11n
22
(K11n
22
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 9 4 5 11 6 8 10
Solving Sequence
5,9
6
2,10
4 7 1 3 11 8
c
5
c
9
c
4
c
6
c
1
c
3
c
11
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.10514 × 10
39
u
35
+ 3.11173 × 10
39
u
34
+ ··· + 2.41739 × 10
40
b + 4.96908 × 10
40
,
9.97702 × 10
39
u
35
+ 3.04436 × 10
39
u
34
+ ··· + 4.83478 × 10
40
a + 6.03959 × 10
39
, u
36
+ 2u
35
+ ··· − 4u + 8i
I
u
2
= hb + 1, u
5
− 2u
3
+ u
2
+ a + 2u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 45 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
= h1.11 × 10
39
u
35
+ 3.11 × 10
39
u
34
+ · · · + 2.42 × 10
40
b + 4.97 × 10
40
, 9.98 ×
10
39
u
35
+3.04×10
39
u
34
+· · ·+4.83×10
40
a+6.04×10
39
, u
36
+2u
35
+· · ·−4u+8i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
2
=
−0.206359u
35
− 0.0629680u
34
+ ··· + 2.74530u − 0.124920
−0.0457161u
35
− 0.128723u
34
+ ··· + 2.35374u − 2.05556
a
10
=
u
−u
3
+ u
a
4
=
0.427443u
35
+ 0.372711u
34
+ ··· + 0.384288u + 4.31112
0.198044u
35
+ 0.422790u
34
+ ··· − 10.2169u + 3.38570
a
7
=
0.0303222u
35
+ 0.0626215u
34
+ ··· − 2.77119u − 0.192221
−0.188410u
35
− 0.280513u
34
+ ··· + 8.45275u − 2.80684
a
1
=
0.0303222u
35
+ 0.0626215u
34
+ ··· − 2.77119u − 0.192221
0.119317u
35
+ 0.288516u
34
+ ··· − 8.21808u + 2.82265
a
3
=
1.17216u
35
+ 1.26150u
34
+ ··· − 15.1808u + 11.5542
−0.361331u
35
− 0.145692u
34
+ ··· − 1.85662u − 1.41937
a
11
=
0.0556923u
35
+ 0.131200u
34
+ ··· − 4.42903u + 0.594050
0.223465u
35
+ 0.365609u
34
+ ··· − 9.74431u + 3.75163
a
8
=
−0.158088u
35
− 0.217892u
34
+ ··· + 5.68156u − 2.99906
−0.188410u
35
− 0.280513u
34
+ ··· + 8.45275u − 2.80684
a
8
=
−0.158088u
35
− 0.217892u
34
+ ··· + 5.68156u − 2.99906
−0.188410u
35
− 0.280513u
34
+ ··· + 8.45275u − 2.80684
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.408352u
35
+ 0.642649u
34
+ ··· − 18.9306u − 3.95860
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
36
− 8u
35
+ ··· − 6u + 1
c
2
u
36
+ 8u
35
+ ··· + 22u + 1
c
3
, c
6
u
36
− 2u
35
+ ··· − 384u
2
− 64
c
5
, c
9
u
36
− 2u
35
+ ··· + 4u + 8
c
7
u
36
+ 3u
35
+ ··· − u − 1
c
8
, c
10
u
36
− 5u
35
+ ··· + 18u − 1
c
11
u
36
+ 15u
35
+ ··· + 218u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
36
− 8y
35
+ ··· − 22y + 1
c
2
y
36
+ 48y
35
+ ··· − 22y + 1
c
3
, c
6
y
36
+ 42y
35
+ ··· + 49152y + 4096
c
5
, c
9
y
36
− 24y
35
+ ··· − 1488y + 64
c
7
y
36
− 45y
35
+ ··· − 5y + 1
c
8
, c
10
y
36
− 15y
35
+ ··· − 218y + 1
c
11
y
36
+ 17y
35
+ ··· − 43646y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876781 + 0.467791I
a = 0.771077 − 0.499574I
