11n
60
(K11n
60
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 9 10 11 4 1 7 6
Solving Sequence
7,11 4,8
3 10 6 1 2 5 9
c
7
c
3
c
10
c
6
c
11
c
2
c
4
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
19
+ u
18
+ ··· + b − 2, u
18
+ u
17
+ ··· + a + 2, u
20
+ 2u
19
+ ··· + 3u − 1i
I
u
2
= hu
4
− u
2
+ b − u, −u
4
+ u
3
+ u
2
+ a − u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 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
= h2u
19
+ u
18
+ · · · + b − 2, u
18
+ u
17
+ · · · + a + 2, u
20
+ 2u
19
+ · · · + 3u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−u
18
− u
17
+ ··· − 5u
2
− 2
−2u
19
− u
18
+ ··· − 5u + 2
a
8
=
1
−u
2
a
3
=
−u
19
− u
18
+ ··· − 2u − 1
u
19
+ u
18
+ ··· + u
2
+ 2u
a
10
=
−u
u
a
6
=
−u
2
+ 1
u
2
a
1
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
2
=
−u
18
− u
17
+ ··· − u − 1
−u
19
+ 8u
17
+ ··· − u + 1
a
5
=
−u
16
+ 7u
14
− 19u
12
+ 24u
10
− 13u
8
+ 2u
6
− 1
u
16
− 6u
14
+ 12u
12
− 6u
10
− 6u
8
+ 2u
6
+ 4u
4
a
9
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
− u
u
9
− 3u
7
+ u
5
+ 2u
3
+ u
a
9
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
− u
u
9
− 3u
7
+ u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
19
− 16u
17
+ 3u
16
+ 49u
15
− 22u
14
− 61u
13
+ 58u
12
− 8u
11
−
54u
10
+ 91u
9
− 20u
8
− 50u
7
+ 52u
6
− 40u
5
+ 26u
3
− 12u
2
+ 9u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 6u
19
+ ··· + 7u − 1
c
2
u
20
+ 30u
19
+ ··· + 13u + 1
c
3
, c
8
u
20
− u
19
+ ··· + 32u + 32
c
5
u
20
+ 2u
19
+ ··· − 3u − 1
c
6
, c
7
, c
10
u
20
− 2u
19
+ ··· − 3u − 1
c
9
u
20
− 6u
19
+ ··· + 81u − 9
c
11
u
20
+ 6u
19
+ ··· + 35u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− 30y
19
+ ··· − 13y + 1
c
2
y
20
− 74y
19
+ ··· + 355y + 1
c
3
, c
8
y
20
− 33y
19
+ ··· + 3584y + 1024
c
5
y
20
− 42y
19
+ ··· − 11y + 1
c
6
, c
7
, c
10
y
20
− 18y
19
+ ··· − 11y + 1
c
9
y
20
− 6y
19
+ ··· − 5031y + 81
c
11
y
20
+ 6y
19
+ ··· − 335y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917550 + 0.464269I
a = 0.887708 + 0.822675I
b = −2.03002 − 1.48307I
−12.36330 − 0.65965I −5.32167 − 1.11773I
u = 0.917550 − 0.464269I
a = 0.887708 − 0.822675I
b = −2.03002 + 1.48307I
−12.36330 + 0.65965I −5.32167 + 1.11773I
u = 0.243336 + 0.826957I
a = −2.56703 − 1.06992I
b = 0.1190440 − 0.0724083I
−14.4810 + 5.2607I −7.68359 − 3.29127I
u = 0.243336 − 0.826957I
a = −2.56703 + 1.06992I
b = 0.1190440 + 0.0724083I
−14.4810 − 5.2607I −7.68359 + 3.29127I
u = 1.238020 + 0.241187I
a = −1.48735 − 1.05770I
b = 2.32454 + 1.44360I
−0.14678 + 1.84866I −3.98019 − 2.83860I
u = 1.238020 − 0.241187I
a = −1.48735 + 1.05770I
b = 2.32454 − 1.44360I
−0.14678 − 1.84866I −3.98019 + 2.83860I
u = −1.278360 + 0.104707I
a = 0.191843 − 0.012837I
b = −1.001270 + 0.473795I
3.00168 − 0.46375I 0.380412 − 0.924408I
u = −1.278360 − 0.104707I
a = 0.191843 + 0.012837I
b = −1.001270 − 0.473795I
3.00168 + 0.46375I 0.380412 + 0.924408I
u = 0.069392 + 0.685215I
a = 2.21387 + 0.78494I
b = 0.040683 − 0.477218I
−3.69282 + 1.48185I −9.31815 − 1.78036I
u = 0.069392 − 0.685215I
a = 2.21387 − 0.78494I
b = 0.040683 + 0.477218I
−3.69282 − 1.48185I −9.31815 + 1.78036I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.314810 + 0.281063I
a = −0.578126 + 0.956901I
b = 1.58117 − 2.41766I
0.65473 − 4.99045I −3.53301 + 4.53534I
u = −1.314810 − 0.281063I
a = −0.578126 − 0.956901I
