11n
93
(K11n
93
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 11 3 11 7 5 8
Solving Sequence
1,5
2 3
6,8
7 11 10 9 4
c
1
c
2
c
5
c
7
c
11
c
10
c
9
c
3
c
4
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.36953 × 10
20
u
33
− 1.71275 × 10
20
u
32
+ ··· + 2.52092 × 10
19
b + 1.79272 × 10
20
,
2.14966 × 10
20
u
33
+ 2.97471 × 10
20
u
32
+ ··· + 2.52092 × 10
19
a − 2.61593 × 10
20
, u
34
+ 2u
33
+ ··· − 3u − 1i
I
u
2
= hu
10
− 3u
8
+ u
7
+ 5u
6
− u
5
− 5u
4
+ 2u
3
+ 3u
2
+ b − 1,
3u
10
+ 2u
9
− 9u
8
− 6u
7
+ 15u
6
+ 13u
5
− 13u
4
− 9u
3
+ 6u
2
+ a + 5u − 4,
u
11
+ u
10
− 3u
9
− 3u
8
+ 5u
7
+ 6u
6
− 4u
5
− 5u
4
+ 2u
3
+ 3u
2
− u − 1i
* 2 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
= h−1.37×10
20
u
33
−1.71×10
20
u
32
+· · ·+2.52×10
19
b+1.79×10
20
, 2.15×
10
20
u
33
+2.97×10
20
u
32
+· · ·+2.52×10
19
a−2.62×10
20
, u
34
+2u
33
+· · ·−3u−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
8
=
−8.52729u
33
− 11.8001u
32
+ ··· + 4.46895u + 10.3769
5.43266u
33
+ 6.79414u
32
+ ··· − 10.8889u − 7.11138
a
7
=
−5.44195u
33
− 7.75886u
32
+ ··· − 0.159734u + 6.36806
8.48937u
33
+ 10.7511u
32
+ ··· − 17.6044u − 11.3972
a
11
=
0.678159u
33
+ 0.639889u
32
+ ··· + 4.60728u + 2.39805
4.96030u
33
+ 6.55238u
32
+ ··· − 11.3046u − 7.35481
a
10
=
0.678159u
33
+ 0.639889u
32
+ ··· + 4.60728u + 2.39805
3.98582u
33
+ 5.46449u
32
+ ··· − 9.83347u − 6.63838
a
9
=
0.605729u
33
− 0.505670u
32
+ ··· − 20.5146u − 2.20921
−0.341296u
33
+ 0.0744426u
32
+ ··· + 1.81668u − 0.281935
a
4
=
4.14625u
33
+ 3.90637u
32
+ ··· − 34.9982u − 9.83659
−4.60795u
33
− 5.18060u
32
+ ··· + 10.8857u + 5.66173
a
4
=
4.14625u
33
+ 3.90637u
32
+ ··· − 34.9982u − 9.83659
−4.60795u
33
− 5.18060u
32
+ ··· + 10.8857u + 5.66173
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
45272021734023345182
25209200843466515639
u
33
−
27918280350195858852
25209200843466515639
u
32
+ ··· +
482980842236749416852
25209200843466515639
u −
268074501698973471381
25209200843466515639
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
34
+ 2u
33
+ ··· − 3u − 1
c
2
u
34
+ 20u
33
+ ··· + 23u + 1
c
3
, c
10
u
34
− u
33
+ ··· + 10u − 1
c
4
u
34
− 3u
33
+ ··· + 16u + 1
c
6
u
34
+ 2u
33
+ ··· − 2561u − 1007
c
7
u
34
+ u
33
+ ··· − 36u − 9
c
8
, c
11
u
34
− 4u
33
+ ··· + 5u − 7
c
9
u
34
− 2u
33
+ ··· − 415u + 31
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
34
− 20y
33
+ ··· − 23y + 1
c
2
y
34
− 4y
33