b = 0.458159 + 0.388133I
1.44120 − 1.68807I 1.23787 + 2.98942I
u = −0.876781 − 0.467791I
a = 0.771077 + 0.499574I
b = 0.458159 − 0.388133I
1.44120 + 1.68807I 1.23787 − 2.98942I
u = 0.562796 + 0.711448I
a = 0.798144 + 0.463491I
b = 0.364530 + 0.110500I
−2.24151 − 1.11055I −4.16932 + 0.85691I
u = 0.562796 − 0.711448I
a = 0.798144 − 0.463491I
b = 0.364530 − 0.110500I
−2.24151 + 1.11055I −4.16932 − 0.85691I
u = −1.149490 + 0.105847I
a = −0.69354 − 2.02575I
b = 0.973276 + 0.948498I
3.87982 − 3.49544I −3.17810 + 2.67745I
u = −1.149490 − 0.105847I
a = −0.69354 + 2.02575I
b = 0.973276 − 0.948498I
3.87982 + 3.49544I −3.17810 − 2.67745I
u = 1.151290 + 0.136717I
a = −0.050534 + 0.984743I
b = −1.156680 − 0.402174I
0.196716 + 1.191220I −3.75367 − 2.76129I
u = 1.151290 − 0.136717I
a = −0.050534 − 0.984743I
b = −1.156680 + 0.402174I
0.196716 − 1.191220I −3.75367 + 2.76129I
u = 1.012080 + 0.596945I
a = 0.812755 + 0.396273I
b = 0.666828 − 0.220770I
−0.90609 + 6.15586I −1.06826 − 8.23147I
u = 1.012080 − 0.596945I
a = 0.812755 − 0.396273I
b = 0.666828 + 0.220770I
−0.90609 − 6.15586I −1.06826 + 8.23147I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132013 + 0.796085I
a = 0.530905 + 0.123801I
b = −0.363392 − 0.400261I
−1.17315 − 1.43837I −4.87286 + 4.95965I
u = 0.132013 − 0.796085I
a = 0.530905 − 0.123801I
b = −0.363392 + 0.400261I
−1.17315 + 1.43837I −4.87286 − 4.95965I
u = −1.188780 + 0.305866I
a = −0.477194 + 1.088200I
b = −1.293690 − 0.259633I
−0.19217 − 3.89522I −3.75583 + 3.33691I
u = −1.188780 − 0.305866I
a = −0.477194 − 1.088200I
b = −1.293690 + 0.259633I
−0.19217 + 3.89522I −3.75583 − 3.33691I
u = −0.114291 + 1.235990I
a = 0.468464 − 0.379839I
b = 0.919988 + 1.004770I
5.76584 − 0.88624I −3.08966 − 0.19737I
u = −0.114291 − 1.235990I
a = 0.468464 + 0.379839I
b = 0.919988 − 1.004770I
5.76584 + 0.88624I −3.08966 + 0.19737I
u = −0.299008 + 1.238570I
a = 0.478366 + 0.338536I
b = 1.040320 − 0.944822I
5.37775 + 6.26456I −3.90154 − 4.74503I
u = −0.299008 − 1.238570I
a = 0.478366 − 0.338536I
b = 1.040320 + 0.944822I
5.37775 − 6.26456I −3.90154 + 4.74503I
u = −1.282480 + 0.078351I
a = 0.406471 + 1.116480I
b = −0.272152 − 0.810511I
3.60869 − 0.40430I −0.180320 + 0.512361I
u = −1.282480 − 0.078351I
a = 0.406471 − 1.116480I
b = −0.272152 + 0.810511I
3.60869 + 0.40430I −0.180320 − 0.512361I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.300550 + 0.426752I
a = 0.110638 − 1.292420I
b = −0.510437 + 0.832243I
2.60051 + 6.07581I −2.58564 − 6.03076I
u = 1.300550 − 0.426752I
a = 0.110638 + 1.292420I
b = −0.510437 − 0.832243I
2.60051 − 6.07581I −2.58564 + 6.03076I
