11n
102
(K11n
102
)
A knot diagram
1
Linearized knot diagam
7 1 8 7 10 2 4 1 11 5 9
Solving Sequence
1,8 4,9
3 2 7 5 11 10 6
c
8
c
3
c
2
c
7
c
4
c
11
c
10
c
5
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h36u
6
+ 57u
5
+ 296u
4
− 153u
3
+ 267u
2
+ 1118b − 1115u − 122,
181u
6
+ 240u
5
+ 805u
4
− 1468u
3
− 288u
2
+ 2236a − 5342u − 955,
u
7
+ 2u
6
+ 5u
5
− 6u
4
− 6u
3
− 24u
2
− 15u − 4i
I
u
2
= hu
2
+ b − a + u + 2, −2u
2
a + a
2
− 2au + 2u
2
− 4a + u + 4, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 13 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
= h36u
6
+ 57u
5
+ · · · + 1118b − 122, 181u
6
+ 240u
5
+ · · · + 2236a −
955, u
7
+ 2u
6
+ 5u
5
− 6u
4
− 6u
3
− 24u
2
− 15u − 4i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.0809481u
6
− 0.107335u
5
+ ··· + 2.38909u + 0.427102
−0.0322004u
6
− 0.0509839u
5
+ ··· + 0.997317u + 0.109123
a
9
=
1
−u
2
a
3
=
−0.0487478u
6
− 0.0563506u
5
+ ··· + 1.39177u + 0.317979
−0.0322004u
6
− 0.0509839u
5
+ ··· + 0.997317u + 0.109123
a
2
=
−0.0487478u
6
− 0.0563506u
5
+ ··· + 1.39177u + 0.317979
−0.0983900u
6
− 0.0724508u
5
+ ··· + 0.575134u − 0.0554562
a
7
=
0.0272809u
6
+ 0.0223614u
5
+ ··· − 0.893560u + 0.588104
0.0411449u
6
+ 0.148479u
5
+ ··· − 0.413238u − 0.194991
a
5
=
−0.129696u
6
− 0.163685u
5
+ ··· + 3.78086u + 0.745081
−0.130590u
6
− 0.123435u
5
+ ··· + 0.572451u + 0.0536673
a
11
=
−u
u
3
+ u
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
−0.0134168u
6
+ 0.103757u
5
+ ··· + 1.37388u − 0.371199
0.0420394u
6
− 0.391771u
5
+ ··· − 0.704830u − 0.00357782
a
6
=
−0.0134168u
6
+ 0.103757u
5
+ ··· + 1.37388u − 0.371199
0.0420394u
6
− 0.391771u
5
+ ··· − 0.704830u − 0.00357782
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
681
559
u
6
−
1218
559
u
5
−
3177
559
u
4
+
4711
559
u
3
+
2915
559
u
2
+
16294
559
u +
8550
559
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
u
7
+ u
6
− 3u
5
− 15u
4
+ 7u
3
− 9u
2
+ 3u − 1
c
2
u
7
− 7u
6
+ 53u
5
− 243u
4
− 237u
3
− 69u
2
− 9u − 1
c
5
, c
10
u
7
− 4u
6
+ 9u
5
− 12u
4
+ 10u
3
− 6u
2
+ 3u − 2
c
8
, c
9
, c
11
u
7
− 2u
6
+ 5u
5
+ 6u
4
− 6u
3
+ 24u
2
− 15u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
y
7
− 7y
6
+ 53y
5
− 243y
4
− 237y
3
− 69y
2
− 9y −1
c
2
y
7
+ 57y
6
− 1067y
5
− 85155y
4
+ 21667y
3
− 981y
2
− 57y −1
c
5
, c
10
y
7
+ 2y
6
+ 5y
5
− 6y
4
− 6y
3
− 24y
2
− 15y −4
c
8
, c
9
, c
11
y
7
+ 6y
6
+ 37y
5
− 30y
4
− 386y
3
− 444y
2
+ 33y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170370 + 1.378620I
a = −0.017505 + 0.896353I
b = −0.027229 + 0.619612I
−4.84599 − 2.93728I 3.03833 + 3.35250I
u = −0.170370 − 1.378620I
a = −0.017505 − 0.896353I
b = −0.027229 − 0.619612I
−4.84599 + 2.93728I 3.03833 − 3.35250I
u = −0.339374 + 0.259459I
a = −0.349016 + 0.650489I
b = −0.229714 + 0.315113I
0.336860 − 0.937443I 6.03846 + 7.34722I
u = −0.339374 − 0.259459I
a = −0.349016 − 0.650489I
b = −0.229714 − 0.315113I
0.336860 + 0.937443I 6.03846 − 7.34722I
u = 1.75678
a = 0.976487
b = −2.45542
4.12134 1.88290
u = −1.36864 + 2.14303I
a = −0.496722 − 0.581190I
b = 1.98465 − 1.73888I
8.20573 − 7.24432I 2.98176 + 3.02276I
u = −1.36864 − 2.14303I
a = −0.496722 + 0.581190I
b = 1.98465 + 1.73888I
8.20573 + 7.24432I 2.98176 − 3.02276I
5
II.
