11n
120
(K11n
120
)
A knot diagram
1
Linearized knot diagam
5 1 8 11 2 9 10 5 1 4 7
Solving Sequence
1,5
2 3
6,9
10 8 7 11 4
c
1
c
2
c
5
c
9
c
8
c
7
c
11
c
4
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.10700 × 10
42
u
32
− 8.32114 × 10
42
u
31
+ ··· + 1.04181 × 10
43
b + 3.11913 × 10
43
,
− 3.50718 × 10
43
u
32
+ 1.44547 × 10
44
u
31
+ ··· + 1.04181 × 10
43
a − 2.21436 × 10
44
,
u
33
− 4u
32
+ ··· + 20u + 1i
I
u
2
= h−u
7
− u
6
+ 4u
5
+ 5u
4
− 2u
3
− 4u
2
+ b + u + 1, u
9
+ u
8
− 5u
7
− 6u
6
+ 6u
5
+ 9u
4
− 4u
3
− 6u
2
+ a + u + 2,
u
10
+ u
9
− 5u
8
− 6u
7
+ 6u
6
+ 9u
5
− 4u
4
− 6u
3
+ 2u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 43 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
= h2.11 × 10
42
u
32
− 8.32 × 10
42
u
31
+ · · · + 1.04 × 10
43
b + 3.12 ×
10
43
, −3.51 × 10
43
u
32
+ 1.45 × 10
44
u
31
+ · · · + 1.04 × 10
43
a − 2.21 ×
10
44
, u
33
− 4u
32
+ · · · + 20u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
3.36643u
32
− 13.8746u
31
+ ··· + 359.454u + 21.2550
−0.202245u
32
+ 0.798722u
31
+ ··· − 30.1211u − 2.99396
a
10
=
3.56868u
32
− 14.6734u
31
+ ··· + 389.575u + 24.2489
−0.202245u
32
+ 0.798722u
31
+ ··· − 30.1211u − 2.99396
a
8
=
3.36643u
32
− 13.8746u
31
+ ··· + 359.454u + 21.2550
−0.242116u
32
+ 0.964369u
31
+ ··· − 34.9325u − 3.40285
a
7
=
−2.39153u
32
+ 9.65565u
31
+ ··· − 322.155u − 32.6535
−0.333028u
32
+ 1.39186u
31
+ ··· − 27.7757u − 1.13662
a
11
=
−0.0378953u
32
− 0.0228553u
31
+ ··· − 72.9307u − 16.7529
−0.414218u
32
+ 1.71120u
31
+ ··· − 42.6953u − 2.83658
a
4
=
−1.41343u
32
+ 6.01740u
31
+ ··· − 83.5671u + 7.88298
0.510036u
32
− 2.09654u
31
+ ··· + 58.5090u + 4.26540
a
4
=
−1.41343u
32
+ 6.01740u
31
+ ··· − 83.5671u + 7.88298
0.510036u
32
− 2.09654u
31
+ ··· + 58.5090u + 4.26540
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.43631u
32
− 5.67419u
31
+ ··· + 211.371u + 17.0575
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
33
+ 4u
32
+ ··· + 20u − 1
c
2
u
33
+ 48u
32
+ ··· + 88u + 1
c
3
u
33
− u
32
+ ··· + 864u − 691
c
4
, c
10
u
33
− 11u
31
+ ··· − u − 1
c
6
u
33
+ 6u
32
+ ··· − 2315u + 1751
c
7
u
33
+ 10u
32
+ ··· + 108u + 11
c
8
u
33
− 32u
31
+ ··· + 138u − 193
c
9
u
33
− 8u
32
+ ··· + 8781u − 1799
c
11
u
33
− 2u
32
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
33
− 48y
32
+ ··· + 88y −1
c
2
y
33
− 124y
32
+ ··· − 3924y −1
c
3
y
33
− 21y
32
+ ··· + 2800148y −477481
