11a
37
(K11a
37
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 3 5 7 6 9
Solving Sequence
2,5
4 1
3,9
8 7 11 6 10
c
4
c
1
c
2
c
8
c
7
c
11
c
5
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−48u
49
+ 213u
48
+ ··· + 4b + 63, 29u
49
− 118u
48
+ ··· + 4a − 19, u
50
− 5u
49
+ ··· − u + 1i
I
u
2
= hb
4
− b
3
+ b
2
+ 1, a, u + 1i
* 2 irreducible components of dim
C
= 0, with total 54 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
= h−48u
49
+ 213u
48
+ · · · + 4b + 63, 29u
49
− 118u
48
+ · · · + 4a −
19, u
50
− 5u
49
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
9
=
−
29
4
u
49
+
59
2
u
48
+ ··· +
5
2
u +
19
4
12u
49
−
213
4
u
48
+ ··· −
1
4
u −
63
4
a
8
=
−19.2500u
49
+ 82.7500u
48
+ ··· + 2.75000u + 20.5000
12u
49
−
213
4
u
48
+ ··· −
1
4
u −
63
4
a
7
=
−9u
49
+
149
4
u
48
+ ··· +
17
4
u +
35
4
51
4
u
49
−
223
4
u
48
+ ··· +
5
4
u − 15
a
11
=
−u
10
+ 3u
8
− 2u
7
− 4u
6
+ 4u
5
+ u
4
− 4u
3
+ u
2
+ 2u − 1
1
8
u
49
−
1
2
u
48
+ ··· + 2u −
1
8
a
6
=
−
1
8
u
49
+
1
2
u
48
+ ··· − 2u +
9
8
21
8
u
49
−
43
4
u
48
+ ··· −
1
4
u −
23
8
a
10
=
−
1
2
u
49
+
9
4
u
48
+ ··· +
17
4
u −
1
4
7
2
u
49
− 17u
48
+ ··· − 2u − 7
a
10
=
−
1
2
u
49
+
9
4
u
48
+ ··· +
17
4
u −
1
4
7
2
u
49
− 17u
48
+ ··· − 2u − 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
85
4
u
49
+
399
4
u
48
+ ··· −
53
4
u +
65
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
− 5u
49
+ ··· − u + 1
c
2
u
50
+ 23u
49
+ ··· − 15u + 1
c
3
, c
7
u
50
+ u
49
+ ··· + 24u + 16
c
5
, c
6
, c
9
c
10
u
50
− 2u
49
+ ··· − 3u + 1
c
8
u
50
− 2u
49
+ ··· − 1491u + 445
c
11
u
50
+ 14u
49
+ ··· + 1257u + 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
50
− 23y
49
+ ··· + 15y + 1
c
2
y
50
+ 13y
49
+ ··· + 3y + 1
c
3
, c
7
y
50
− 27y
49
+ ··· − 2624y + 256
c
5
, c
6
, c
9
c
10
y
50
+ 58y
49
+ ··· + y + 1
c
8
y
50
− 22y
49
+ ··· − 648671y + 198025
c
11
y
50
− 10y
49
+ ··· + 86009y + 17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.582859 + 0.818130I
a = −0.981092 + 0.022618I
b = −1.038970 − 0.194067I
5.74926 − 1.32005I 5.01799 + 3.45627I
u = 0.582859 − 0.818130I
a = −0.981092 − 0.022618I
b = −1.038970 + 0.194067I
5.74926 + 1.32005I 5.01799 − 3.45627I
u = 0.435613 + 0.882797I
a = −1.36085 − 0.66520I
b = −1.36121 − 0.51636I
4.77931 + 5.21174I 3.15504 − 5.31436I
u = 0.435613 − 0.882797I
a = −1.36085 + 0.66520I
b = −1.36121 + 0.51636I
4.77931 − 5.21174I 3.15504 + 5.31436I
u = −0.928435 + 0.426925I
a = −1.46100 + 0.63623I
b = −0.719839 − 0.472231I
−1.61695 + 1.61236I −6.30739 − 1.92987I
u = −0.928435 − 0.426925I
a = −1.46100 − 0.63623I
b = −0.719839 + 0.472231I
−1.61695 − 1.61236I −6.30739 + 1.92987I
u = 0.429603 + 0.933534I
a = 1.62869 + 0.71121I
b = 1.52592 + 0.52069I
12.7949 + 7.4878I 5.12788 − 3.72934I
u = 0.429603 − 0.933534I
a = 1.62869 − 0.71121I
b = 1.52592 − 0.52069I
12.7949 − 7.4878I 5.12788 + 3.72934I
u = 0.935093 + 0.462361I
a = 0.633478 + 0.219321I
b = −0.112627 − 1.282310I
−1.42561 − 3.60776I −3.00000 + 7.46646I
u = 0.935093 − 0.462361I
a = 0.633478 − 0.219321I
b = −0.112627 + 1.282310I
