11n
172
(K11n
172
)
A knot diagram
1
Linearized knot diagam
6 9 1 10 2 4 11 2 7 5 9
Solving Sequence
2,9 3,6
1 4 5 8 11 7 10
c
2
c
1
c
3
c
5
c
8
c
11
c
7
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.80403 × 10
129
u
39
+ 1.00269 × 10
129
u
38
+ ··· + 1.55952 × 10
133
b − 4.83307 × 10
132
,
3.18557 × 10
131
u
39
− 1.42090 × 10
132
u
38
+ ··· + 6.95548 × 10
135
a + 3.12217 × 10
135
,
u
40
− u
39
+ ··· + 492u − 892i
I
u
2
= h−3007418546u
15
+ 933342897u
14
+ ··· + 9161883482b + 4813387670,
− 1873381418u
15
− 2988794220u
14
+ ··· + 9161883482a − 21851752726,
u
16
+ 5u
14
− 5u
13
− u
11
− 24u
10
+ 16u
9
+ 4u
8
− 16u
7
+ 20u
6
− 4u
5
− 17u
4
+ 4u
3
+ 10u
2
− 4i
* 2 irreducible components of dim
C
= 0, with total 56 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
= h2.80 × 10
129
u
39
+ 1.00 × 10
129
u
38
+ · · · + 1.56 × 10
133
b − 4.83 ×
10
132
, 3.19 × 10
131
u
39
− 1.42 × 10
132
u
38
+ · · · + 6.96 × 10
135
a + 3.12 ×
10
135
, u
40
− u
39
+ · · · + 492u − 892i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
−0.0000457994u
39
+ 0.000204285u
38
+ ··· + 0.0708298u − 0.448879
−0.000179801u
39
− 0.0000642943u
38
+ ··· + 1.95559u + 0.309907
a
1
=
0.0000420568u
39
− 0.000112360u
38
+ ··· − 2.24245u + 0.0906996
−0.000731650u
39
+ 0.000562011u
38
+ ··· + 0.278566u − 0.727739
a
4
=
−0.000151445u
39
− 0.0000710102u
38
+ ··· + 2.55187u + 2.12193
0.000373065u
39
− 0.000239614u
38
+ ··· − 0.711429u + 0.439973
a
5
=
0.000134001u
39
+ 0.000268580u
38
+ ··· − 1.88476u − 0.758785
−0.000179801u
39
− 0.0000642943u
38
+ ··· + 1.95559u + 0.309907
a
8
=
−u
u
a
11
=
0.0000420568u
39
− 0.000112360u
38
+ ··· − 2.24245u + 0.0906996
−0.000736091u
39
+ 0.000525007u
38
+ ··· + 0.350670u − 0.790450
a
7
=
0.000166450u
39
− 0.000130525u
38
+ ··· − 1.45638u + 1.06015
0.000220629u
39
− 0.0000136383u
38
+ ··· − 0.303665u − 0.108440
a
10
=
−0.000515912u
39
+ 0.000203912u
38
+ ··· − 0.148443u − 0.735075
−0.000308939u
39
+ 0.000237175u
38
+ ··· − 0.241184u − 0.390016
a
10
=
−0.000515912u
39
+ 0.000203912u
38
+ ··· − 0.148443u − 0.735075
−0.000308939u
39
+ 0.000237175u
38
+ ··· − 0.241184u − 0.390016
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000707464u
39
− 0.00139771u
38
+ ··· − 3.97400u − 0.836131
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
40
− 2u
39
+ ··· + 14u − 1
c
2
, c
8
u
40
− u
39
+ ··· + 492u − 892
c
3
u
40
− 5u
39
+ ··· − 248u + 88
c
4
, c
10
u
40
− u
39
+ ··· − 12u + 4
c
