11n
132
(K11n
132
)
A knot diagram
1
Linearized knot diagam
7 1 10 9 8 2 11 5 1 7 4
Solving Sequence
1,7
2
4,6
11 8 5 10 3 9
c
1
c
6
c
11
c
7
c
5
c
10
c
3
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.33308 × 10
15
u
20
− 1.72888 × 10
17
u
19
+ ··· + 1.09599 × 10
19
b − 8.78124 × 10
18
,
− 2.80505 × 10
18
u
20
+ 4.20368 × 10
18
u
19
+ ··· + 7.67190 × 10
19
a − 6.10889 × 10
19
,
u
21
− u
20
+ ··· − 18u + 28i
I
u
2
= hu
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ b + u − 1, −u
2
+ a − 2, u
9
+ 4u
7
+ u
6
+ 5u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 30 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
= h−7.33 × 10
15
u
20
− 1.73 × 10
17
u
19
+ · · · + 1.10 × 10
19
b − 8.78 ×
10
18
, −2.81 × 10
18
u
20
+ 4.20 × 10
18
u
19
+ · · · + 7.67 × 10
19
a − 6.11 ×
10
19
, u
21
− u
20
+ · · · − 18u + 28i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
4
=
0.0365627u
20
− 0.0547932u
19
+ ··· + 1.60738u + 0.796268
0.000669086u
20
+ 0.0157746u
19
+ ··· − 0.933535u + 0.801219
a
6
=
−u
u
3
+ u
a
11
=
−0.0196295u
20
− 0.0100507u
19
+ ··· + 1.18048u + 0.217188
0.00797850u
20
− 0.0158077u
19
+ ··· + 0.180611u − 0.795772
a
8
=
−0.0142692u
20
+ 0.0411108u
19
+ ··· − 0.773349u + 1.95583
−0.00351504u
20
+ 0.0137854u
19
+ ··· − 0.476341u + 0.0864955
a
5
=
0.0138798u
20
− 0.0293691u
19
+ ··· + 1.58093u + 0.793197
0.00952514u
20
− 0.0122960u
19
+ ··· + 0.486832u + 0.362072
a
10
=
−0.0196295u
20
− 0.0100507u
19
+ ··· + 1.18048u + 0.217188
0.0175759u
20
− 0.0166603u
19
+ ··· + 0.195992u + 0.0352752
a
3
=
u
2
+ 1
−u
2
a
9
=
−0.00205357u
20
− 0.0267111u
19
+ ··· + 1.37648u + 0.252463
0.0175759u
20
− 0.0166603u
19
+ ··· + 0.195992u + 0.0352752
a
9
=
−0.00205357u
20
− 0.0267111u
19
+ ··· + 1.37648u + 0.252463
0.0175759u
20
− 0.0166603u
19
+ ··· + 0.195992u + 0.0352752
(ii) Obstruction class = −1
(iii) Cusp Shapes =
445709904941671169
2739962993558394514
u
20
−
891361635722125989
5479925987116789028
u
19
+ ··· +
14080564157258258655
2739962993558394514
u +
2949485749258559055
1369981496779197257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
21
+ u
20
+ ··· − 18u − 28
c
2
u
21
+ 33u
20
+ ··· − 1972u − 784
c
3
u
21
− 24u
19
+ ··· + 1851u − 281
c
4
, c
5
, c
8
u
21
+ 2u
20
+ ··· − 12u − 11
c
7
, c
10
u
21
− 3u
20
+ ··· − 10u − 47
c
9
u
21
− 17u
19
+ ··· + 73u − 13
c
11
u
21
− 4u
20
+ ··· + 19u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
21
+ 33y
20
+ ··· − 1972y −784
c
2
y
21
− 87y
20
+ ··· + 22145008y −614656
c
3
y
21
− 48y
20
+ ··· + 982063y −78961
c
4
, c
5
, c
8
y
21
+ 26y
20
