11n
89
(K11n
89
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 2 3 11 3 4 7 10
Solving Sequence
4,10 5,7
11 1 9 3 2 6 8
c
4
c
10
c
11
c
9
c
3
c
2
c
6
c
8
c
1
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h1.81408 × 10
16
u
35
+ 4.53180 × 10
15
u
34
+ ··· + 1.44921 × 10
16
b + 6.92452 × 10
16
,
− 7.36698 × 10
15
u
35
− 2.71053 × 10
15
u
34
+ ··· + 1.44921 × 10
16
a − 3.17098 × 10
16
, u
36
− u
35
+ ··· + 12u − 4i
I
u
2
= hb
2
+ 2bu − b − u + 3, 2a − u, u
2
− 2i
I
v
1
= ha, b + v −1, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 42 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
= h1.81×10
16
u
35
+4.53×10
15
u
34
+· · ·+1.45×10
16
b+6.92×10
16
, −7.37×
10
15
u
35
−2.71×10
15
u
34
+· · ·+1.45×10
16
a−3.17×10
16
, u
36
−u
35
+· · ·+12u−4i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
7
=
0.508345u
35
+ 0.187035u
34
+ ··· − 3.81933u + 2.18808
−1.25177u
35
− 0.312708u
34
+ ··· + 10.6982u − 4.77814
a
11
=
0.995471u
35
+ 0.0679041u
34
+ ··· − 10.1216u + 3.89180
−0.252045u
35
+ 0.0577695u
34
+ ··· + 3.24270u − 1.30174
a
1
=
0.995471u
35
+ 0.0679041u
34
+ ··· − 10.1216u + 3.89180
−1.49385u
35
− 0.192804u
34
+ ··· + 12.0213u − 5.55524
a
9
=
−u
u
a
3
=
−u
2
+ 1
u
2
a
2
=
1.29114u
35
+ 0.157626u
34
+ ··· − 12.6782u + 5.68748
−1.28270u
35
− 0.365443u
34
+ ··· + 10.3098u − 3.90050
a
6
=
0.498382u
35
+ 0.124900u
34
+ ··· − 1.89976u + 1.66344
−1.49385u
35
− 0.192804u
34
+ ··· + 12.0213u − 5.55524
a
8
=
u
3
− 2u
−u
3
+ u
a
8
=
u
3
− 2u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2185176855038490
3623024810197363
u
35
−
2137823921618481
3623024810197363
u
34
+ ···−
32140848155027584
3623024810197363
u +
31012404119150980
3623024810197363
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
− 2u
35
+ ··· − 6u + 1
c
2
u
36
+ 20u
35
+ ··· − 6u + 1
c
3
, c
4
, c
8
c
9
u
36
− u
35
+ ··· + 12u − 4
c
6
u
36
+ 2u
35
+ ··· + 6u + 13
c
7
, c
10
u
36
− 3u
35
+ ··· + 13u − 7
c
11
u
36
− 13u
35
+ ··· − 687u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
+ 20y
35
+ ··· − 6y + 1
c
2
y
36
− 4y
35
+ ··· − 142y + 1
c
3
, c
4
, c
8
c
9
y
36
− 31y
35
+ ··· + 80y + 16
c
6
y
36
− 28y
35
+ ··· − 3962y + 169
c
7
, c
10
y
36
− 13y
35
+ ··· − 687y + 49
c
11
y
36
+ 27y
35
+ ··· − 44983y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.194833 + 0.923873I
a = −1.10823 − 0.89470I
b = 1.34994 + 0.54291I
−6.59180 − 8.00171I 4.29537 + 5.98015I
u = −0.194833 − 0.923873I
a = −1.10823 + 0.89470I
b = 1.34994 − 0.54291I
−6.59180 + 8.00171I 4.29537 − 5.98015I
u = 0.006560 + 0.931824I
a = −1.025890 − 0.856109I
b = 1.239880 + 0.450718I
−7.38383 + 1.35991I 2.81294 − 0.73046I
u = 0.006560 − 0.931824I
a = −1.025890 + 0.856109I
b = 1.239880 − 0.450718I
−7.38383 − 1.35991I 2.81294 + 0.73046I
u = 0.109745 + 0.850278I
a = 1.058100 − 0.923490I
b = −1.266800 + 0.563919I
−3.22625 + 3.00094I 6.75961 − 2.89336I