6
u
40
− 5u
39
+ ··· + 457u + 29
c
7
u
40
− 3u
39
+ ··· − 26575u + 7349
c
9
u
40
+ 5u
39
+ ··· + 96u + 11
c
11
u
40
+ u
39
+ ··· − 1168u − 424
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
40
+ 38y
39
+ ··· − 78y + 1
c
2
, c
8
y
40
+ 63y
39
+ ··· + 6026912y + 795664
c
3
y
40
− 59y
39
+ ··· − 199840y + 7744
c
4
, c
10
y
40
− 35y
39
+ ··· + 1888y + 16
c
6
y
40
− 15y
39
+ ··· − 262383y + 841
c
7
y
40
+ 47y
39
+ ··· + 923130863y + 54007801
c
9
y
40
+ 7y
39
+ ··· − 218y + 121
c
11
y
40
+ 57y
39
+ ··· + 1150944y + 179776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972209 + 0.363644I
a = −0.691473 − 0.726212I
b = 0.246524 − 1.044100I
−1.63884 − 2.52981I −3.46896 + 4.78238I
u = −0.972209 − 0.363644I
a = −0.691473 + 0.726212I
b = 0.246524 + 1.044100I
−1.63884 + 2.52981I −3.46896 − 4.78238I
u = −0.777438 + 0.253101I
a = −0.28608 − 2.07418I
b = 0.0965200 − 0.0759702I
−0.55843 − 5.04023I 8.92316 + 6.11668I
u = −0.777438 − 0.253101I
a = −0.28608 + 2.07418I
b = 0.0965200 + 0.0759702I
−0.55843 + 5.04023I 8.92316 − 6.11668I
u = −1.028590 + 0.641044I
a = 0.812402 + 0.180660I
b = −0.05196 + 1.65626I
−6.89381 + 4.31374I −3.00921 − 2.52408I
u = −1.028590 − 0.641044I
a = 0.812402 − 0.180660I
b = −0.05196 − 1.65626I
−6.89381 − 4.31374I −3.00921 + 2.52408I
u = 1.28769
a = −1.23762
b = 1.21545
2.31916 3.45590
u = −0.004586 + 0.662077I
a = −0.110517 − 1.374950I
b = −0.440412 − 1.198770I
−6.21063 + 2.44288I −1.57019 − 3.53786I
u = −0.004586 − 0.662077I
a = −0.110517 + 1.374950I
b = −0.440412 + 1.198770I
−6.21063 − 2.44288I −1.57019 + 3.53786I
u = 0.606580 + 0.241726I
a = −0.989022 − 0.886345I
b = 0.197863 + 0.060558I
1.31470 + 0.60771I 8.49421 − 3.04989I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606580 − 0.241726I
a = −0.989022 + 0.886345I
b = 0.197863 − 0.060558I
1.31470 − 0.60771I 8.49421 + 3.04989I
u = 0.584454 + 0.231728I
a = −0.083035 + 1.313620I
b = −0.458127 + 1.196180I
−5.71740 − 6.20191I −6.05433 + 5.08780I
u = 0.584454 − 0.231728I
a = −0.083035 − 1.313620I
b = −0.458127 − 1.196180I
−5.71740 + 6.20191I −6.05433 − 5.08780I
u = −0.607336
a = 2.89129
b = −1.09842
3.09539 −9.16160
u = 0.13576 + 1.42105I
a = −0.158909 − 0.108207I
b = −0.742397 − 0.144685I
−4.59373 + 2.98825I 4.81250 − 3.01552I
u = 0.13576 − 1.42105I
a = −0.158909 + 0.108207I
b = −0.742397 + 0.144685I
−4.59373 − 2.98825I 4.81250 + 3.01552I
u = −0.292078 + 0.391717I
a = −0.559269 + 0.026373I
b = −0.768195 + 0.090718I
