11a
117
(K11a
117
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 11 3 10 4 8 6
Solving Sequence
2,6
5 1 3 11 7 8 4 10 9
c
5
c
1
c
2
c
11
c
6
c
7
c
4
c
10
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
57
− 2u
56
+ ··· + 4u − 1i
I
u
2
= hu + 1i
* 2 irreducible components of dim
C
= 0, with total 58 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
57
− 2u
56
+ · · · + 4u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
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
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
16
− 4u
14
+ 8u
12
− 8u
10
+ 4u
8
a
4
=
−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
33
− 8u
31
+ ··· − 4u
5
+ u
−u
35
+ 9u
33
+ ··· − u
3
+ u
a
9
=
−u
52
+ 13u
50
+ ··· + u
2
+ 1
u
54
− 14u
52
+ ··· − 2u
4
+ u
2
a
9
=
−u
52
+ 13u
50
+ ··· + u
2
+ 1
u
54
− 14u
52
+ ··· − 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
56
+ 12u
55
+ ··· + 36u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
57
+ 2u
56
+ ··· + 4u + 1
c
2
u
57
+ 30u
56
+ ··· + 2u + 1
c
3
, c
9
u
57
− 9u
55
+ ··· + 2u + 1
c
4
u
57
− 8u
56
+ ··· + 4u + 5
c
6
, c
11
u
57
+ 3u
56
+ ··· + 192u + 23
c
7
u
57
+ 2u
56
+ ··· + 170u + 25
c
8
, c
10
u
57
+ 18u
56
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
57
− 30y
56
+ ··· + 2y −1
c
2
y
57
− 6y
56
+ ··· + 10y −1
c
3
, c
9
y
57
− 18y
56
+ ··· + 2y −1
c
4
y
57
+ 6y
56
+ ··· − 1114y −25
c
6
, c
11
y
57
+ 45y
56
+ ··· − 20314y −529
c
7
y
57
− 6y
56
+ ··· + 20350y −625
c
8
, c
10
y
57
+ 42y
56
+ ··· + 26y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.836048 + 0.550317I
4.33306 + 3.41463I −2.47924 − 4.18588I
u = −0.836048 − 0.550317I
4.33306 − 3.41463I −2.47924 + 4.18588I
u = 0.871162 + 0.481731I
−1.78928 − 4.12553I −10.51550 + 7.67121I
u = 0.871162 − 0.481731I
−1.78928 + 4.12553I −10.51550 − 7.67121I
u = 0.976200 + 0.175447I
−0.260427 − 0.093386I −10.10428 + 0.75716I
u = 0.976200 − 0.175447I
−0.260427 + 0.093386I −10.10428 − 0.75716I
u = 0.854260 + 0.553633I
3.54472 − 9.12902I −4.29187 + 9.35832I
u = 0.854260 − 0.553633I
3.54472 + 9.12902I −4.29187 − 9.35832I
u = −1.025370 + 0.120940I
−0.97680 + 5.27922I −11.94161 − 5.93896I
u = −1.025370 − 0.120940I
−0.97680 − 5.27922I −11.94161 + 5.93896I
u = −0.776284 + 0.476241I
1.34370 + 1.99239I −1.22032 − 4.61457I
u = −0.776284 − 0.476241I
1.34370 − 1.99239I −1.22032 + 4.61457I
u = −0.685277 + 0.557032I
4.76168 + 1.02575I −1.09591 − 2.82669I
u = −0.685277 − 0.557032I
4.76168 − 1.02575I −1.09591 + 2.82669I
u = 0.659353 + 0.565162I
4.09639 + 4.65710I −2.54128 − 2.76987I
u = 0.659353 − 0.565162I
4.09639 − 4.65710I −2.54128 + 2.76987I
u = 0.152096 + 0.803844I
0.21111 + 9.73679I −6.35596 − 6.96593I
u = 0.152096 − 0.803844I
0.21111 − 9.73679I −6.35596 + 6.96593I
u = −0.155610 + 0.790091I
1.21747 − 4.03618I −4.49079 + 2.19532I
u = −0.155610 − 0.790091I
1.21747 + 4.03618I −4.49079 − 2.19532I
u = 0.111905 + 0.792068I
−5.01846 + 3.97499I −12.06289 − 3.93262I
u = 0.111905 − 0.792068I
−5.01846 − 3.97499I −12.06289 + 3.93262I
