11a
183
(K11a
183
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 3 4 5 6 8
Solving Sequence
6,9
5 10 11 4 3 8 1 2 7
c
5
c
9
c
10
c
4
c
3
c
8
c
11
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
57
+ u
56
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 57 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
+ u
56
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
u
u
3
+ u
a
11
=
u
3
+ 2u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
8
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
u
15
+ 6u
13
+ 14u
11
+ 14u
9
+ 2u
7
− 6u
5
− 2u
3
+ 2u
u
17
+ 7u
15
+ 19u
13
+ 22u
11
+ 3u
9
− 14u
7
− 6u
5
+ 4u
3
+ u
a
2
=
u
42
+ 17u
40
+ ··· + u
2
+ 1
u
44
+ 18u
42
+ ··· − 5u
4
+ 2u
2
a
7
=
−u
27
− 12u
25
+ ··· + 2u
5
+ 5u
3
−u
27
− 11u
25
+ ··· + u
3
+ u
a
7
=
−u
27
− 12u
25
+ ··· + 2u
5
+ 5u
3
−u
27
− 11u
25
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
56
+ 4u
55
+ ··· − 4u
2
+ 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
57
+ u
56
+ ··· − u − 1
c
2
u
57
+ 27u
56
+ ··· + u − 1
c
3
u
57
+ 7u
56
+ ··· + 49u + 5
c
4
, c
5
, c
9
u
57
− u
56
+ ··· + u − 1
c
7
u
57
− u
56
+ ··· + 231u − 53
c
8
, c
10
u
57
+ u
56
+ ··· − 29u − 17
c
11
u
57
+ 5u
56
+ ··· − 264u − 112
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
57
+ 27y
56
+ ··· + y −1
c
2
y
57
+ 7y
56
+ ··· − 3y −1
c
3
y
57
+ 3y
56
+ ··· − 519y −25
c
4
, c
5
, c
9
y
57
+ 47y
56
+ ··· + y −1
c
7
y
57
− 13y
56
+ ··· + 82617y −2809
c
8
, c
10
y
57
− 37y
56
+ ··· − 1267y −289
c
11
y
57
+ 15y
56
+ ··· − 381664y −12544
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.277649 + 1.138010I
−2.98923 − 1.15216I 0
u = −0.277649 − 1.138010I
−2.98923 + 1.15216I 0
u = −0.343977 + 1.120270I
−0.58525 + 6.08343I 0
u = −0.343977 − 1.120270I
−0.58525 − 6.08343I 0
u = −0.804549 + 0.125513I
2.43881 − 10.27360I 7.12723 + 7.98252I
u = −0.804549 − 0.125513I
2.43881 + 10.27360I 7.12723 − 7.98252I
u = 0.337618 + 1.140540I
1.53395 − 1.08977I 0
u = 0.337618 − 1.140540I
1.53395 + 1.08977I 0
u = 0.799720 + 0.113827I
4.65256 + 5.23405I 10.45155 − 4.02810I
u = 0.799720 − 0.113827I
4.65256 − 5.23405I 10.45155 + 4.02810I
u = 0.797777 + 0.076863I
5.78308 + 2.96634I 12.01643 − 3.84738I
u = 0.797777 − 0.076863I
5.78308 − 2.96634I 12.01643 + 3.84738I
u = −0.798784 + 0.053217I
4.63483 + 1.87363I 10.12440 − 2.27509I
u = −0.798784 − 0.053217I
4.63483 − 1.87363I 10.12440 + 2.27509I
u = −0.771308 + 0.122509I
0.04467 − 2.73028I 4.01382 + 2.71873I
u = −0.771308 − 0.122509I
0.04467 + 2.73028I 4.01382 − 2.71873I
u = 0.342759 + 1.189140I
2.38357 + 1.16168I 0
u = 0.342759 − 1.189140I
2.38357 − 1.16168I 0
u = −0.348811 + 1.212550I
1.07430 − 6.01691I 0