−2.47058 + 1.70720I 0.230221 − 0.591796I
u = −0.292078 − 0.391717I
a = −0.559269 − 0.026373I
b = −0.768195 − 0.090718I
−2.47058 − 1.70720I 0.230221 + 0.591796I
u = 0.011693 + 0.471366I
a = −0.639263 − 0.198812I
b = 0.381500 + 0.672173I
0.03644 + 1.50292I 1.25089 − 6.14683I
u = 0.011693 − 0.471366I
a = −0.639263 + 0.198812I
b = 0.381500 − 0.672173I
0.03644 − 1.50292I 1.25089 + 6.14683I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281701 + 0.359944I
a = −2.19829 − 0.09585I
b = 0.325667 + 1.141170I
−1.21242 + 1.07873I −3.63948 + 1.17826I
u = 0.281701 − 0.359944I
a = −2.19829 + 0.09585I
b = 0.325667 − 1.141170I
−1.21242 − 1.07873I −3.63948 − 1.17826I
u = −0.11719 + 1.62482I
a = 0.403686 − 0.292336I
b = −0.345255 − 0.125454I
−8.09181 − 0.67197I 0
u = −0.11719 − 1.62482I
a = 0.403686 + 0.292336I
b = −0.345255 + 0.125454I
−8.09181 + 0.67197I 0
u = 1.60181 + 1.05960I
a = 0.323648 − 0.513185I
b = 0.10749 − 1.61398I
−6.22320 + 3.43752I 0
u = 1.60181 − 1.05960I
a = 0.323648 + 0.513185I
b = 0.10749 + 1.61398I
−6.22320 − 3.43752I 0
u = −0.48768 + 1.87046I
a = 0.445879 + 1.224510I
b = −0.14644 + 1.58425I
−14.3940 − 1.3454I 0
u = −0.48768 − 1.87046I
a = 0.445879 − 1.224510I
b = −0.14644 − 1.58425I
−14.3940 + 1.3454I 0
u = −0.11349 + 1.97784I
a = 0.128360 + 1.333720I
b = −0.27705 + 1.55024I
−10.55230 − 6.76566I 0
u = −0.11349 − 1.97784I
a = 0.128360 − 1.333720I
b = −0.27705 − 1.55024I
−10.55230 + 6.76566I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00542 + 2.12395I
a = 0.124816 − 1.215410I
b = −0.28024 − 1.51688I
−9.55118 + 0.96633I 0
u = −0.00542 − 2.12395I
a = 0.124816 + 1.215410I
b = −0.28024 + 1.51688I
−9.55118 − 0.96633I 0
u = 0.21330 + 2.22331I
a = −0.0303329 + 0.0193746I
b = 1.75447 − 0.27463I
−10.09040 − 5.18311I 0
u = 0.21330 − 2.22331I
a = −0.0303329 − 0.0193746I
b = 1.75447 + 0.27463I
−10.09040 + 5.18311I 0
u = −0.79762 + 2.19173I
a = −0.440868 − 0.873034I
b = 0.84317 − 1.82666I
−14.8294 − 4.4956I 0
u = −0.79762 − 2.19173I
a = −0.440868 + 0.873034I
b = 0.84317 + 1.82666I
−14.8294 + 4.4956I 0
u = 0.56414 + 2.26378I
a = −0.363789 + 1.003570I
b = 0.63008 + 1.69717I
−16.3560 + 13.3915I 0
u = 0.56414 − 2.26378I
a = −0.363789 − 1.003570I
b = 0.63008 − 1.69717I
−16.3560 − 13.3915I 0
u = 0.75669 + 2.48566I
a = 0.256526 − 1.062360I
b = −0.13173 − 1.46303I
−12.97920 + 2.42998I 0
u = 0.75669 − 2.48566I
a = 0.256526 + 1.062360I
b = −0.13173 + 1.46303I
−12.97920 − 2.42998I 0
8
II.