u = 1.102490 + 0.477153I
0.600300 − 0.796809I 0
u = 1.102490 − 0.477153I
0.600300 + 0.796809I 0
u = −1.119950 + 0.489456I
0.82059 + 6.47261I 0
u = −1.119950 − 0.489456I
0.82059 − 6.47261I 0
u = 0.044927 + 0.773200I
−2.60957 − 1.93878I −9.59639 + 2.80772I
u = 0.044927 − 0.773200I
−2.60957 + 1.93878I −9.59639 − 2.80772I
u = 1.180170 + 0.409792I
−4.63162 − 1.95472I 0
u = 1.180170 − 0.409792I
−4.63162 + 1.95472I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.198100 + 0.370055I
−2.82122 + 0.17822I 0
u = 1.198100 − 0.370055I
−2.82122 − 0.17822I 0
u = −0.107682 + 0.735407I
−0.97923 − 1.98324I −4.77053 + 3.25742I
u = −0.107682 − 0.735407I
−0.97923 + 1.98324I −4.77053 − 3.25742I
u = −1.208710 + 0.369755I
−3.88380 − 5.81260I 0
u = −1.208710 − 0.369755I
−3.88380 + 5.81260I 0
u = −1.207110 + 0.396302I
−8.92696 + 0.08907I 0
u = −1.207110 − 0.396302I
−8.92696 − 0.08907I 0
u = −1.177440 + 0.489853I
−4.05781 + 6.54158I 0
u = −1.177440 − 0.489853I
−4.05781 − 6.54158I 0
u = −1.201970 + 0.429227I
−6.25189 + 6.18788I 0
u = −1.201970 − 0.429227I
−6.25189 − 6.18788I 0
u = 1.193890 + 0.471955I
−5.94721 − 2.57635I 0
u = 1.193890 − 0.471955I
−5.94721 + 2.57635I 0
u = −1.185350 + 0.514468I
−1.80837 + 8.85455I 0
u = −1.185350 − 0.514468I
−1.80837 − 8.85455I 0
u = 1.194420 + 0.499684I
−8.19464 − 8.71399I 0
u = 1.194420 − 0.499684I
−8.19464 + 8.71399I 0
u = 0.573785 + 0.409516I
−1.012750 + 0.227361I −8.27265 − 0.51249I
u = 0.573785 − 0.409516I
−1.012750 − 0.227361I −8.27265 + 0.51249I
u = 1.190800 + 0.516494I
−2.8518 − 14.5970I 0
u = 1.190800 − 0.516494I
−2.8518 + 14.5970I 0
u = −0.260945 + 0.634945I
3.29597 − 2.09703I −2.01630 + 2.69781I
u = −0.260945 − 0.634945I
3.29597 + 2.09703I −2.01630 − 2.69781I
u = 0.305661 + 0.608350I
2.89549 − 3.46679I −2.84958 + 3.34170I
u = 0.305661 − 0.608350I
2.89549 + 3.46679I −2.84958 − 3.34170I
u = 0.677040
−0.929485 −11.1190
6
II. I
u
2
= hu + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
5
=
1
−1
a
1
=
−1
0
a
3
=
1
−1
a
11
=
−1
0
a
7
=
1
0
a
8
=
0
1
a
4
=
0
−1
a
10
=
−1
1
a
9
=
−1
2
a
9
=
−1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
u − 1
c
2
, c
4
, c
8
c
10
u + 1
c
6
, c
11
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
7
c
8
, c
9
, c
10
y −1
c
6
, c
11
y
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
−4.93480 −18.0000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
57
+ 2u
56
+ ··· + 4u + 1)
c
2
(u + 1)(u
57
+ 30u
56
+ ··· + 2u + 1)
c
3
, c
9
(u − 1)(u
57
− 9u
55
+ ··· + 2u + 1)
c
4
(u + 1)(u
57
− 8u
56
+ ··· + 4u + 5)
c
6
, c
11
u(u
57
+ 3u
56
+ ··· + 192u + 23)
c
7
(u − 1)(u
57
+ 2u
56
+ ··· + 170u + 25)
c
8
, c
10
(u + 1)(u
57
+ 18u
56
+ ··· + 2u + 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)(y
57
− 30y
56
+ ··· + 2y −1)
c
2
(y −1)(y
57
− 6y
56
+ ··· + 10y −1)
c
3
, c
9
(y −1)(y
57
− 18y
56
+ ··· + 2y −1)
c
4
(y −1)(y
57
+ 6y
56
+ ··· − 1114y −25)
c
6
, c
11
y(y
57
+ 45y
56
+ ··· − 20314y −529)
c
7
(y −1)(y
57
− 6y
56
+ ··· + 20350y −625)
c
8
, c
10
(y −1)(y
57
+ 42y
56
+ ··· + 26y −1)
12