I
u
2
= hu
2
+b −a +u +2, −2u
2
a + a
2
−2au +2u
2
−4a +u +4, u
3
+u
2
+2u +1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
a
−u
2
+ a − u − 2
a
9
=
1
−u
2
a
3
=
u
2
+ u + 2
−u
2
+ a − u − 2
a
2
=
u
2
+ u + 2
−u
2
+ a − 2
a
7
=
u
2
a + au − 2u
2
+ 2a − u − 3
−1
a
5
=
−u
2
+ a − u − 2
0
a
11
=
−u
−u
2
− u − 1
a
10
=
u
2
+ 1
−u
2
− u − 1
a
6
=
0
−au − 1
a
6
=
0
−au − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4u + 4
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
3
c
2
(u + 1)
6
c
5
, c
10
u
6
+ u
4
+ 2u
2
+ 1
c
8
, c
9
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 2u − 1)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(y + 1)
6
c
2
(y −1)
6
c
5
, c
10
(y
3
+ y
2
+ 2y + 1)
2
c
8
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.122561 − 0.255138I
b = − 1.000000I
−6.31400 − 2.82812I −3.50976 + 2.97945I
u = −0.215080 + 1.307140I
a = 0.12256 + 1.74486I
b = 1.000000I
−6.31400 − 2.82812I −3.50976 + 2.97945I
u = −0.215080 − 1.307140I
a = 0.122561 + 0.255138I
b = 1.000000I
−6.31400 + 2.82812I −3.50976 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.12256 − 1.74486I
b = − 1.000000I
−6.31400 + 2.82812I −3.50976 − 2.97945I
u = −0.569840
a = 1.75488 + 1.00000I
b = 1.000000I
−2.17641 3.01950
u = −0.569840
a = 1.75488 − 1.00000I
b = − 1.000000I
−2.17641 3.01950
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
3
(u
7
+ u
6
− 3u
5
− 15u
4
+ 7u
3
− 9u
2
+ 3u − 1)
c
2
(u + 1)
6
(u
7
− 7u
6
+ 53u
5
− 243u
4
− 237u
3
− 69u
2
− 9u − 1)
c
5
, c
10
(u
6
+ u
4
+ 2u
2
+ 1)(u
7
− 4u
6
+ 9u
5
− 12u
4
+ 10u
3
− 6u
2
+ 3u − 2)
c
8
, c
9
(u
3
+ u
2
+ 2u + 1)
2
(u
7
− 2u
6
+ 5u
5
+ 6u
4
− 6u
3
+ 24u
2
− 15u + 4)
c
11
(u
3
− u
2
+ 2u − 1)
2
(u
7
− 2u
6
+ 5u
5
+ 6u
4
− 6u
3
+ 24u
2
− 15u + 4)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(y + 1)
6
(y
7
− 7y
6
+ 53y
5
− 243y
4
− 237y
3
− 69y
2
− 9y −1)
c
2
(y −1)
6
· (y
7
+ 57y
6
− 1067y
5
− 85155y
4
+ 21667y
3
− 981y
2
− 57y −1)
c
5
, c
10
(y
3
+ y
2
+ 2y + 1)
2
(y
7
+ 2y
6
+ 5y
5
− 6y
4
− 6y
3
− 24y
2
− 15y −4)
c
8
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
· (y
7
+ 6y
6
+ 37y
5
− 30y
4
− 386y
3
− 444y
2
+ 33y −16)
11