I
u
2
= h−3.01 × 10
9
u
15
+ 9.33 × 10
8
u
14
+ · · · + 9.16 × 10
9
b + 4.81 × 10
9
, −1.87 ×
10
9
u
15
−2.99×10
9
u
14
+· · ·+9.16×10
9
a−2.19×10
10
, u
16
+5u
14
+· · ·+10u
2
−4i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0.204476u
15
+ 0.326221u
14
+ ··· − 0.0881222u + 2.38507
0.328253u
15
− 0.101872u
14
+ ··· + 1.42300u − 0.525371
a
1
=
0.197482u
15
− 0.179148u
14
+ ··· + 1.09215u − 1.18979
−0.196147u
15
+ 0.172594u
14
+ ··· − 1.16409u + 0.366552
a
4
=
−0.0632878u
15
− 0.0676739u
14
+ ··· − 0.398063u + 1.03749
−0.00954759u
15
+ 0.0961985u
14
+ ··· − 0.151211u + 0.663053
a
5
=
−0.123778u
15
+ 0.428093u
14
+ ··· − 1.51112u + 2.91044
0.328253u
15
− 0.101872u
14
+ ··· + 1.42300u − 0.525371
a
8
=
−u
u
a
11
=
0.197482u
15
− 0.179148u
14
+ ··· + 1.09215u − 1.18979
−0.0923248u
15
+ 0.0842185u
14
+ ··· − 0.374160u − 0.350040
a
7
=
−0.0660443u
15
+ 0.133020u
14
+ ··· − 2.18472u + 1.03736
0.0529067u
15
+ 0.140450u
14
+ ··· + 0.570148u + 0.302746
a
10
=
−0.0419856u
15
− 0.418545u
14
+ ··· + 1.04104u − 2.75923
−0.120621u
15
− 0.0702787u
14
+ ··· − 0.632997u − 0.128181
a
10
=
−0.0419856u
15
− 0.418545u
14
+ ··· + 1.04104u − 2.75923
−0.120621u
15
− 0.0702787u
14
+ ··· − 0.632997u − 0.128181
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7739992772
4580941741
u
15
+
9173770896
4580941741
u
14
+ ··· −
57525934822
4580941741
u +
47024714230
4580941741
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− u
15
+ ··· − 2u − 1
c
2
u
16
+ 5u
14
+ ··· + 10u
2
− 4
c
3
u
16
+ 8u
15
+ ··· + 12u + 8
c
4
u
16
− 6u
14
+ ··· − 14u
2
+ 4
c
5
u
16
+ u
15
+ ··· + 2u − 1
c
6
u
16
+ 2u
15
+ ··· + 11u + 1
c
7
u
16
− 2u
15
+ ··· + 13u + 1
c
8
u
16
+ 5u
14
+ ··· + 10u
2
− 4
c
9
u
16
− 6u
15
+ ··· − 2u + 1
c
10
u
16
− 6u
14
+ ··· − 14u
2
+ 4
c
11
u
16
+ 4u
14
+ ··· + 4u
2
− 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
+ 9y
15
+ ··· + 10y + 1
c
2
, c
8
y
16
+ 10y
15
+ ··· − 80y + 16
c
3
y
16
− 20y
15
+ ··· − 1168y + 64
c
4
, c
10
y
16
− 12y
15
+ ··· − 112y + 16
c
6
y
16
+ 4y
14
+ ··· − 91y + 1
c
7
y
16
+ 10y
15
+ ··· − 69y + 1
c
9
y
16
− 2y
15
+ ··· − 2y + 1
c
11
y
16
+ 8y
15
+ ··· − 8y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.044910 + 0.084383I
a = 0.057226 + 0.245893I
b = 0.361947 + 1.340670I
−4.61886 + 6.15067I 1.67402 − 4.95826I
u = −1.044910 − 0.084383I
a = 0.057226 − 0.245893I
b = 0.361947 − 1.340670I
−4.61886 − 6.15067I 1.67402 + 4.95826I
u = 0.203156 + 1.098810I
a = −0.741658 − 0.024758I
b = −0.379929 − 0.431781I
−5.56667 + 2.95635I −4.74772 − 2.75237I
u = 0.203156 − 1.098810I
a = −0.741658 + 0.024758I
b = −0.379929 + 0.431781I
−5.56667 − 2.95635I −4.74772 + 2.75237I
u = 0.701325 + 0.516464I
a = 1.021890 − 0.280960I
