11n
11
(K11n
11
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 10 3 11 1 7 9
Solving Sequence
1,9 3,10
2 11 8 4 5 6 7
c
9
c
2
c
11
c
8
c
3
c
4
c
5
c
7
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.47912 × 10
16
u
30
− 9.15523 × 10
16
u
29
+ ··· + 4.49053 × 10
16
b − 7.04624 × 10
16
,
9.09026 × 10
16
u
30
+ 2.68470 × 10
17
u
29
+ ··· + 8.98106 × 10
16
a − 6.04967 × 10
16
, u
31
+ 3u
30
+ ··· − 2u − 1i
I
u
2
= hau + b, a
2
+ au + a + u + 2, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 35 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−1.48×10
16
u
30
−9.16×10
16
u
29
+· · ·+4.49×10
16
b−7.05×10
16
, 9.09×
10
16
u
30
+2.68×10
17
u
29
+· · ·+8.98×10
16
a−6.05×10
16
, u
31
+3u
30
+· · ·−2u−1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
3
=
−1.01216u
30
− 2.98929u
29
+ ··· + 1.56951u + 0.673603
0.329386u
30
+ 2.03879u
29
+ ··· + 4.20243u + 1.56913
a
10
=
1
u
2
a
2
=
−1.01216u
30
− 2.98929u
29
+ ··· + 1.56951u + 0.673603
0.286170u
30
+ 2.18539u
29
+ ··· + 5.12021u + 1.52195
a
11
=
u
u
a
8
=
−u
2
+ 1
−u
2
a
4
=
−1.10717u
30
− 3.23912u
29
+ ··· + 2.61916u + 1.31094
0.286732u
30
+ 2.01767u
29
+ ··· + 4.39808u + 1.64078
a
5
=
−0.337359u
30
− 1.17932u
29
+ ··· − 1.54516u − 1.51176
0.771351u
30
+ 3.37765u
29
+ ··· + 4.57039u + 1.23084
a
6
=
0.366419u
30
+ 0.837409u
29
+ ··· − 2.16675u + 1.16374
0.563901u
30
+ 2.05823u
29
+ ··· − 0.204628u + 0.0803200
a
7
=
0.0898867u
30
+ 0.521942u
29
+ ··· + 2.11940u − 0.821574
−0.252282u
30
− 0.960869u
29
+ ··· + 0.641800u − 0.0898867
a
7
=
0.0898867u
30
+ 0.521942u
29
+ ··· + 2.11940u − 0.821574
−0.252282u
30
− 0.960869u
29
+ ··· + 0.641800u − 0.0898867
(ii) Obstruction class = −1
(iii) Cusp Shapes =
395916855656835617
89810629950487196
u
30
+
295100668624657463
22452657487621799
u
29
+···+
1130836942834652079
89810629950487196
u+
259777290233574227
44905314975243598
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
31
+ 3u
30
+ ··· + 8u − 1
c
2
u
31
+ 9u
30
+ ··· + 60u − 1
c
3
, c
7
u
31
+ 3u
30
+ ··· + 112u + 16
c
5
u
31
− 3u
30
+ ··· + 4454u − 977
c
6
, c
10
u
31
+ 3u
30
+ ··· − 2u
2
+ 1
c
8
, c
9
, c
11
u
31
− 3u
30
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
31
+ 9y
30
+ ··· + 60y −1
c
2
y
31
+ 29y
30
+ ··· + 5084y −1
c
3
, c
7
y
31
− 25y
30
+ ··· + 1152y −256
c
5
y
31
+ 49y
30
+ ··· + 44552308y −954529
c
6
, c
10
y
31
− 3y
30
+ ··· + 4y −1
c
8
, c
9
, c
11
y
31
− 23y
30
+ ··· + 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931324 + 0.285581I
a = 0.99198 − 1.54847I
b = 0.81708 − 1.15583I
0.02246 + 4.44381I −1.53825 − 8.61147I
u = −0.931324 − 0.285581I
a = 0.99198 + 1.54847I
b = 0.81708 + 1.15583I