+ ··· − 215y + 1
c
3
, c
10
y
34
− 45y
33
+ ··· + 54y + 1
c
4
y
34
− 61y
33
+ ··· + 4y + 1
c
6
y
34
− 48y
33
+ ··· − 16050703y + 1014049
c
7
y
34
+ 11y
33
+ ··· − 576y + 81
c
8
, c
11
y
34
+ 12y
33
+ ··· − 375y + 49
c
9
y
34
− 48y
33
+ ··· − 50333y + 961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.977418 + 0.219996I
a = −0.444506 + 0.228131I
b = −1.177060 + 0.358042I
−3.42083 − 0.72607I −14.2661 + 6.0469I
u = 0.977418 − 0.219996I
a = −0.444506 − 0.228131I
b = −1.177060 − 0.358042I
−3.42083 + 0.72607I −14.2661 − 6.0469I
u = 0.573841 + 0.727686I
a = 0.107760 + 0.779562I
b = 0.238183 − 0.951299I
3.89256 − 0.89641I −5.46445 + 2.96652I
u = 0.573841 − 0.727686I
a = 0.107760 − 0.779562I
b = 0.238183 + 0.951299I
3.89256 + 0.89641I −5.46445 − 2.96652I
u = −1.000090 + 0.396450I
a = 0.995356 + 0.586804I
b = 0.091298 − 0.895598I
−0.300266 + 0.779117I −12.61952 − 0.14976I
u = −1.000090 − 0.396450I
a = 0.995356 − 0.586804I
b = 0.091298 + 0.895598I
−0.300266 − 0.779117I −12.61952 + 0.14976I
u = −0.878110 + 0.672399I
a = 0.639488 + 0.722914I
b = −0.282345 − 0.793763I
−0.041134 + 0.639337I −11.81438 + 0.98279I
u = −0.878110 − 0.672399I
a = 0.639488 − 0.722914I
b = −0.282345 + 0.793763I
−0.041134 − 0.639337I −11.81438 − 0.98279I
u = −0.300493 + 1.118760I
a = −0.628604 − 1.104010I
b = 0.708856 + 1.113100I
−5.84181 − 6.21635I −10.71032 + 3.59890I
u = −0.300493 − 1.118760I
a = −0.628604 + 1.104010I
b = 0.708856 − 1.113100I
−5.84181 + 6.21635I −10.71032 − 3.59890I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.953057 + 0.668360I
a = −0.53608 − 1.54146I
b = −0.645636 + 0.835280I
−0.43138 + 4.55558I −13.3660 − 5.8441I
u = −0.953057 − 0.668360I
a = −0.53608 + 1.54146I
b = −0.645636 − 0.835280I
−0.43138 − 4.55558I −13.3660 + 5.8441I
u = 1.031700 + 0.655009I
a = 0.830682 − 0.780653I
b = 0.594629 + 0.693125I
2.55533 − 4.41329I −7.45627 + 1.89093I
u = 1.031700 − 0.655009I
a = 0.830682 + 0.780653I
b = 0.594629 − 0.693125I
2.55533 + 4.41329I −7.45627 − 1.89093I
u = −1.192910 + 0.280924I
a = −0.484338 + 0.191067I
b = −0.644248 + 0.614710I
−0.99260 + 2.94608I −14.2242 − 4.1884I
u = −1.192910 − 0.280924I
a = −0.484338 − 0.191067I
b = −0.644248 − 0.614710I
−0.99260 − 2.94608I −14.2242 + 4.1884I
u = 1.163230 + 0.443799I
a = 0.54848 − 1.89291I
b = 0.592978 + 1.071570I
−10.91160 − 3.58899I −13.7786 + 3.7180I
u = 1.163230 − 0.443799I
a = 0.54848 + 1.89291I
b = 0.592978 − 1.071570I