u = −0.348811 − 1.212550I
1.07430 + 6.01691I 0
u = −0.052037 + 1.291330I
−3.68835 − 1.96306I 0
u = −0.052037 − 1.291330I
−3.68835 + 1.96306I 0
u = −0.266975 + 1.304600I
−2.86692 − 3.28224I 0
u = −0.266975 − 1.304600I
−2.86692 + 3.28224I 0
u = 0.236806 + 1.324490I
−5.56866 − 0.84775I 0
u = 0.236806 − 1.324490I
−5.56866 + 0.84775I 0
u = −0.346838 + 1.301460I
0.40457 − 2.25231I 0
u = −0.346838 − 1.301460I
0.40457 + 2.25231I 0
u = 0.634619 + 0.140548I
−1.62790 + 3.37240I 3.27495 − 5.30685I
u = 0.634619 − 0.140548I
−1.62790 − 3.37240I 3.27495 + 5.30685I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.638377
1.27831 8.28660
u = 0.346920 + 1.317510I
1.41577 + 7.09232I 0
u = 0.346920 − 1.317510I
1.41577 − 7.09232I 0
u = 0.277893 + 1.335410I
−6.25104 + 6.75305I 0
u = 0.277893 − 1.335410I
−6.25104 − 6.75305I 0
u = 0.337361 + 0.533102I
−1.72047 + 6.62089I 2.54306 − 8.39817I
u = 0.337361 − 0.533102I
−1.72047 − 6.62089I 2.54306 + 8.39817I
u = −0.058345 + 1.369800I
−5.26507 − 3.02226I 0
u = −0.058345 − 1.369800I
−5.26507 + 3.02226I 0
u = −0.331323 + 1.341910I
−4.56299 − 6.72032I 0
u = −0.331323 − 1.341910I
−4.56299 + 6.72032I 0
u = 0.032432 + 1.383040I
−9.34182 + 0.07828I 0
u = 0.032432 − 1.383040I
−9.34182 − 0.07828I 0
u = 0.346087 + 1.339690I
0.08340 + 9.36804I 0
u = 0.346087 − 1.339690I
0.08340 − 9.36804I 0
u = 0.063733 + 1.386370I
−7.68595 + 7.77424I 0
u = 0.063733 − 1.386370I
−7.68595 − 7.77424I 0
u = −0.347692 + 1.346470I
−2.1926 − 14.4304I 0
u = −0.347692 − 1.346470I
−2.1926 + 14.4304I 0
u = 0.192189 + 0.576599I
−3.37572 − 0.51768I −1.48190 − 0.98551I
u = 0.192189 − 0.576599I
−3.37572 + 0.51768I −1.48190 + 0.98551I
u = −0.310416 + 0.472368I
0.42908 − 1.95168I 6.05217 + 4.83311I
u = −0.310416 − 0.472368I
0.42908 + 1.95168I 6.05217 − 4.83311I
u = 0.499130 + 0.251121I
−0.85109 − 3.57978I 5.03586 + 1.38706I
u = 0.499130 − 0.251121I
−0.85109 + 3.57978I 5.03586 − 1.38706I
u = −0.367153 + 0.287513I
0.979056 − 0.679070I 8.79507 + 4.86357I
u = −0.367153 − 0.287513I
0.979056 + 0.679070I 8.79507 − 4.86357I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
57
+ u
56
+ ··· − u − 1
c
2
u
57
+ 27u
56
+ ··· + u − 1
c
3
u
57
+ 7u
56
+ ··· + 49u + 5
c
4
, c
5
, c
9
u
57
− u
56
+ ··· + u − 1
c
7
u
57
− u
56
+ ··· + 231u − 53
c
8
, c
10
u
57
+ u
56
+ ··· − 29u − 17
c
11
u
57
+ 5u
56
+ ··· − 264u − 112
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
57
+ 27y
56
+ ··· + y −1
c
2
y
57
+ 7y
56
+ ··· − 3y −1
c
3
y
57
+ 3y
56
+ ··· − 519y −25
c
4
, c
5
, c
9
y
57
+ 47y
56
+ ··· + y −1
c
7
y
57
− 13y
56
+ ··· + 82617y −2809
c
8
, c
10
y
57
− 37y
56
+ ··· − 1267y −289
c
11
y
57
+ 15y
56
+ ··· − 381664y −12544
8