+ ··· − 846y −121
c
7
, c
10
y
21
+ 7y
20
+ ··· − 7232y −2209
c
9
y
21
− 34y
20
+ ··· + 2495y −169
c
11
y
21
− 4y
20
+ ··· + 319y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667126 + 0.763695I
a = 0.82594 − 1.23941I
b = 0.258218 + 1.151380I
1.34010 − 2.53227I 0.85890 + 6.43019I
u = −0.667126 − 0.763695I
a = 0.82594 + 1.23941I
b = 0.258218 − 1.151380I
1.34010 + 2.53227I 0.85890 − 6.43019I
u = −0.354561 + 1.008430I
a = −0.227436 + 0.200357I
b = 0.917813 − 0.821950I
−7.02572 + 3.49738I −2.24629 − 2.87148I
u = −0.354561 − 1.008430I
a = −0.227436 − 0.200357I
b = 0.917813 + 0.821950I
−7.02572 − 3.49738I −2.24629 + 2.87148I
u = −0.135425 + 0.749831I
a = 2.26639 + 0.24841I
b = 0.299503 − 0.694156I
1.72913 + 0.18094I 3.57258 − 0.16926I
u = −0.135425 − 0.749831I
a = 2.26639 − 0.24841I
b = 0.299503 + 0.694156I
1.72913 − 0.18094I 3.57258 + 0.16926I
u = 0.137433 + 0.625721I
a = 0.041014 − 0.214438I
b = 0.721689 + 0.405487I
−1.28019 − 1.09527I −2.70112 + 3.21254I
u = 0.137433 − 0.625721I
a = 0.041014 + 0.214438I
b = 0.721689 − 0.405487I
−1.28019 + 1.09527I −2.70112 − 3.21254I
u = 0.576539 + 0.104726I
a = 0.14734 − 1.76070I
b = −0.906943 − 0.072981I
−4.46536 − 3.00711I 1.90224 + 0.80232I
u = 0.576539 − 0.104726I
a = 0.14734 + 1.76070I
b = −0.906943 + 0.072981I
−4.46536 + 3.00711I 1.90224 − 0.80232I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.534365
a = 2.09662
b = −0.0562424
1.11788 11.2410
u = 0.07520 + 1.61647I
a = −0.453620 − 0.070826I
b = −0.793621 − 0.491574I
−8.87305 + 0.26805I −1.47803 + 0.75243I
u = 0.07520 − 1.61647I
a = −0.453620 + 0.070826I
b = −0.793621 + 0.491574I
−8.87305 − 0.26805I −1.47803 − 0.75243I
u = 1.10769 + 1.23434I
a = 0.723626 + 0.961597I
b = 1.194160 − 0.750185I
−7.93629 + 2.97451I −2.24011 − 2.11283I
u = 1.10769 − 1.23434I
a = 0.723626 − 0.961597I
b = 1.194160 + 0.750185I
−7.93629 − 2.97451I −2.24011 + 2.11283I
u = −0.31257 + 1.99292I
a = −0.345671 + 0.172538I
b = −1.21980 + 1.39213I
−17.7841 − 0.7836I −1.50922 + 0.14627I
u = −0.31257 − 1.99292I
a = −0.345671 − 0.172538I
b = −1.21980 − 1.39213I
−17.7841 + 0.7836I −1.50922 − 0.14627I
u = 0.42977 + 2.01390I
a = −0.984072 − 0.475371I
b = −1.34381 + 1.14589I
−18.4994 + 10.2668I −1.32790 − 4.15834I
u = 0.42977 − 2.01390I
a = −0.984072 + 0.475371I
b = −1.34381 − 1.14589I
−18.4994 − 10.2668I −1.32790 + 4.15834I
u = −0.08976 + 2.09219I
a = −1.363250 + 0.356504I
b = −1.099090 − 0.439233I
−10.14110 − 4.18838I −1.95156 + 4.03302I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08976 − 2.09219I
a = −1.363250 − 0.356504I
b = −1.099090 + 0.439233I