−10.91160 + 3.58899I −13.7786 − 3.7180I
u = −0.739045 + 0.052216I
a = −0.93579 − 1.67559I
b = −0.394062 + 1.339380I
1.56826 + 1.68408I −13.99827 − 0.91587I
u = −0.739045 − 0.052216I
a = −0.93579 + 1.67559I
b = −0.394062 − 1.339380I
1.56826 − 1.68408I −13.99827 + 0.91587I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.162070 + 0.498975I
a = −0.258485 − 0.047341I
b = 1.31485 + 0.79996I
−10.50350 + 4.65202I −13.9876 − 3.4886I
u = −1.162070 − 0.498975I
a = −0.258485 + 0.047341I
b = 1.31485 − 0.79996I
−10.50350 − 4.65202I −13.9876 + 3.4886I
u = 1.183220 + 0.495063I
a = −0.910271 + 1.014240I
b = −0.63178 − 1.27610I
−0.32497 − 7.07104I −12.7900 + 6.5034I
u = 1.183220 − 0.495063I
a = −0.910271 − 1.014240I
b = −0.63178 + 1.27610I
−0.32497 + 7.07104I −12.7900 − 6.5034I
u = 0.182031 + 0.670224I
a = 0.59393 − 1.62022I
b = −0.306134 + 1.218490I
2.61338 + 2.54071I −8.06134 − 4.21753I
u = 0.182031 − 0.670224I
a = 0.59393 + 1.62022I
b = −0.306134 − 1.218490I
2.61338 − 2.54071I −8.06134 + 4.21753I
u = −0.158687 + 0.575572I
a = 0.27697 + 2.86042I
b = 0.950893 − 0.442875I
−7.71465 − 0.24390I −10.88322 − 1.02866I
u = −0.158687 − 0.575572I
a = 0.27697 − 2.86042I
b = 0.950893 + 0.442875I
−7.71465 + 0.24390I −10.88322 + 1.02866I
u = −1.27133 + 0.67164I
a = 0.65445 + 1.29088I
b = 0.91249 − 1.24105I
−8.8655 + 12.5839I −13.0129 − 6.3971I
u = −1.27133 − 0.67164I
a = 0.65445 − 1.29088I
b = 0.91249 + 1.24105I
−8.8655 − 12.5839I −13.0129 + 6.3971I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55789 + 0.27506I
a = −0.265249 − 0.006903I
b = 0.571671 − 0.692974I
−12.18800 + 1.09324I −11.00000 − 4.94776I
u = 1.55789 − 0.27506I
a = −0.265249 + 0.006903I
b = 0.571671 + 0.692974I
−12.18800 − 1.09324I −11.00000 + 4.94776I
u = −0.331451
a = 1.15110
b = −0.282626
−0.627282 −15.7510
u = 0.304363
a = −8.51870
b = 0.493445
−7.76994 −5.58750
8
II.
I
u
2
= hu
10
− 3u
8
+ · · · + b − 1, 3u
10
+ 2u
9
+ · · · + a − 4, u
11
+ u
10
+ · · · − u − 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
8
=
−3u
10
− 2u
9
+ 9u
8
+ 6u
7
− 15u
6
− 13u
5
+ 13u
4
+ 9u
3
− 6u
2
− 5u + 4
−u
10
+ 3u
8
− u
7
− 5u
6
+ u
5
+ 5u
4
− 2u
3
− 3u
2
+ 1
a
7
=
−2u
10
− u
9
+ 6u
8
+ 3u
7
− 10u
6
− 7u
5
+ 9u
4
+ 5u
3
− 4u
2
− 4u + 3
−u
10
+ 3u
8
− u
7
− 5u
6
+ u
5
+ 5u
4
− 3u
3
− 3u
2
+ u + 1
a
11
=
2u
10
+ u
9
− 6u
8
− 2u
7
+ 10u
6
+ 4u
5
− 9u
4
− u
3
+ 5u
2
+ u − 3
−u
8
− u
7
+ 3u
6
+ 2u
5
− 5u
4
− 3u
3
+ 3u
2
+ u − 1
a