−1.42561 + 3.60776I −3.00000 − 7.46646I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.861919 + 0.408962I
a = −0.508762 − 0.083121I
b = 0.521608 + 1.221570I
−1.048050 + 0.087468I −1.42204 + 0.46193I
u = 0.861919 − 0.408962I
a = −0.508762 + 0.083121I
b = 0.521608 − 1.221570I
−1.048050 − 0.087468I −1.42204 − 0.46193I
u = 0.469477 + 0.811158I
a = 1.016760 + 0.499666I
b = 1.154940 + 0.462231I
2.92925 + 1.64742I −0.497780 − 0.432754I
u = 0.469477 − 0.811158I
a = 1.016760 − 0.499666I
b = 1.154940 − 0.462231I
2.92925 − 1.64742I −0.497780 + 0.432754I
u = 0.632917 + 0.878463I
a = 1.205340 − 0.345103I
b = 1.089650 − 0.054007I
14.1472 − 2.8867I 6.24429 + 0.I
u = 0.632917 − 0.878463I
a = 1.205340 + 0.345103I
b = 1.089650 + 0.054007I
14.1472 + 2.8867I 6.24429 + 0.I
u = −0.947722 + 0.527766I
a = 1.90433 − 0.66549I
b = 1.091640 + 0.560170I
−0.06909 + 4.84703I 0. − 7.27549I
u = −0.947722 − 0.527766I
a = 1.90433 + 0.66549I
b = 1.091640 − 0.560170I
−0.06909 − 4.84703I 0. + 7.27549I
u = −0.682129 + 0.592727I
a = −1.61933 + 1.77257I
b = −1.041110 + 0.419266I
8.58536 − 2.27131I 2.70256 + 0.I
u = −0.682129 − 0.592727I
a = −1.61933 − 1.77257I
b = −1.041110 − 0.419266I
8.58536 + 2.27131I 2.70256 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957660 + 0.583300I
a = −2.17619 + 0.70245I
b = −1.33546 − 0.59049I
7.74509 + 6.95904I 0
u = −0.957660 − 0.583300I
a = −2.17619 − 0.70245I
b = −1.33546 + 0.59049I
7.74509 − 6.95904I 0
u = −1.123510 + 0.157529I
a = −0.550330 − 0.046161I
b = 0.309772 − 0.513002I
−2.34402 + 0.36505I 0
u = −1.123510 − 0.157529I
a = −0.550330 + 0.046161I
b = 0.309772 + 0.513002I
−2.34402 − 0.36505I 0
u = 0.803708 + 0.317036I
a = 0.479992 − 0.047063I
b = −0.96186 − 1.16924I
5.81553 + 2.38249I 3.49858 + 1.94330I
u = 0.803708 − 0.317036I
a = 0.479992 + 0.047063I
b = −0.96186 + 1.16924I
5.81553 − 2.38249I 3.49858 − 1.94330I
u = 1.027460 + 0.497180I
a = −0.894781 − 0.329352I
b = −0.41118 + 1.40760I
4.51917 − 5.78869I 0
u = 1.027460 − 0.497180I
a = −0.894781 + 0.329352I
b = −0.41118 − 1.40760I
4.51917 + 5.78869I 0
u = −0.701181 + 0.467599I
a = 1.30386 − 1.46602I
b = 0.748263 − 0.194492I
0.729964 − 0.675494I 1.06714 + 1.67748I
u = −0.701181 − 0.467599I
a = 1.30386 + 1.46602I
b = 0.748263 + 0.194492I
0.729964 + 0.675494I 1.06714 − 1.67748I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.131350 + 0.330216I
a = 1.100770 + 0.196944I
b = 0.101239 + 1.026310I
3.45731 + 1.19827I 0
u = −1.131350 − 0.330216I
a = 1.100770 − 0.196944I
b = 0.101239 − 1.026310I
3.45731 − 1.19827I 0
u = 1.036300 + 0.664231I
a = −0.840415 − 1.006820I
b = −0.822961 + 0.495838I
4.37658 − 4.22003I 0
u = 1.036300 − 0.664231I
a = −0.840415 + 1.006820I
b = −0.822961 − 0.495838I
4.37658 + 4.22003I 0
u = −1.251000 + 0.108910I
a = 0.284422 + 0.232631I
b = −0.871117 + 0.511779I
−1.11589 − 2.48404I 0
u = −1.251000 − 0.108910I
a = 0.284422 − 0.232631I
b = −0.871117 − 0.511779I
−1.11589 + 2.48404I 0
u = 1.028110 + 0.728538I
a = 0.69726 + 1.30827I
b = 0.829533 − 0.089406I
12.94610 − 3.03404I 0
u = 1.028110 − 0.728538I
a = 0.69726 − 1.30827I
b = 0.829533 + 0.089406I
12.94610 + 3.03404I 0