b = −0.299377 − 1.065240I
−0.62726 + 1.86405I 2.38240 − 3.76150I
u = 0.701325 − 0.516464I
a = 1.021890 + 0.280960I
b = −0.299377 + 1.065240I
−0.62726 − 1.86405I 2.38240 + 3.76150I
u = −0.813758
a = 2.21481
b = −1.08888
3.38602 19.6050
u = 0.752983 + 0.179131I
a = 0.79516 − 2.54506I
b = −0.050757 − 0.668728I
−1.13425 + 5.09162I −5.21325 − 6.81011I
u = 0.752983 − 0.179131I
a = 0.79516 + 2.54506I
b = −0.050757 + 0.668728I
−1.13425 − 5.09162I −5.21325 + 6.81011I
u = −0.474047 + 0.462486I
a = 1.29761 − 1.51241I
b = −0.190166 − 0.829536I
0.363930 + 0.209601I 0.372974 + 0.607008I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.474047 − 0.462486I
a = 1.29761 + 1.51241I
b = −0.190166 + 0.829536I
0.363930 − 0.209601I 0.372974 − 0.607008I
u = 1.43010
a = −1.12981
b = 1.62094
1.43155 −5.25650
u = 0.13607 + 1.51148I
a = −0.173098 − 0.201972I
b = 0.597072 − 0.748618I
−8.25349 − 1.91163I −5.00806 + 3.84199I
u = 0.13607 − 1.51148I
a = −0.173098 + 0.201972I
b = 0.597072 + 0.748618I
−8.25349 + 1.91163I −5.00806 − 3.84199I
u = −0.58274 + 2.26201I
a = −0.299629 − 1.085740I
b = 0.19518 − 1.54614I
−12.18100 − 1.94801I −0.634861 − 0.077298I
u = −0.58274 − 2.26201I
a = −0.299629 + 1.085740I
b = 0.19518 + 1.54614I
−12.18100 + 1.94801I −0.634861 + 0.077298I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− u
15
+ ··· − 2u − 1)(u
40
− 2u
39
+ ··· + 14u − 1)
c
2
(u
16
+ 5u
14
+ ··· + 10u
2
− 4)(u
40
− u
39
+ ··· + 492u − 892)
c
3
(u
16
+ 8u
15
+ ··· + 12u + 8)(u
40
− 5u
39
+ ··· − 248u + 88)
c
4
(u
16
− 6u
14
+ ··· − 14u
2
+ 4)(u
40
− u
39
+ ··· − 12u + 4)
c
5
(u
16
+ u
15
+ ··· + 2u − 1)(u
40
− 2u
39
+ ··· + 14u − 1)
c
6
(u
16
+ 2u
15
+ ··· + 11u + 1)(u
40
− 5u
39
+ ··· + 457u + 29)
c
7
(u
16
− 2u
15
+ ··· + 13u + 1)(u
40
− 3u
39
+ ··· − 26575u + 7349)
c
8
(u
16
+ 5u
14
+ ··· + 10u
2
− 4)(u
40
− u
39
+ ··· + 492u − 892)
c
9
(u
16
− 6u
15
+ ··· − 2u + 1)(u
40
+ 5u
39
+ ··· + 96u + 11)
c
10
(u
16
− 6u
14
+ ··· − 14u
2
+ 4)(u
40
− u
39
+ ··· − 12u + 4)
c
11
(u
16
+ 4u
14
+ ··· + 4u
2
− 1)(u
40
+ u
39
+ ··· − 1168u − 424)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
16
+ 9y
15
+ ··· + 10y + 1)(y
40
+ 38y
39
+ ··· − 78y + 1)
c
2
, c
8
(y
16
+ 10y
15
+ ··· − 80y + 16)
· (y
40
+ 63y
39
+ ··· + 6026912y + 795664)
c
3
(y
16
− 20y
15
+ ··· − 1168y + 64)
· (y
40
− 59y
39
+ ··· − 199840y + 7744)
c
4
, c
10
(y
16
− 12y
15
+ ··· − 112y + 16)(y
40
− 35y
39
+ ··· + 1888y + 16)
c
6
(y
16
+ 4y
14
+ ··· − 91y + 1)(y
40
− 15y
39
+ ··· − 262383y + 841)
c
7
(y
16
+ 10y
15
+ ··· − 69y + 1)
· (y
40
+ 47y
39
+ ··· + 923130863y + 54007801)
c
9
(y
16
− 2y
15
+ ··· − 2y + 1)(y
40
+ 7y
39
+ ··· − 218y + 121)
c
11
(y
16
+ 8y
15
+ ··· − 8y + 1)(y
40
+ 57y
39
+ ··· + 1150944y + 179776)
15