−10.14110 + 4.18838I −1.95156 − 4.03302I
7
II. I
u
2
= hu
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ b + u − 1, −u
2
+ a − 2, u
9
+ 4u
7
+
u
6
+ 5u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
4
=
u
2
+ 2
−u
8
− 3u
6
− u
5
− 2u
4
− u
3
− u
2
− u + 1
a
6
=
−u
u
3
+ u
a
11
=
u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u − 1
2u
8
+ u
7
+ 7u
6
+ 5u
5
+ 7u
4
+ 5u
3
+ 3u
2
+ 3u
a
8
=
−u
8
+ u
7
− 3u
6
+ 3u
5
− u
4
+ 3u
3
+ u
2
+ 2
−2u
8
− u
7
− 7u
6
− 4u
5
− 7u
4
− 2u
3
− 2u
2
− u + 1
a
5
=
u
8
+ 3u
6
+ u
4
− 2u
3
− 2u
2
− 2u − 1
−u
8
− 3u
6
− u
5
− 2u
4
− u
3
− 2u
2
− 2u
a
10
=
u
8
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u − 1
u
8
+ u
7
+ 4u
6
+ 4u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ 2u
a
3
=
u
2
+ 1
−u
2
a
9
=
2u
8
+ u
7
+ 7u
6
+ 5u
5
+ 7u
4
+ 5u
3
+ 3u
2
+ 3u − 1
u
8
+ u
7
+ 4u
6
+ 4u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ 2u
a
9
=
2u
8
+ u
7
+ 7u
6
+ 5u
5
+ 7u
4
+ 5u
3
+ 3u
2
+ 3u − 1
u
8
+ u
7
+ 4u
6
+ 4u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
8
− 3u
7
− 8u
6
− 12u
5
− 15u
4
− 12u
3
− 14u
2
− 7u − 4
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 4u
7
+ u
6
+ 5u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 1
c
2
u
9
+ 8u
8
+ 26u
7
+ 45u
6
+ 45u
5
+ 22u
4
− u
3
− 8u
2
− 4u − 1
c
3
u
9
+ u
8
− 2u
7
− 3u
6
− u
5
+ 4u
4
+ 7u
3
+ 6u
2
+ 3u + 1
c
4
, c
5
u
9
+ u
8
+ 5u
7
+ 5u
6
+ 9u
5
+ 10u
4
+ 7u
3
+ 8u
2
+ 2u + 1
c
6
u
9
+ 4u
7
− u
6
+ 5u
5
− 2u
4
+ 3u
3
− 2u
2
− 1
c
7
u
9
− 2u
8
− u
7
+ 4u
6
− 3u
5
+ 4u
3
− 3u
2
+ 1
c
8
u
9
− u
8
+ 5u
7
− 5u
6
+ 9u
5
− 10u
4
+ 7u
3
− 8u
2
+ 2u − 1
c
9
u
9
− 3u
8
− u
7
+ 9u
6
− 2u
5
− 10u
4
+ 7u
3
+ 2u
2
− u − 1
c
10
u
9
+ 2u
8
− u
7
− 4u
6
− 3u
5
+ 4u
3
+ 3u
2
− 1
c
11
u
9
− 3u
8
+ 6u
7
− 7u
6
+ 4u
5
+ u
4
− 3u
3
+ 2u
2
+ u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
9
+ 8y
8
+ 26y
7
+ 45y
6
+ 45y
5
+ 22y
4
− y
3
− 8y
2
− 4y −1
c
2
y
9
− 12y
8
+ 46y
7
− 39y
6
+ 113y
5
− 46y
4
+ 83y
3
− 12y
2
− 1
c
3
y
9
− 5y
8
+ 8y
7
+ y
6
− 9y
5
− 8y
4
+ y
3
− 2y
2
− 3y −1
c
4
, c
5
, c
8
y
9
+ 9y
8
+ 33y
7
+ 59y
6
+ 39y
5
− 36y
4
− 85y
3
− 56y
2
− 12y −1
c
7
, c
10
y
9
− 6y
8
+ 11y
7
− 2y
6
− 11y
5
+ 4y
4
+ 8y
3
− 9y
2
+ 6y −1
c
9
y
9
− 11y
8
+ 51y
7
− 123y
6
+ 180y
5
− 168y
4
+ 111y
3
− 38y
2
+ 5y −1
c
11
y
9
+ 3y
8
+ 2y
7
− y
6
+ 8y
5
+ 9y
4
− y
3
− 8y
2
+ 5y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.338665 + 0.974837I
a = 1.164390 + 0.660286I
b = 0.35504 − 1.42610I
−1.24626 + 1.32727I −0.553077 − 1.214568I
u = 0.338665 − 0.974837I
a = 1.164390 − 0.660286I