u = 1.100010 + 0.633178I
a = 1.17840 + 0.90974I
b = 1.17520 − 0.79670I
1.03930 − 7.06574I 0
u = 1.100010 − 0.633178I
a = 1.17840 − 0.90974I
b = 1.17520 + 0.79670I
1.03930 + 7.06574I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.133290 + 0.650060I
a = −1.34813 − 1.01237I
b = −1.43569 + 0.74867I
2.67414 − 10.86920I 0
u = 1.133290 − 0.650060I
a = −1.34813 + 1.01237I
b = −1.43569 − 0.74867I
2.67414 + 10.86920I 0
u = −1.311520 + 0.106975I
a = −0.125488 − 0.322812I
b = 1.176990 − 0.583698I
6.58516 − 4.39707I 0
u = −1.311520 − 0.106975I
a = −0.125488 + 0.322812I
b = 1.176990 + 0.583698I
6.58516 + 4.39707I 0
u = 1.154930 + 0.665889I
a = 1.46673 + 1.10969I
b = 1.62351 − 0.67827I
10.5867 − 13.3384I 0
u = 1.154930 − 0.665889I
a = 1.46673 − 1.10969I
b = 1.62351 + 0.67827I
10.5867 + 13.3384I 0
u = 0.004533 + 0.531412I
a = 0.34509 − 1.83693I
b = −0.385670 − 0.859631I
6.72549 + 2.13344I 2.98920 − 3.27411I
u = 0.004533 − 0.531412I
a = 0.34509 + 1.83693I
b = −0.385670 + 0.859631I
6.72549 − 2.13344I 2.98920 + 3.27411I
u = −0.101318 + 0.238648I
a = −0.87875 + 2.12555I
b = 0.149430 + 0.468790I
−0.000511 + 1.051120I −0.14079 − 6.76805I
u = −0.101318 − 0.238648I
a = −0.87875 − 2.12555I
b = 0.149430 − 0.468790I
−0.000511 − 1.051120I −0.14079 + 6.76805I
9
II. I
u
2
= hb
4
− b
3
+ b
2
+ 1, a, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
1
=
−1
0
a
3
=
1
−1
a
9
=
0
b
a
8
=
−b
b
a
7
=
−b
b
a
11
=
−1
−b
2
a
6
=
b
2
+ 1
b
3
− b
2
− 1
a
10
=
−b
3
b
3
+ b
a
10
=
−b
3
b
3
+ b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4b
2
+ 3b − 5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
7
u
4
c
5
, c
6
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
, c
11
u
4
+ u
3
+ u
2
+ 1
c
9
, c
10
u
4
+ u
3
+ 3u
2
+ 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = −0.351808 + 0.720342I
−1.85594 − 1.41510I −4.47493 + 4.18840I
u = −1.00000
a = 0
b = −0.351808 − 0.720342I
−1.85594 + 1.41510I −4.47493 − 4.18840I
u = −1.00000
a = 0
b = 0.851808 + 0.911292I
5.14581 + 3.16396I −2.02507 − 3.47609I
u = −1.00000
a = 0
b = 0.851808 − 0.911292I
5.14581 − 3.16396I −2.02507 + 3.47609I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
50
− 5u
49
+ ··· − u + 1)
c
2
((u + 1)
4
)(u
50
+ 23u
49
+ ··· − 15u + 1)
c
3
, c
7
u
4
(u
50
+ u
49
+ ··· + 24u + 16)
c
4
((u + 1)
4
)(u
50
− 5u
49
+ ··· − u + 1)
c
5
, c
6
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
50
− 2u
49
+ ··· − 3u + 1)
c
8
(u
4
+ u
3
+ u
2
+ 1)(u
50
− 2u
49
+ ··· − 1491u + 445)
c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
50
− 2u
49
+ ··· − 3u + 1)
c
11
(u
4
+ u
3
+ u
2
+ 1)(u
50
+ 14u
49
+ ··· + 1257u + 131)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
50
− 23y
49
+ ··· + 15y + 1)
c
2
((y −1)
4
)(y
50
+ 13y
49
+ ··· + 3y + 1)
c
3
, c
7
y
4
(y
50
− 27y
49
+ ··· − 2624y + 256)
c
5
, c
6
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
50
+ 58y
49
+ ··· + y + 1)
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
50
− 22y
49
+ ··· − 648671y + 198025)
c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
50
− 10y
49
+ ··· + 86009y + 17161)
15