c
4
, c
10
y
33
− 22y
32
+ ··· + 11y −1
c
6
y
33
− 58y
32
+ ··· + 8486511y −3066001
c
7
y
33
+ 2y
32
+ ··· + 48y −121
c
8
y
33
− 64y
32
+ ··· − 45418y −37249
c
9
y
33
− 36y
32
+ ··· + 44853489y −3236401
c
11
y
33
+ 2y
32
+ ··· − 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403017 + 0.814677I
a = 0.107700 − 0.226447I
b = −0.856763 + 0.231979I
2.50185 − 1.42660I −0.894808 − 0.237180I
u = −0.403017 − 0.814677I
a = 0.107700 + 0.226447I
b = −0.856763 − 0.231979I
2.50185 + 1.42660I −0.894808 + 0.237180I
u = 1.032610 + 0.451125I
a = −0.534105 + 0.421030I
b = −0.605715 + 0.947070I
0.20621 + 3.24394I −3.32595 − 5.32169I
u = 1.032610 − 0.451125I
a = −0.534105 − 0.421030I
b = −0.605715 − 0.947070I
0.20621 − 3.24394I −3.32595 + 5.32169I
u = −0.617495 + 0.594331I
a = 0.228591 + 0.499559I
b = 0.686667 + 0.747422I
−0.659531 − 0.792248I −4.14798 − 2.75904I
u = −0.617495 − 0.594331I
a = 0.228591 − 0.499559I
b = 0.686667 − 0.747422I
−0.659531 + 0.792248I −4.14798 + 2.75904I
u = −0.709464 + 0.375757I
a = −0.54330 − 1.82882I
b = −1.28499 + 0.81921I
1.69477 − 3.95490I −4.65099 + 5.53433I
u = −0.709464 − 0.375757I
a = −0.54330 + 1.82882I
b = −1.28499 − 0.81921I
1.69477 + 3.95490I −4.65099 − 5.53433I
u = 0.788903 + 0.039022I
a = −1.048110 − 0.208486I
b = −0.390987 − 0.219065I
−1.46450 − 0.11042I −7.61890 − 0.69071I
u = 0.788903 − 0.039022I
a = −1.048110 + 0.208486I
b = −0.390987 + 0.219065I
−1.46450 + 0.11042I −7.61890 + 0.69071I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.025720 + 0.722645I
a = 0.176298 − 0.905575I
b = 1.54028 + 0.15435I
−2.74722 − 2.04706I −9.49316 + 3.23628I
u = 1.025720 − 0.722645I
a = 0.176298 + 0.905575I
b = 1.54028 − 0.15435I
−2.74722 + 2.04706I −9.49316 − 3.23628I
u = −1.065340 + 0.919963I
a = −0.237358 − 0.585233I
b = −1.334700 + 0.176044I
0.59436 + 7.58146I 0. − 6.03486I
u = −1.065340 − 0.919963I
a = −0.237358 + 0.585233I
b = −1.334700 − 0.176044I
0.59436 − 7.58146I 0. + 6.03486I
u = −0.577387 + 0.118189I
a = 1.51353 − 0.89064I
b = 0.632385 − 0.535325I
−0.92676 + 3.03549I −5.42554 − 8.81658I
u = −0.577387 − 0.118189I
a = 1.51353 + 0.89064I
b = 0.632385 + 0.535325I
−0.92676 − 3.03549I −5.42554 + 8.81658I
u = 1.64269 + 0.08860I
a = 1.325930 − 0.361396I
b = 1.159390 + 0.130829I
−8.66188 + 2.58631I 0
u = 1.64269 − 0.08860I
a = 1.325930 + 0.361396I
b = 1.159390 − 0.130829I
−8.66188 − 2.58631I 0
u = −0.083136 + 0.281660I