u = 0.109745 − 0.850278I
a = 1.058100 + 0.923490I
b = −1.266800 − 0.563919I
−3.22625 − 3.00094I 6.75961 + 2.89336I
u = 1.160570 + 0.158096I
a = 1.122800 − 0.199847I
b = −1.61805 + 0.12059I
3.84173 + 3.51209I 9.42797 − 4.38206I
u = 1.160570 − 0.158096I
a = 1.122800 + 0.199847I
b = −1.61805 − 0.12059I
3.84173 − 3.51209I 9.42797 + 4.38206I
u = −1.077610 + 0.525072I
a = 0.298720 + 0.977705I
b = 0.481253 + 0.080718I
−3.88454 + 2.88072I 5.75517 − 2.19113I
u = −1.077610 − 0.525072I
a = 0.298720 − 0.977705I
b = 0.481253 − 0.080718I
−3.88454 − 2.88072I 5.75517 + 2.19113I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202650 + 0.097073I
a = −0.646364 − 0.353578I
b = −0.21399 − 1.65792I
4.33907 − 0.62358I 10.41420 − 0.63892I
u = 1.202650 − 0.097073I
a = −0.646364 + 0.353578I
b = −0.21399 + 1.65792I
4.33907 + 0.62358I 10.41420 + 0.63892I
u = 1.182650 + 0.387668I
a = −0.269222 + 0.813754I
b = −0.610573 + 0.189166I
0.05037 + 1.45720I 9.46667 − 0.65893I
u = 1.182650 − 0.387668I
a = −0.269222 − 0.813754I
b = −0.610573 − 0.189166I
0.05037 − 1.45720I 9.46667 + 0.65893I
u = −1.236460 + 0.192085I
a = 0.735931 − 0.323447I
b = −0.46964 − 1.88597I
4.64327 − 4.73682I 11.38513 + 6.59168I
u = −1.236460 − 0.192085I
a = 0.735931 + 0.323447I
b = −0.46964 + 1.88597I
4.64327 + 4.73682I 11.38513 − 6.59168I
u = −0.577288 + 0.463180I
a = 0.811817 − 0.556107I
b = −0.692193 − 0.136688I
−2.03068 − 1.81473I 2.83557 + 4.64572I
u = −0.577288 − 0.463180I
a = 0.811817 + 0.556107I
b = −0.692193 + 0.136688I
−2.03068 + 1.81473I 2.83557 − 4.64572I
u = −1.31774
a = −0.894179
b = 1.49912
6.40417 14.3790
u = 1.280170 + 0.461183I
a = −0.895029 − 0.349023I
b = 1.40509 − 1.14928I
−3.43518 + 3.60339I 6.07450 − 2.50762I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.280170 − 0.461183I
a = −0.895029 + 0.349023I
b = 1.40509 + 1.14928I
−3.43518 − 3.60339I 6.07450 + 2.50762I
u = −1.290060 + 0.452109I
a = 0.147894 + 0.839120I
b = 0.685533 + 0.078345I
−3.35690 − 6.29314I 6.15059 + 3.94061I
u = −1.290060 − 0.452109I
a = 0.147894 − 0.839120I
b = 0.685533 − 0.078345I
−3.35690 + 6.29314I 6.15059 − 3.94061I
u = −1.355620 + 0.380756I
a = 0.878387 − 0.297489I
b = −1.57977 − 1.46639I
1.38910 − 7.43800I 11.20734 + 4.77385I
u = −1.355620 − 0.380756I
a = 0.878387 + 0.297489I
b = −1.57977 + 1.46639I
1.38910 + 7.43800I 11.20734 − 4.77385I
u = −1.43819 + 0.07165I
a = −0.701955 − 0.180604I
b = 1.401880 + 0.072692I
6.55786 − 0.26724I 12.41884 − 1.59842I
u = −1.43819 − 0.07165I
a = −0.701955 + 0.180604I
b = 1.401880 − 0.072692I
6.55786 + 0.26724I 12.41884 + 1.59842I
u = 1.41123 + 0.40473I
a = −0.905027 − 0.281003I
b = 1.79130 − 1.37903I
−1.51226 + 12.78080I 7.00000 − 7.80857I
u = 1.41123 − 0.40473I
a = −0.905027 + 0.281003I
b = 1.79130 + 1.37903I
−1.51226 − 12.78080I 7.00000 + 7.80857I
u = 1.50740 + 0.00063I
a = 0.404596 + 0.237890I
b = −1.296770 − 0.039394I