10
=
2u
10
+ u
9
− 6u
8
− 2u
7
+ 10u
6
+ 4u
5
− 9u
4
− u
3
+ 5u
2
+ u − 3
−u
10
− u
9
+ 2u
8
+ 2u
7
− 2u
6
− 3u
5
− u
4
+ u
2
a
9
=
−4u
10
− 2u
9
+ ··· − 6u + 7
−u
10
− u
9
+ 2u
8
+ 2u
7
− 2u
6
− 4u
5
− u
4
+ 2u
3
+ u
2
− 2u
a
4
=
6u
10
+ 2u
9
− 19u
8
− 5u
7
+ 32u
6
+ 14u
5
− 31u
4
− 8u
3
+ 15u
2
+ 7u − 9
2u
10
+ u
9
− 7u
8
− 2u
7
+ 13u
6
+ 4u
5
− 13u
4
− 2u
3
+ 9u
2
+ u − 3
a
4
=
6u
10
+ 2u
9
− 19u
8
− 5u
7
+ 32u
6
+ 14u
5
− 31u
4
− 8u
3
+ 15u
2
+ 7u − 9
2u
10
+ u
9
− 7u
8
− 2u
7
+ 13u
6
+ 4u
5
− 13u
4
− 2u
3
+ 9u
2
+ u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 10u
10
+ 2u
9
− 35u
8
− 4u
7
+ 63u
6
+ 16u
5
− 67u
4
− 11u
3
+ 40u
2
+ 11u − 30
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ u
10
− 3u
9
− 3u
8
+ 5u
7
+ 6u
6
− 4u
5
− 5u
4
+ 2u
3
+ 3u
2
− u − 1
c
2
u
11
+ 7u
10
+ ··· + 7u + 1
c
3
u
11
− 6u
9
− u
8
+ 14u
7
+ 3u
6
− 18u
5
− 4u
4
+ 12u
3
+ 3u
2
− 4u − 1
c
4
u
11
− 4u
10
+ ··· − 10u + 1
c
5
u
11
− u
10
− 3u
9
+ 3u
8
+ 5u
7
− 6u
6
− 4u
5
+ 5u
4
+ 2u
3
− 3u
2
− u + 1
c
6
u
11
+ u
10
− u
9
+ 4u
8
− 4u
7
+ u
6
+ 4u
5
− 9u
4
+ 9u
3
− 7u
2
+ 3u − 1
c
7
u
11
+ 4u
9
− u
8
+ 5u
7
− 3u
6
− 3u
4
− 5u
3
− 2u
2
− 4u − 1
c
8
u
11
− 3u
10
+ 7u
9
− 9u
8
+ 9u
7
− 4u
6
− u
5
+ 4u
4
− 4u
3
+ u
2
− u − 1
c
9
u
11
+ 3u
10
+ u
9
+ 3u
7
+ u
5
− u
4
− u
3
+ 2u
2
− u + 1
c
10
u
11
− 6u
9
+ u
8
+ 14u
7
− 3u
6
− 18u
5
+ 4u
4
+ 12u
3
− 3u
2
− 4u + 1
c
11
u
11
+ 3u
10
+ 7u
9
+ 9u
8
+ 9u
7
+ 4u
6
− u
5
− 4u
4
− 4u
3
− u
2
− u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
11
− 7y
10
+ ··· + 7y −1
c
2
y
11
+ y
10
+ ··· + 3y −1
c
3
, c
10
y
11
− 12y
10
+ ··· + 22y −1
c
4
y
11
− 4y
10
+ ··· + 16y −1
c
6
y
11
− 3y
10
+ ··· − 5y −1
c
7
y
11
+ 8y
10
+ ··· + 12y −1
c
8
, c
11
y
11
+ 5y
10
+ ··· + 3y −1
c
9
y
11
− 7y
10
+ 7y
9
+ 8y
8
+ 15y
7
− 10y
6
− 13y
5
− 9y
4
+ 3y
3
− 3y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699469 + 0.611146I
a = 0.428957 + 0.652621I
b = −0.620153 − 1.221950I
3.01958 − 0.56743I −9.71824 − 0.39336I
u = −0.699469 − 0.611146I
a = 0.428957 − 0.652621I
b = −0.620153 + 1.221950I
3.01958 + 0.56743I −9.71824 + 0.39336I
u = 0.875804
a = −0.670673
b = −1.06635
−3.03217 −10.2530
u = −1.006850 + 0.637757I
a = −0.820799 − 1.074540I
b = −0.831904 + 0.975863I
2.01933 + 5.51593I −10.60882 − 6.86396I
u = −1.006850 − 0.637757I
a = −0.820799 + 1.074540I
b = −0.831904 − 0.975863I
2.01933 − 5.51593I −10.60882 + 6.86396I
u = 0.626035 + 0.508829I
