4
c
9
c
10
c
3
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
43
− u
42
+ ··· + u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 43 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
43
− u
42
+ · · · + u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
7
=
u
8
− 3u
6
+ u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
1
=
−u
12
+ 5u
10
− 7u
8
+ 2u
4
+ 3u
2
+ 1
u
12
− 6u
10
+ 12u
8
− 8u
6
+ u
4
− 2u
2
a
2
=
u
31
− 14u
29
+ ··· + 20u
5
+ 8u
3
−u
31
+ 15u
29
+ ··· − 8u
5
+ u
a
6
=
u
20
− 9u
18
+ ··· + 3u
2
+ 1
−u
22
+ 10u
20
+ ··· − 10u
4
− u
2
a
6
=
u
20
− 9u
18
+ ··· + 3u
2
+ 1
−u
22
+ 10u
20
+ ··· − 10u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
41
+ 80u
39
+ ··· + 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
43
− u
42
+ ··· + 2u − 1
c
2
u
43
+ 19u
42
+ ··· − 2u − 1
c
3
u
43
− 3u
42
+ ··· − 165u + 88
c
4
, c
8
, c
9
u
43
+ u
42
+ ··· − u
2
− 1
c
6
u
43
+ u
42
+ ··· − 3u − 2
c
7
, c
10
, c
11
u
43
− 5u
42
+ ··· + 52u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
43
+ 19y
42
+ ··· − 2y −1
c
2
y
43
+ 11y
42
+ ··· − 10y −1
c
3
y
43
− 21y
42
+ ··· + 171017y −7744
c
4
, c
8
, c
9
y
43
− 41y
42
+ ··· − 2y −1
c
6
y
43
+ 3y
42
+ ··· − 163y −4
c
7
, c
10
, c
11
y
43
+ 47y
42
+ ··· − 1090y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450941 + 0.686624I
5.35054 − 9.10731I 3.33084 + 7.84073I
u = −0.450941 − 0.686624I
5.35054 + 9.10731I 3.33084 − 7.84073I
u = 0.463007 + 0.675614I
7.17544 + 3.78029I 6.09678 − 3.29694I
u = 0.463007 − 0.675614I
7.17544 − 3.78029I 6.09678 + 3.29694I
u = −0.512233 + 0.637578I
5.58121 + 4.70276I 4.01683 − 1.90768I
u = −0.512233 − 0.637578I
5.58121 − 4.70276I 4.01683 + 1.90768I
u = 1.180680 + 0.070474I
−0.12031 + 3.39708I −1.05977 − 4.64882I
u = 1.180680 − 0.070474I
−0.12031 − 3.39708I −1.05977 + 4.64882I
u = 0.496416 + 0.648800I
7.30167 + 0.61667I 6.46762 − 2.84316I
u = 0.496416 − 0.648800I
7.30167 − 0.61667I 6.46762 + 2.84316I
u = −0.447772 + 0.632332I
1.69784 − 2.06717I 0.16713 + 3.29698I
u = −0.447772 − 0.632332I
1.69784 + 2.06717I 0.16713 − 3.29698I
u = −1.25034
2.53757 3.48810
u = −1.304990 + 0.171072I
1.15199 − 1.78064I 0
u = −1.304990 − 0.171072I
1.15199 + 1.78064I 0
u = 0.206694 + 0.605749I
−2.00685 + 5.68843I −2.34470 − 8.72951I
u = 0.206694 − 0.605749I
−2.00685 − 5.68843I −2.34470 + 8.72951I
u = −1.356100 + 0.215927I
2.91900 − 8.67200I 0
u = −1.356100 − 0.215927I
2.91900 + 8.67200I 0
u = 1.366840 + 0.185574I
5.03487 + 4.10356I 0
u = 1.366840 − 0.185574I
5.03487 − 4.10356I 0
u = 1.403260 + 0.118432I
6.22218 + 2.77486I 0
u = 1.403260 − 0.118432I
6.22218 − 2.77486I 0
u = −1.411730 + 0.074872I
5.35002 + 1.81991I 0
u = −1.411730 − 0.074872I
5.35002 − 1.81991I 0
u = 0.089033 + 0.575299I
−3.14805 − 0.90482I −6.51420 − 0.21846I
u = 0.089033 − 0.575299I
−3.14805 + 0.90482I −6.51420 + 0.21846I
u = −0.221219 + 0.523394I
0.01425 − 1.49737I 1.74832 + 5.31506I
u = −0.221219 − 0.523394I
0.01425 + 1.49737I 1.74832 − 5.31506I
u = 0.504381 + 0.191157I
−0.50303 − 2.82096I 3.24990 + 2.85228I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504381 − 0.191157I
−0.50303 + 2.82096I 3.24990 − 2.85228I
u = 1.47320 + 0.22968I
7.89812 + 5.22510I 0
u = 1.47320 − 0.22968I
7.89812 − 5.22510I 0
u = −0.353298 + 0.351162I
0.686131 − 1.038760I 5.50415 + 5.16099I
u = −0.353298 − 0.351162I
0.686131 + 1.038760I 5.50415 − 5.16099I
u = 1.48315 + 0.24777I
11.6071 + 12.5188I 0
u = 1.48315 − 0.24777I
11.6071 − 12.5188I 0
u = −1.48567 + 0.24134I
13.4835 − 7.1271I 0
u = −1.48567 − 0.24134I
13.4835 + 7.1271I 0
u = −1.49208 + 0.22410I
13.7502 − 3.7932I 0
u = −1.49208 − 0.22410I
13.7502 + 3.7932I 0
u = 1.49455 + 0.21615I
12.09380 − 1.60453I 0
u = 1.49455 − 0.21615I
12.09380 + 1.60453I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
43
− u
42
+ ··· + 2u − 1
c
2
u
43
+ 19u
42
+ ··· − 2u − 1
c
3
u
43
− 3u
42
+ ··· − 165u + 88
c
4
, c
8
, c
9
u
43
+ u
42
+ ··· − u
2
− 1
c
6
u
43
+ u
42
+ ··· − 3u − 2
c
7
, c
10
, c
11
u
43
− 5u
42
+ ··· + 52u − 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
43
+ 19y
42
+ ··· − 2y −1
c
2
y
43
+ 11y
42
+ ··· − 10y −1
c
3
y
43
− 21y
42
+ ··· + 171017y −7744
c
4
, c
8
, c
9
y
43
− 41y
42
+ ··· − 2y −1
c
6
y
43
+ 3y
42
+ ··· − 163y −4
c
7
, c
10
, c
11
y
43
+ 47y
42
+ ··· − 1090y −49
8