b = 1.58117 + 2.41766I
0.65473 + 4.99045I −3.53301 − 4.53534I
u = 1.39777 + 0.21985I
a = 0.535073 + 0.493687I
b = −0.802086 − 0.653876I
5.26329 + 4.10687I 5.09324 − 3.12286I
u = 1.39777 − 0.21985I
a = 0.535073 − 0.493687I
b = −0.802086 + 0.653876I
5.26329 − 4.10687I 5.09324 + 3.12286I
u = −0.243428 + 0.530766I
a = −0.710922 − 0.053518I
b = 0.009442 + 0.295836I
0.003151 − 1.284380I −0.00392 + 4.85690I
u = −0.243428 − 0.530766I
a = −0.710922 + 0.053518I
b = 0.009442 − 0.295836I
0.003151 + 1.284380I −0.00392 − 4.85690I
u = −1.41087 + 0.34270I
a = 0.67202 − 2.01481I
b = −1.37414 + 3.84768I
−9.22640 − 9.48716I −3.68120 + 4.58970I
u = −1.41087 − 0.34270I
a = 0.67202 + 2.01481I
b = −1.37414 − 3.84768I
−9.22640 + 9.48716I −3.68120 − 4.58970I
u = −1.49993
a = 0.998510
b = −0.427242
−4.28328 −1.87430
u = 0.262728
a = −2.31269
b = 0.692511
−1.18420 −8.02950
6
II. I
u
2
= hu
4
− u
2
+ b − u, −u
4
+ u
3
+ u
2
+ a − u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
u
4
− u
3
− u
2
+ u
−u
4
+ u
2
+ u
a
8
=
1
−u
2
a
3
=
u
4
− u
3
− u
2
+ u
−u
4
+ u
2
+ u
a
10
=
−u
u
a
6
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
− 1
−u
4
− u
3
+ u
2
+ 2u + 1
a
2
=
2u
4
− u
3
− 2u
2
+ u − 1
−2u
4
− u
3
+ 2u
2
+ 3u + 1
a
5
=
−u
4
+ u
2
+ 1
u
4
+ u
3
− u
2
− 2u − 1
a
9
=
1
−u
2
a
9
=
1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
+ u
2
+ 8u − 3
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
8
u
5
c
5
, c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
11
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
8
y
5
c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
7
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 1.30408
b = −1.93379
0.756147 −2.23020
u = −0.309916 + 0.549911I
a = −0.428550 + 1.039280I
b = −0.442672 + 0.068387I
−1.31583 − 1.53058I −6.94263 + 4.09764I
u = −0.309916 − 0.549911I
a = −0.428550 − 1.039280I
b = −0.442672 − 0.068387I
−1.31583 + 1.53058I −6.94263 − 4.09764I
u = 1.41878 + 0.21917I
a = 0.276511 + 0.728237I
b = −0.09043 − 1.60288I
4.22763 + 4.40083I −2.94226 − 4.18967I
u = 1.41878 − 0.21917I
a = 0.276511 − 0.728237I
b = −0.09043 + 1.60288I
4.22763 − 4.40083I −2.94226 + 4.18967I
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
20
− 6u
19
+ ··· + 7u − 1)
c
2
((u + 1)
5
)(u
20
+ 30u
19
+ ··· + 13u + 1)
c
3
, c
8
u
5
(u
20
− u
19
+ ··· + 32u + 32)
c
4
((u + 1)
5
)(u
20
− 6u
19
+ ··· + 7u − 1)
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
20
+ 2u
19
+ ··· − 3u − 1)
c
6
, c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
20
− 2u
19
+ ··· − 3u − 1)
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
20
− 6u
19
+ ··· + 81u − 9)
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
20
− 2u
19
+ ··· − 3u − 1)
c
11
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
20
+ 6u
19
+ ··· + 35u + 5)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
20
− 30y
19
+ ··· − 13y + 1)
c
2
((y −1)
5
)(y
20
− 74y
19
+ ··· + 355y + 1)
c
3
, c
8
y
5
(y
20
− 33y
19
+ ··· + 3584y + 1024)
c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
20
− 42y
19
+ ··· − 11y + 1)
c
6
, c
7
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
20
− 18y
19
+ ··· − 11y + 1)
c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
20
− 6y
19
+ ··· − 5031y + 81)
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
20
+ 6y
19
+ ··· − 335y + 25)
12