5.02009 + 2.85591I 7.00000 − 5.56949I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50740 − 0.00063I
a = 0.404596 − 0.237890I
b = −1.296770 + 0.039394I
5.02009 − 2.85591I 7.00000 + 5.56949I
u = 0.226004 + 0.427139I
a = −0.81515 + 2.22304I
b = −0.0399825 − 0.0159679I
1.14397 − 1.32004I 4.86119 − 2.11551I
u = 0.226004 − 0.427139I
a = −0.81515 − 2.22304I
b = −0.0399825 + 0.0159679I
1.14397 + 1.32004I 4.86119 + 2.11551I
u = 0.452153
a = −1.04552
b = 0.187974
0.718633 13.9020
u = 0.015889 + 0.435860I
a = 0.37848 − 1.46882I
b = −0.410669 + 1.206820I
0.87457 + 2.36441I 2.54968 − 4.98912I
u = 0.015889 − 0.435860I
a = 0.37848 + 1.46882I
b = −0.410669 − 1.206820I
0.87457 − 2.36441I 2.54968 + 4.98912I
8
II. I
u
2
= hb
2
+ 2bu − b − u + 3, 2a − u, u
2
− 2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−2
a
7
=
1
2
u
b
a
11
=
1
2
u
b + u
a
1
=
1
2
u
b
a
9
=
−u
u
a
3
=
−1
2
a
2
=
1
2
bu
−bu + b + u − 1
a
6
=
b +
3
2
u
−b − 2u
a
8
=
0
−u
a
8
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b + 4u + 12
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
7
, c
11
(u − 1)
4
c
10
(u + 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
c
7
, c
10
, c
11
(y −1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.707107
b = −0.914214 + 0.866025I
6.57974 − 2.02988I 14.0000 + 3.4641I
u = 1.41421
a = 0.707107
b = −0.914214 − 0.866025I
6.57974 + 2.02988I 14.0000 − 3.4641I
u = −1.41421
a = −0.707107
b = 1.91421 + 0.86603I
6.57974 − 2.02988I 14.0000 + 3.4641I
u = −1.41421
a = −0.707107
b = 1.91421 − 0.86603I
6.57974 + 2.02988I 14.0000 − 3.4641I
12
III. I
v
1
= ha, b + v − 1, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
v
0
a
5
=
1
0
a
7
=
0
−v + 1
a
11
=
v
v − 1
a
1
=
0
v − 1
a
9
=
v
0
a
3
=
1
0
a
2
=
1
v
a
6
=
−v + 1
−v + 1
a
8
=
v
0
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u + 1)
2
c
10
, c
11
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 12.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 12.00000 + 3.46410I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
36
− 2u
35
+ ··· − 6u + 1)
c
2
((u
2
+ u + 1)
3
)(u
36
+ 20u
35
+ ··· − 6u + 1)
c
3
, c
4
, c
8
c
9
u
2
(u
2
− 2)
2
(u
36
− u
35
+ ··· + 12u − 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
36
− 2u
35
+ ··· − 6u + 1)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
36
+ 2u
35
+ ··· + 6u + 13)
c
7
((u − 1)
4
)(u + 1)
2
(u
36
− 3u
35
+ ··· + 13u − 7)
c
10
((u − 1)
2
)(u + 1)
4
(u
36
− 3u
35
+ ··· + 13u − 7)
c
11
((u − 1)
6
)(u
36
− 13u
35
+ ··· − 687u + 49)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
36
+ 20y
35
+ ··· − 6y + 1)
c
2
((y
2
+ y + 1)
3
)(y
36
− 4y
35
+ ··· − 142y + 1)
c
3
, c
4
, c
8
c
9
y
2
(y − 2)
4
(y
36
− 31y
35
+ ··· + 80y + 16)
c
6
((y
2
+ y + 1)
3
)(y
36
− 28y
35
+ ··· − 3962y + 169)
c
7
, c
10
((y − 1)
6
)(y
36
− 13y
35
+ ··· − 687y + 49)
c
11
((y − 1)
6
)(y
36
+ 27y
35
+ ··· − 44983y + 2401)
18