0.02246 − 4.44381I −1.53825 + 8.61147I
u = −0.094951 + 1.070970I
a = 1.345330 − 0.258911I
b = 0.0113180 + 0.1250270I
7.95570 − 0.85651I 0.056335 − 0.135364I
u = −0.094951 − 1.070970I
a = 1.345330 + 0.258911I
b = 0.0113180 − 0.1250270I
7.95570 + 0.85651I 0.056335 + 0.135364I
u = 0.912773 + 0.075536I
a = −0.542493 − 0.971836I
b = −0.20963 + 2.46157I
−1.30863 − 2.18648I −32.4747 − 4.2586I
u = 0.912773 − 0.075536I
a = −0.542493 + 0.971836I
b = −0.20963 − 2.46157I
−1.30863 + 2.18648I −32.4747 + 4.2586I
u = 0.039656 + 1.102600I
a = −1.49064 + 0.23083I
b = −0.1140800 − 0.0213786I
7.38206 − 7.22461I −1.02588 + 4.93399I
u = 0.039656 − 1.102600I
a = −1.49064 − 0.23083I
b = −0.1140800 + 0.0213786I
7.38206 + 7.22461I −1.02588 − 4.93399I
u = 1.193910 + 0.091335I
a = −0.565824 − 0.262901I
b = −1.10325 − 1.58386I
−2.79337 − 1.66318I −5.72575 + 2.19283I
u = 1.193910 − 0.091335I
a = −0.565824 + 0.262901I
b = −1.10325 + 1.58386I
−2.79337 + 1.66318I −5.72575 − 2.19283I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.168090 + 0.283606I
a = 1.41177 − 0.15034I
b = 2.29367 − 0.71716I
−4.01618 + 5.37811I −8.38800 − 7.62748I
u = −1.168090 − 0.283606I
a = 1.41177 + 0.15034I
b = 2.29367 + 0.71716I
−4.01618 − 5.37811I −8.38800 + 7.62748I
u = 0.779230
a = 0.0180125
b = 0.854641
−1.12597 −9.35890
u = 0.623364 + 0.404541I
a = −0.331674 + 0.339809I
b = 0.348918 + 0.935748I
−1.47821 − 0.10102I −8.24537 + 0.31125I
u = 0.623364 − 0.404541I
a = −0.331674 − 0.339809I
b = 0.348918 − 0.935748I
−1.47821 + 0.10102I −8.24537 − 0.31125I
u = −0.679882 + 0.287551I
a = −0.567508 − 1.103750I
b = −1.142870 − 0.115620I
1.58742 + 1.54591I 2.94722 − 4.18501I
u = −0.679882 − 0.287551I
a = −0.567508 + 1.103750I
b = −1.142870 + 0.115620I
1.58742 − 1.54591I 2.94722 + 4.18501I
u = −1.287250 + 0.574250I
a = −0.687751 + 0.701116I
b = −1.54338 + 1.46018I
4.28029 + 6.65397I −2.65676 − 3.57953I
u = −1.287250 − 0.574250I
a = −0.687751 − 0.701116I
b = −1.54338 − 1.46018I
4.28029 − 6.65397I −2.65676 + 3.57953I
u = 1.33715 + 0.61035I
a = 0.347578 + 0.887087I
b = 0.72674 + 1.60463I
3.39903 + 1.19447I −2.39419 − 1.64836I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33715 − 0.61035I
a = 0.347578 − 0.887087I
b = 0.72674 − 1.60463I
3.39903 − 1.19447I −2.39419 + 1.64836I
u = −1.37851 + 0.54460I
a = 0.783190 − 0.923039I
b = 1.65294 − 1.72229I
2.96987 + 13.05180I −4.52638 − 7.60952I
u = −1.37851 − 0.54460I
a = 0.783190 + 0.923039I
b = 1.65294 + 1.72229I
2.96987 − 13.05180I −4.52638 + 7.60952I
u = 1.42534 + 0.52079I
a = −0.471444 − 0.858825I
b = −0.80212 − 1.62813I
3.19514 − 4.83034I −3.00000 + 3.70838I
u = 1.42534 − 0.52079I
a = −0.471444 + 0.858825I
b = −0.80212 + 1.62813I