u = −0.607835 + 0.068419I
a = 0.588549 + 0.355335I
b = 0.895986 − 0.665316I
1.96162 + 2.57896I 2.96196 − 0.32171I
u = −0.607835 − 0.068419I
a = 0.588549 − 0.355335I
b = 0.895986 + 0.665316I
1.96162 − 2.57896I 2.96196 + 0.32171I
u = −0.203337 + 0.520719I
a = −4.57730 + 1.89887I
b = −1.060050 + 0.082275I
−3.21515 + 0.53565I −7.7422 + 12.1700I
u = −0.203337 − 0.520719I
a = −4.57730 − 1.89887I
b = −1.060050 − 0.082275I
−3.21515 − 0.53565I −7.7422 − 12.1700I
u = 0.529202
a = 4.14663
b = −0.467103
−2.39731 2.58440
u = 1.45234 + 0.47903I
a = 0.18492 + 1.55929I
b = 1.12508 − 0.97464I
10.93880 + 6.87915I 0. − 3.18853I
u = 1.45234 − 0.47903I
a = 0.18492 − 1.55929I
b = 1.12508 + 0.97464I
10.93880 − 6.87915I 0. + 3.18853I
u = −1.36361 + 0.70201I
a = 0.52721 − 1.55915I
b = 1.17133 + 0.91175I
8.7659 − 13.1890I −5.00000 + 7.32457I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36361 − 0.70201I
a = 0.52721 + 1.55915I
b = 1.17133 − 0.91175I
8.7659 + 13.1890I −5.00000 − 7.32457I
u = 1.51813 + 0.32802I
a = −0.632543 − 0.937060I
b = 0.89682 + 1.12852I
11.70850 − 0.74205I 0
u = 1.51813 − 0.32802I
a = −0.632543 + 0.937060I
b = 0.89682 − 1.12852I
11.70850 + 0.74205I 0
u = −1.43939 + 0.60179I
a = −0.705793 + 0.628179I
b = 0.790568 − 1.152680I
10.03080 − 5.72886I −5.00000 + 3.03607I
u = −1.43939 − 0.60179I
a = −0.705793 − 0.628179I
b = 0.790568 + 1.152680I
10.03080 + 5.72886I −5.00000 − 3.03607I
u = 0.262401
a = 1.77219
b = −0.825866
−1.19842 −8.63080
8
II. I
u
2
= hb + 1, u
5
− 2u
3
+ u
2
+ a + 2u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
2
=
−u
5
+ 2u
3
− u
2
− 2u
−1
a
10
=
u
−u
3
+ u
a
4
=
−u
5
+ 2u
3
− u
2
− 2u + 1
−1
a
7
=
1
−u
2
a
1
=
−1
0
a
3
=
−u
5
+ 2u
3
− u
2
− 2u + 1
−1
a
11
=
−u
4
+ u
2
− 1
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
8
=
−u
2
+ 1
−u
2
a
8
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
− 5u
4
− u
3
+ 7u
2
− 4u − 12
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
6
u
6
c
5
, c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
, c
9
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
8
, c
9
c
10
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
7
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.230593 + 0.497010I
b = −1.00000
0.245672 − 0.924305I −3.44826 + 0.47256I
u = −1.002190 − 0.295542I
a = −0.230593 − 0.497010I
b = −1.00000
0.245672 + 0.924305I −3.44826 − 0.47256I
u = 0.428243 + 0.664531I
a = −1.66103 − 1.45708I
b = −1.00000
−3.53554 − 0.92430I −13.66012 + 2.42665I
u = 0.428243 − 0.664531I
a = −1.66103 + 1.45708I
b = −1.00000
−3.53554 + 0.92430I −13.66012 − 2.42665I