a = −1.76082 + 0.45809I
b = 0.590245 + 0.696368I
−0.08685 − 1.51365I −1.21011 + 3.17114I
u = −0.083136 − 0.281660I
a = −1.76082 − 0.45809I
b = 0.590245 − 0.696368I
−0.08685 + 1.51365I −1.21011 − 3.17114I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71660
a = −1.37178
b = −1.15039
−10.7048 0
u = 1.83781 + 0.30594I
a = 0.936033 − 0.283350I
b = 1.307470 + 0.126378I
−9.28497 − 3.68135I 0
u = 1.83781 − 0.30594I
a = 0.936033 + 0.283350I
b = 1.307470 − 0.126378I
−9.28497 + 3.68135I 0
u = −1.86212 + 0.06903I
a = −1.061290 − 0.082463I
b = −1.269770 + 0.034873I
−11.16570 + 0.07120I 0
u = −1.86212 − 0.06903I
a = −1.061290 + 0.082463I
b = −1.269770 − 0.034873I
−11.16570 − 0.07120I 0
u = 1.86596 + 0.26633I
a = −1.240120 − 0.046944I
b = −1.72861 − 1.20268I
−9.6038 − 12.7751I 0
u = 1.86596 − 0.26633I
a = −1.240120 + 0.046944I
b = −1.72861 + 1.20268I
−9.6038 + 12.7751I 0
u = −0.0996406 + 0.0510585I
a = −5.49416 + 8.68590I
b = −0.746822 − 0.713371I
3.57986 − 4.96677I 0.77431 + 5.63197I
u = −0.0996406 − 0.0510585I
a = −5.49416 − 8.68590I
b = −0.746822 + 0.713371I
3.57986 + 4.96677I 0.77431 − 5.63197I
u = −1.87441 + 0.23423I
a = 1.251320 − 0.104385I
b = 1.86854 − 1.38190I
−13.1119 + 6.5830I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.87441 − 0.23423I
a = 1.251320 + 0.104385I
b = 1.86854 + 1.38190I
−13.1119 − 6.5830I 0
u = 1.95662 + 0.23174I
a = −1.43425 − 0.24933I
b = −2.99143 − 2.15365I
−7.19656 − 0.44528I 0
u = 1.95662 − 0.23174I
a = −1.43425 + 0.24933I
b = −2.99143 + 2.15365I
−7.19656 + 0.44528I 0
8
II. I
u
2
= h−u
7
− u
6
+ 4u
5
+ 5u
4
− 2u
3
− 4u
2
+ b + u + 1, u
9
+ u
8
+ · · · + a +
2, u
10
+ u
9
+ · · · + 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
−u
9
− u
8
+ 5u
7
+ 6u
6
− 6u
5
− 9u
4
+ 4u
3
+ 6u
2
− u − 2
u
7
+ u
6
− 4u
5
− 5u
4
+ 2u
3
+ 4u
2
− u − 1
a
10
=
−u
9
− u
8
+ 4u
7
+ 5u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
− 1
u
7
+ u
6
− 4u
5
− 5u
4
+ 2u
3
+ 4u
2
− u − 1
a
8
=
−u
9
− u
8
+ 5u
7
+ 6u
6
− 6u
5
− 9u
4
+ 4u
3
+ 6u
2
− u − 2
u
7
+ u
6
− 4u
5
− 5u
4
+ u
3
+ 4u
2
− 1
a
7
=
−2u
9
− 2u
8
+ 10u
7
+ 12u
6
− 11u
5
− 18u
4
+ 4u
3
+ 11u
2
− u − 3
u
7
+ u
6
− 4u
5
− 5u
4
+ u
3
+ 4u
2
+ u − 1
a
11
=
u
9
− 5u
7
− u
6
+ 6u
5
+ 2u
4
− 2u
3
+ u
2
− 1
u
8
+ u
7
− 3u
6
− 5u
5
− 3u
4
+ 3u
3
+ 4u
2
− 2
a
4
=
u
9
+ 2u
8
− 4u
7
− 10u
6
+ 10u
4
+ 4u
3
− 4u
2
− 2u + 1
−u
8
+ 5u
6
+ u
5
− 7u
4
− 2u
3
+ 6u
2
+ u − 2
a
4
=
u
9
+ 2u