a = 0.12930 + 1.93949I
b = −0.138001 − 1.197500I
2.51249 − 2.42581I −7.49749 + 5.02500I
u = 0.626035 − 0.508829I
a = 0.12930 − 1.93949I
b = −0.138001 + 1.197500I
2.51249 + 2.42581I −7.49749 − 5.02500I
u = 1.163860 + 0.576096I
a = 0.961303 − 0.429407I
b = 0.036813 + 0.809877I
0.66663 − 2.01787I −8.86455 + 3.07109I
u = 1.163860 − 0.576096I
a = 0.961303 + 0.429407I
b = 0.036813 − 0.809877I
0.66663 + 2.01787I −8.86455 − 3.07109I
u = −0.580365
a = 4.86388
b = 0.747290
−8.15261 −27.3410
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46259
a = −0.590722
b = 0.425554
−11.8310 −12.0270
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ u
10
− 3u
9
− 3u
8
+ 5u
7
+ 6u
6
− 4u
5
− 5u
4
+ 2u
3
+ 3u
2
− u − 1)
· (u
34
+ 2u
33
+ ··· − 3u − 1)
c
2
(u
11
+ 7u
10
+ ··· + 7u + 1)(u
34
+ 20u
33
+ ··· + 23u + 1)
c
3
(u
11
− 6u
9
− u
8
+ 14u
7
+ 3u
6
− 18u
5
− 4u
4
+ 12u
3
+ 3u
2
− 4u − 1)
· (u
34
− u
33
+ ··· + 10u − 1)
c
4
(u
11
− 4u
10
+ ··· − 10u + 1)(u
34
− 3u
33
+ ··· + 16u + 1)
c
5
(u
11
− u
10
− 3u
9
+ 3u
8
+ 5u
7
− 6u
6
− 4u
5
+ 5u
4
+ 2u
3
− 3u
2
− u + 1)
· (u
34
+ 2u
33
+ ··· − 3u − 1)
c
6
(u
11
+ u
10
− u
9
+ 4u
8
− 4u
7
+ u
6
+ 4u
5
− 9u
4
+ 9u
3
− 7u
2
+ 3u − 1)
· (u
34
+ 2u
33
+ ··· − 2561u − 1007)
c
7
(u
11
+ 4u
9
− u
8
+ 5u
7
− 3u
6
− 3u
4
− 5u
3
− 2u
2
− 4u − 1)
· (u
34
+ u
33
+ ··· − 36u − 9)
c
8
(u
11
− 3u
10
+ 7u
9
− 9u
8
+ 9u
7
− 4u
6
− u
5
+ 4u
4
− 4u
3
+ u
2
− u − 1)
· (u
34
− 4u
33
+ ··· + 5u − 7)
c
9
(u
11
+ 3u
10
+ u
9
+ 3u
7
+ u
5
− u
4
− u
3
+ 2u
2
− u + 1)
· (u
34
− 2u
33
+ ··· − 415u + 31)
c
10
(u
11
− 6u
9
+ u
8
+ 14u
7
− 3u
6
− 18u
5
+ 4u
4
+ 12u
3
− 3u
2
− 4u + 1)
· (u
34
− u
33
+ ··· + 10u − 1)
c
11
(u
11
+ 3u
10
+ 7u
9
+ 9u
8
+ 9u
7
+ 4u
6
− u
5
− 4u
4
− 4u
3
− u
2
− u + 1)
· (u
34
− 4u
33
+ ··· + 5u − 7)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
11
− 7y
10
+ ··· + 7y −1)(y
34
− 20y
33
+ ··· − 23y + 1)
c
2
(y
11
+ y
10
+ ··· + 3y −1)(y
34
− 4y
33
+ ··· − 215y + 1)
c
3
, c
10
(y
11
− 12y
10
+ ··· + 22y −1)(y
34
− 45y
33
+ ··· + 54y + 1)
c
4
(y
11
− 4y
10
+ ··· + 16y −1)(y
34
− 61y
33
+ ··· + 4y + 1)
c
6
(y
11
− 3y
10
+ ··· − 5y −1)
· (y
34
− 48y
33
+ ··· − 16050703y + 1014049)
c
7
(y
11
+ 8y
10
+ ··· + 12y −1)(y
34
+ 11y
33
+ ··· − 576y + 81)
c
8
, c
11
(y
11
+ 5y
10
+ ··· + 3y −1)(y
34
+ 12y
33
+ ··· − 375y + 49)
c
9
(y
11
− 7y
10
+ 7y
9
+ 8y
8
+ 15y
7
− 10y
6
− 13y
5
− 9y
4
+ 3y
3
− 3y −1)
· (y
34
− 48y
33
+ ··· − 50333y + 961)
15