u = 1.073950 + 0.558752I
a = −0.608378 − 0.558752I
b = −1.00000
−1.64493 + 5.69302I −8.89162 − 3.92918I
u = 1.073950 − 0.558752I
a = −0.608378 + 0.558752I
b = −1.00000
−1.64493 − 5.69302I −8.89162 + 3.92918I
12
III. I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
v
0
a
6
=
1
0
a
2
=
0
v
2
+ 3v − 1
a
10
=
v
0
a
4
=
1
−2v
2
− 5v + 3
a
7
=
−2v
2
− 5v + 4
v
2
+ 2v − 3
a
1
=
v
2
+ 3v − 1
−v
2
− 2v + 3
a
3
=
−2v
2
− 5v + 4
−2v
2
− 5v + 3
a
11
=
v
2
+ 4v − 1
−v
2
− 2v + 3
a
8
=
−v
2
− 3v + 1
v
2
+ 2v − 3
a
8
=
−v
2
− 3v + 1
v
2
+ 2v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6v
2
+ 19v − 21
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
, c
9
u
3
c
7
u
3
− 3u
2
+ 2u + 1
c
8
(u − 1)
3
c
10
, c
11
(u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− y
2
+ 2y − 1
c
2
, c
3
, c
6
y
3
+ 3y
2
+ 2y − 1
c
5
, c
9
y
3
c
7
y
3
− 5y
2
+ 10y − 1
c
8
, c
10
, c
11
(y − 1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −9.19557 + 4.65175I
v = 0.539798 − 0.182582I
a = 0
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −9.19557 − 4.65175I
v = −3.07960
a = 0
b = −0.754878
−2.75839 −22.6090
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
+ u
2
− 1)(u
36
− 8u
35
+ ··· − 6u + 1)
c
2
((u + 1)
6
)(u
3
+ u
2
+ 2u + 1)(u
36
+ 8u
35
+ ··· + 22u + 1)
c
3
u
6
(u
3
− u
2
+ 2u − 1)(u
36
− 2u
35
+ ··· − 384u
2
− 64)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)(u
36
− 8u
35
+ ··· − 6u + 1)
c
5
u
3
(u
6
− u
5
+ ··· − u + 1)(u
36
− 2u
35
+ ··· + 4u + 8)
c
6
u
6
(u
3
+ u
2
+ 2u + 1)(u
36
− 2u
35
+ ··· − 384u
2
− 64)
c
7
(u
3
− 3u
2
+ 2u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
36
+ 3u
35
+ ··· − u − 1)
c
8
((u − 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
36
− 5u
35
+ ··· + 18u − 1)
c
9
u
3
(u
6
+ u
5
+ ··· + u + 1)(u
36
− 2u
35
+ ··· + 4u + 8)
c
10
((u + 1)
3
)(u
6
− u
5
+ ··· − u + 1)(u
36
− 5u
35
+ ··· + 18u − 1)
c
11
(u + 1)
3
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
36
+ 15u
35
+ ··· + 218u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y − 1)
6
)(y
3
− y
2
+ 2y − 1)(y
36
− 8y
35
+ ··· − 22y + 1)
c
2
((y − 1)
6
)(y
3
+ 3y
2
+ 2y − 1)(y
36
+ 48y
35
+ ··· − 22y + 1)
c
3
, c
6
y
6
(y
3
+ 3y
2
+ 2y − 1)(y
36
+ 42y
35
+ ··· + 49152y + 4096)
c
5
, c
9
y
3
(y
6
− 3y
5
+ ··· − y + 1)(y
36
− 24y
35
+ ··· − 1488y + 64)
c
7
(y
3
− 5y
2
+ 10y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
36
− 45y
35
+ ··· − 5y + 1)
c
8
, c
10
(y − 1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
36
− 15y
35
+ ··· − 218y + 1)
c
11
((y − 1)
3
)(y
6
+ y
5
+ ··· + 3y + 1)(y
36
+ 17y
35
+ ··· − 43646y + 1)
18