8
− 4u
7
− 10u
6
+ 10u
4
+ 4u
3
− 4u
2
− 2u + 1
−u
8
+ 5u
6
+ u
5
− 7u
4
− 2u
3
+ 6u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
9
− 7u
8
+ 29u
6
+ 19u
5
− 14u
4
− 12u
3
+ 4u
2
− 3u − 3
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
− 5u
8
− 6u
7
+ 6u
6
+ 9u
5
− 4u
4
− 6u
3
+ 2u
2
+ 2u − 1
c
2
u
10
+ 11u
9
+ ··· + 8u + 1
c
3
u
10
− 2u
8
+ 3u
7
+ u
5
− 6u
4
+ 9u
3
− 6u
2
+ 2u − 1
c
4
u
10
+ u
9
− 4u
8
− 3u
7
+ 6u
6
+ 3u
5
− 3u
4
+ u
3
− u
2
− u + 1
c
5
u
10
− u
9
− 5u
8
+ 6u
7
+ 6u
6
− 9u
5
− 4u
4
+ 6u
3
+ 2u
2
− 2u − 1
c
6
u
10
− 7u
9
+ 20u
8
− 33u
7
+ 37u
6
− 31u
5
+ 21u
4
− 12u
3
+ 7u
2
− 3u + 1
c
7
u
10
+ 3u
9
+ 2u
8
− 5u
7
− 12u
6
− 12u
5
− 6u
4
− u
3
+ 2u
2
+ 2u + 1
c
8
u
10
− u
9
− 5u
8
− 6u
7
+ 4u
6
+ 21u
5
+ 31u
4
+ 28u
3
+ 17u
2
+ 6u + 1
c
9
u
10
+ 3u
9
− u
8
− u
7
+ 3u
6
− 3u
4
− u
3
− u − 1
c
10
u
10
− u
9
− 4u
8
+ 3u
7
+ 6u
6
− 3u
5
− 3u
4
− u
3
− u
2
+ u + 1
c
11
u
10
+ u
9
+ u
7
+ 3u
6
− 3u
4
+ u
3
+ u
2
− 3u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
− 11y
9
+ ··· − 8y + 1
c
2
y
10
− 23y
9
+ ··· + 8y + 1
c
3
y
10
− 4y
9
+ 4y
8
− 21y
7
+ 6y
6
− 33y
5
+ 10y
4
− 13y
3
+ 12y
2
+ 8y + 1
c
4
, c
10
y
10
− 9y
9
+ 34y
8
− 69y
7
+ 74y
6
− 27y
5
− 23y
4
+ 23y
3
− 3y
2
− 3y + 1
c
6
y
10
− 9y
9
+ 12y
8
− y
7
+ 9y
6
+ 41y
5
+ 57y
4
+ 38y
3
+ 19y
2
+ 5y + 1
c
7
y
10
− 5y
9
+ 10y
8
− 13y
7
+ 10y
6
− 12y
5
− 12y
4
− y
3
− 4y
2
+ 1
c
8
y
10
− 11y
9
+ ··· − 2y + 1
c
9
y
10
− 11y
9
+ 13y
8
− 13y
7
+ 21y
6
− 16y
5
+ 9y
4
− 7y
3
+ 4y
2
− y + 1
c
11
y
10
− y
9
+ 4y
8
− 7y
7
+ 9y
6
− 16y
5
+ 21y
4
− 13y
3
+ 13y
2
− 11y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866197 + 0.578531I
a = −0.067855 + 1.111740I
b = 0.877449 + 0.215591I
3.01759 − 3.09606I −0.30900 + 2.81871I
u = −0.866197 − 0.578531I
a = −0.067855 − 1.111740I
b = 0.877449 − 0.215591I
3.01759 + 3.09606I −0.30900 − 2.81871I
u = −1.015340 + 0.405643I
a = −0.166016 + 0.744959I
b = 0.548989 − 0.533884I
2.52872 + 6.76916I −1.54858 − 6.21981I
u = −1.015340 − 0.405643I
a = −0.166016 − 0.744959I
b = 0.548989 + 0.533884I
2.52872 − 6.76916I −1.54858 + 6.21981I
u = 0.798561 + 0.168530I
a = −0.400296 + 0.421539I
b = −0.584842 − 0.825867I
−1.07490 − 2.24450I −6.05768 + 4.70336I
u = 0.798561 − 0.168530I
a = −0.400296 − 0.421539I
b = −0.584842 + 0.825867I
−1.07490 + 2.24450I −6.05768 − 4.70336I
u = 0.496273 + 0.300649I
a = −0.97776 + 1.19364I
b = −0.388447 + 0.692276I