b = 0.35504 + 1.42610I
−1.24626 − 1.32727I −0.553077 + 1.214568I
u = −0.447524 + 0.951550I
a = 1.29483 − 0.85168I
b = 0.362962 + 1.048500I
1.95197 − 1.71727I 4.44186 + 1.84082I
u = −0.447524 − 0.951550I
a = 1.29483 + 0.85168I
b = 0.362962 − 1.048500I
1.95197 + 1.71727I 4.44186 − 1.84082I
u = −0.738179
a = 2.54491
b = 0.647287
0.518289 −4.57070
u = 0.318685 + 0.594099I
a = 1.74861 + 0.37866I
b = 1.063670 − 0.538027I
−4.97869 + 4.28681I 0.36640 − 5.34247I
u = 0.318685 − 0.594099I
a = 1.74861 − 0.37866I
b = 1.063670 + 0.538027I
−4.97869 − 4.28681I 0.36640 + 5.34247I
u = 0.15926 + 1.58292I
a = −0.480277 + 0.504206I
b = −0.605320 − 0.206182I
−9.14564 − 1.83774I −3.46986 + 2.95801I
u = 0.15926 − 1.58292I
a = −0.480277 − 0.504206I
b = −0.605320 + 0.206182I
−9.14564 + 1.83774I −3.46986 − 2.95801I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 4u
7
+ ··· + 2u
2
+ 1)(u
21
+ u
20
+ ··· − 18u − 28)
c
2
(u
9
+ 8u
8
+ 26u
7
+ 45u
6
+ 45u
5
+ 22u
4
− u
3
− 8u
2
− 4u − 1)
· (u
21
+ 33u
20
+ ··· − 1972u − 784)
c
3
(u
9
+ u
8
− 2u
7
− 3u
6
− u
5
+ 4u
4
+ 7u
3
+ 6u
2
+ 3u + 1)
· (u
21
− 24u
19
+ ··· + 1851u − 281)
c
4
, c
5
(u
9
+ u
8
+ 5u
7
+ 5u
6
+ 9u
5
+ 10u
4
+ 7u
3
+ 8u
2
+ 2u + 1)
· (u
21
+ 2u
20
+ ··· − 12u − 11)
c
6
(u
9
+ 4u
7
+ ··· − 2u
2
− 1)(u
21
+ u
20
+ ··· − 18u − 28)
c
7
(u
9
− 2u
8
+ ··· − 3u
2
+ 1)(u
21
− 3u
20
+ ··· − 10u − 47)
c
8
(u
9
− u
8
+ 5u
7
− 5u
6
+ 9u
5
− 10u
4
+ 7u
3
− 8u
2
+ 2u − 1)
· (u
21
+ 2u
20
+ ··· − 12u − 11)
c
9
(u
9
− 3u
8
− u
7
+ 9u
6
− 2u
5
− 10u
4
+ 7u
3
+ 2u
2
− u − 1)
· (u
21
− 17u
19
+ ··· + 73u − 13)
c
10
(u
9
+ 2u
8
+ ··· + 3u
2
− 1)(u
21
− 3u
20
+ ··· − 10u − 47)
c
11
(u
9
− 3u
8
+ 6u
7
− 7u
6
+ 4u
5
+ u
4
− 3u
3
+ 2u
2
+ u − 1)
· (u
21
− 4u
20
+ ··· + 19u − 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 8y
8
+ 26y
7
+ 45y
6
+ 45y
5
+ 22y
4
− y
3
− 8y
2
− 4y −1)
· (y
21
+ 33y
20
+ ··· − 1972y −784)
c
2
(y
9
− 12y
8
+ 46y
7
− 39y
6
+ 113y
5
− 46y
4
+ 83y
3
− 12y
2
− 1)
· (y
21
− 87y
20
+ ··· + 22145008y −614656)
c
3
(y
9
− 5y
8
+ 8y
7
+ y
6
− 9y
5
− 8y
4
+ y
3
− 2y
2
− 3y −1)
· (y
21
− 48y
20
+ ··· + 982063y −78961)
c
4
, c
5
, c
8
(y
9
+ 9y
8
+ 33y
7
+ 59y
6
+ 39y
5
− 36y
4
− 85y
3
− 56y
2
− 12y −1)
· (y
21
+ 26y
20
+ ··· − 846y −121)
c
7
, c
10
(y
9
− 6y
8
+ 11y
7
− 2y
6
− 11y
5
+ 4y
4
+ 8y
3
− 9y
2
+ 6y −1)
· (y
21
+ 7y
20
+ ··· − 7232y −2209)
c
9
(y
9
− 11y
8
+ 51y
7
− 123y
6
+ 180y
5
− 168y
4
+ 111y
3
− 38y
2
+ 5y −1)
· (y
21
− 34y
20
+ ··· + 2495y −169)
c
11
(y
9
+ 3y
8
+ 2y
7
− y
6
+ 8y
5
+ 9y
4
− y
3
− 8y
2
+ 5y −1)
· (y
21
− 4y
20
+ ··· + 319y −1)
13