3.19514 + 4.83034I −3.00000 − 3.70838I
u = −0.391432 + 0.273361I
a = −1.45745 + 1.61435I
b = −0.617930 + 0.788394I
1.30059 − 1.62044I 1.54713 + 2.13328I
u = −0.391432 − 0.273361I
a = −1.45745 − 1.61435I
b = −0.617930 − 0.788394I
1.30059 + 1.62044I 1.54713 − 2.13328I
u = −1.60218 + 0.05522I
a = 0.288465 − 0.371859I
b = 0.245136 − 0.318071I
−9.04764 + 1.61419I −11.37069 + 6.82904I
u = −1.60218 − 0.05522I
a = 0.288465 + 0.371859I
b = 0.245136 + 0.318071I
−9.04764 − 1.61419I −11.37069 − 6.82904I
u = 0.111818 + 0.363270I
a = −2.56254 + 1.50290I
b = 0.510148 + 0.337379I
−0.54852 − 2.74241I −0.76165 + 6.33975I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111818 − 0.363270I
a = −2.56254 − 1.50290I
b = 0.510148 − 0.337379I
−0.54852 + 2.74241I −0.76165 − 6.33975I
8
II. I
u
2
= hau + b, a
2
+ au + a + u + 2, u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
3
=
a
−au
a
10
=
1
−u + 1
a
2
=
a
−a
a
11
=
u
u
a
8
=
u
u − 1
a
4
=
a
−au
a
5
=
a + u + 1
−au − u − 1
a
6
=
0
−u
a
7
=
u
u − 1
a
7
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7au + 6a + 3u − 5
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
7
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
8
, c
9
(u
2
+ u − 1)
2
c
10
, c
11
(u
2
− u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
7
y
4
c
6
, c
8
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.80902 + 1.40126I
b = 0.500000 − 0.866025I
−0.98696 + 2.02988I −4.50000 + 2.34537I
u = 0.618034
a = −0.80902 − 1.40126I
b = 0.500000 + 0.866025I
−0.98696 − 2.02988I −4.50000 − 2.34537I
u = −1.61803
a = 0.309017 + 0.535233I
b = 0.500000 + 0.866025I
−8.88264 − 2.02988I −4.50000 + 9.27358I
u = −1.61803
a = 0.309017 − 0.535233I
b = 0.500000 − 0.866025I
−8.88264 + 2.02988I −4.50000 − 9.27358I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
31
+ 3u
30
+ ··· + 8u − 1)
c
2
((u
2
+ u + 1)
2
)(u
31
+ 9u
30
+ ··· + 60u − 1)
c
3
, c
7
u
4
(u
31
+ 3u
30
+ ··· + 112u + 16)
c
4
((u
2
− u + 1)
2
)(u
31
+ 3u
30
+ ··· + 8u − 1)
c
5
((u
2
+ u + 1)
2
)(u
31
− 3u
30
+ ··· + 4454u − 977)
c
6
((u
2
+ u − 1)
2
)(u
31
+ 3u
30
+ ··· − 2u
2
+ 1)
c
8
, c
9
((u
2
+ u − 1)
2
)(u
31
− 3u
30
+ ··· − 2u + 1)
c
10
((u
2
− u − 1)
2
)(u
31
+ 3u
30
+ ··· − 2u
2
+ 1)
c
11
((u
2
− u − 1)
2
)(u
31
− 3u
30
+ ··· − 2u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
31
+ 9y
30
+ ··· + 60y −1)
c
2
((y
2
+ y + 1)
2
)(y
31
+ 29y
30
+ ··· + 5084y −1)
c
3
, c
7
y
4
(y
31
− 25y
30
+ ··· + 1152y −256)
c
5
((y
2
+ y + 1)
2
)(y
31
+ 49y
30
+ ··· + 4.45523 × 10
7
y −954529)
c
6
, c
10
((y
2
− 3y + 1)
2
)(y
31
− 3y
30
+ ··· + 4y −1)
c
8
, c
9
, c
11
((y
2
− 3y + 1)
2
)(y
31
− 23y
30
+ ··· + 4y −1)
14