−0.68101 + 1.88435I −5.02064 − 2.89096I
u = 0.496273 − 0.300649I
a = −0.97776 − 1.19364I
b = −0.388447 − 0.692276I
−0.68101 − 1.88435I −5.02064 + 2.89096I
u = −1.76945
a = −1.20430
b = −1.03466
−10.1434 1.94620
u = 1.94286
a = 1.42816
b = 3.12836
−7.30701 −11.0740
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ u
9
− 5u
8
− 6u
7
+ 6u
6
+ 9u
5
− 4u
4
− 6u
3
+ 2u
2
+ 2u − 1)
· (u
33
+ 4u
32
+ ··· + 20u − 1)
c
2
(u
10
+ 11u
9
+ ··· + 8u + 1)(u
33
+ 48u
32
+ ··· + 88u + 1)
c
3
(u
10
− 2u
8
+ 3u
7
+ u
5
− 6u
4
+ 9u
3
− 6u
2
+ 2u − 1)
· (u
33
− u
32
+ ··· + 864u − 691)
c
4
(u
10
+ u
9
− 4u
8
− 3u
7
+ 6u
6
+ 3u
5
− 3u
4
+ u
3
− u
2
− u + 1)
· (u
33
− 11u
31
+ ··· − u − 1)
c
5
(u
10
− u
9
− 5u
8
+ 6u
7
+ 6u
6
− 9u
5
− 4u
4
+ 6u
3
+ 2u
2
− 2u − 1)
· (u
33
+ 4u
32
+ ··· + 20u − 1)
c
6
(u
10
− 7u
9
+ 20u
8
− 33u
7
+ 37u
6
− 31u
5
+ 21u
4
− 12u
3
+ 7u
2
− 3u + 1)
· (u
33
+ 6u
32
+ ··· − 2315u + 1751)
c
7
(u
10
+ 3u
9
+ 2u
8
− 5u
7
− 12u
6
− 12u
5
− 6u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
33
+ 10u
32
+ ··· + 108u + 11)
c
8
(u
10
− u
9
− 5u
8
− 6u
7
+ 4u
6
+ 21u
5
+ 31u
4
+ 28u
3
+ 17u
2
+ 6u + 1)
· (u
33
− 32u
31
+ ··· + 138u − 193)
c
9
(u
10
+ 3u
9
− u
8
− u
7
+ 3u
6
− 3u
4
− u
3
− u − 1)
· (u
33
− 8u
32
+ ··· + 8781u − 1799)
c
10
(u
10
− u
9
− 4u
8
+ 3u
7
+ 6u
6
− 3u
5
− 3u
4
− u
3
− u
2
+ u + 1)
· (u
33
− 11u
31
+ ··· − u − 1)
c
11
(u
10
+ u
9
+ ··· − 3u − 1)(u
33
− 2u
32
+ ··· + 5u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
− 11y
9
+ ··· − 8y + 1)(y
33
− 48y
32
+ ··· + 88y −1)
c
2
(y
10
− 23y
9
+ ··· + 8y + 1)(y
33
− 124y
32
+ ··· − 3924y −1)
c
3
(y
10
− 4y
9
+ 4y
8
− 21y
7
+ 6y
6
− 33y
5
+ 10y
4
− 13y
3
+ 12y
2
+ 8y + 1)
· (y
33
− 21y
32
+ ··· + 2800148y −477481)
c
4
, c
10
(y
10
− 9y
9
+ 34y
8
− 69y
7
+ 74y
6
− 27y
5
− 23y
4
+ 23y
3
− 3y
2
− 3y + 1)
· (y
33
− 22y
32
+ ··· + 11y −1)
c
6
(y
10
− 9y
9
+ 12y
8
− y
7
+ 9y
6
+ 41y
5
+ 57y
4
+ 38y
3
+ 19y
2
+ 5y + 1)
· (y
33
− 58y
32
+ ··· + 8486511y −3066001)
c
7
(y
10
− 5y
9
+ 10y
8
− 13y
7
+ 10y
6
− 12y
5
− 12y
4
− y
3
− 4y
2
+ 1)
· (y
33
+ 2y
32
+ ··· + 48y −121)
c
8
(y
10
− 11y
9
+ ··· − 2y + 1)(y
33
− 64y
32
+ ··· − 45418y −37249)
c
9
(y
10
− 11y
9
+ 13y
8
− 13y
7
+ 21y
6
− 16y
5
+ 9y
4
− 7y
3
+ 4y
2
− y + 1)
· (y
33
− 36y
32
+ ··· + 44853489y −3236401)
c
11
(y
10
− y
9
+ 4y
8
− 7y
7
+ 9y
6
− 16y
5
+ 21y
4
− 13y
3
+ 13y
2
− 11y + 1)
· (y
33
+ 2y
32
+ ··· − 17y −1)
14
