11n
180
(K11n
180
)
A knot diagram
1
Linearized knot diagam
6 8 1 9 10 1 4 2 5 4 8
Solving Sequence
1,4 3,8
2 9 7 6 11 10 5
c
3
c
2
c
8
c
7
c
6
c
11
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
15
− 51u
14
+ ··· + 4b − 164, −41u
15
+ 460u
14
+ ··· + 32a + 944, u
16
− 12u
15
+ ··· − 360u
2
+ 32i
I
u
2
= hu
8
+ 2u
7
+ 3u
2
+ b + 1, −u
8
− 2u
7
+ u
6
+ 2u
5
− u
4
− 2u
3
− 2u
2
+ a + u,
u
9
+ 3u
8
+ u
7
− 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 1i
I
u
3
= h39a
9
u − 16a
8
u + ··· + 108a + 311, a
9
u + 8a
8
u + ··· − 58a + 53, u
2
+ u − 1i
* 3 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
= h4u
15
− 51u
14
+ · · · + 4b − 164, −41u
15
+ 460u
14
+ · · · + 32a +
944, u
16
− 12u
15
+ · · · − 360u
2
+ 32i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
41
32
u
15
−
115
8
u
14
+ ··· − 17u −
59
2
−u
15
+
51
4
u
14
+ ··· +
59
2
u + 41
a
2
=
−
1
32
u
15
+
5
16
u
14
+ ··· −
45
8
u
2
+ 1
1
16
u
15
−
5
8
u
14
+ ··· +
41
4
u
2
− 1
a
9
=
7
16
u
15
−
51
16
u
14
+ ··· +
47
4
u +
15
2
−
101
16
u
15
+
519
8
u
14
+ ··· +
79
2
u + 102
a
7
=
9
32
u
15
−
13
8
u
14
+ ··· +
25
2
u +
23
2
−u
15
+
51
4
u
14
+ ··· +
59
2
u + 41
a
6
=
9
32
u
15
−
13
8
u
14
+ ··· +
25
2
u +
23
2
−
11
2
u
15
+ 58u
14
+ ··· +
77
2
u + 97
a
11
=
−
31
32
u
15
+
171
16
u
14
+ ··· + 31u + 31
15
16
u
15
−
83
8
u
14
+ ··· − 30u − 31
a
10
=
−
1
32
u
15
+
5
16
u
14
+ ··· −
45
8
u
2
+ u
15
16
u
15
−
83
8
u
14
+ ··· − 30u − 31
a
5
=
−
33
16
u
15
+
41
2
u
14
+ ··· + u + 26
11
4
u
15
−
223
8
u
14
+ ··· − 11u − 40
a
5
=
−
33
16
u
15
+
41
2
u
14
+ ··· + u + 26
11
4
u
15
−
223
8
u
14
+ ··· − 11u − 40
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
15
+ 56u
14
− 242u
13
+ 661u
12
− 1316u
11
+ 2028u
10
−
2382u
9
+ 1918u
8
− 581u
7
− 1069u
6
+ 2137u
5
− 2069u
4
+ 1166u
3
− 265u
2
− 60u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
16
+ 3u
14
+ ··· − 3u − 1
c
3
u
16
− 12u
15
+ ··· − 360u
2
+ 32
c
4
, c
5
, c
9
u
16
− 5u
15
+ ··· − 10u − 4
c
7
, c
11
u
16
+ u
15
+ ··· − 4u − 1
c
10
u
16
+ 15u
15
+ ··· + 1722u + 196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
16
+ 6y
15
+ ··· − 5y + 1
c
3
y
16
− 10y
15
+ ··· − 23040y + 1024
c
4
, c
5
, c
9
y
16
− 15y
15
+ ··· − 140y + 16
c
7
, c
11
y
16
− 27y
15
+ ··· − 36y + 1
c
10
y
16
− 3y
15
+ ··· − 394156y + 38416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937606
a = −0.432873
b = −0.405864
−5.72940 −16.4540
u = 0.646210 + 0.969563I
a = −0.294430 + 0.642409I
b = 0.813119 − 0.129662I
−0.44623 − 2.35749I −11.39443 + 1.24540I
u = 0.646210 − 0.969563I
a = −0.294430 − 0.642409I
b = 0.813119 + 0.129662I
−0.44623 + 2.35749I −11.39443 − 1.24540I
u = 0.132048 + 1.204660I
a = 0.014404 − 0.499826I
b = −0.604023 + 0.048649I
2.97261 + 1.81783I −9.12623 − 4.02809I
u = 0.132048 − 1.204660I
a = 0.014404 + 0.499826I
b = −0.604023 − 0.048649I
2.97261 − 1.81783I −9.12623 + 4.02809I
u = 1.312260 + 0.342243I
a = 1.36980 − 0.44221I
b = −1.94888 + 0.11150I
−11.54010 − 0.83768I −14.6260 + 5.7551I
u = 1.312260 − 0.342243I
a = 1.36980 + 0.44221I
b = −1.94888 − 0.11150I
−11.54010 + 0.83768I −14.6260 − 5.7551I
u = −0.27007 + 1.38948I
a = 0.071515 + 0.368633I
b = 0.531520 + 0.000186I
−1.44057 + 5.86096I −14.3345 − 7.4758I
u = −0.27007 − 1.38948I
a = 0.071515 − 0.368633I
b = 0.531520 − 0.000186I
−1.44057 − 5.86096I −14.3345 + 7.4758I
u = 1.45999 + 0.54919I
a = −1.051980 + 0.234978I
b = 1.66492 + 0.23467I
−3.42042 − 3.44951I −11.26032 + 2.20716I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45999 − 0.54919I
a = −1.051980 − 0.234978I
b = 1.66492 − 0.23467I
−3.42042 + 3.44951I −11.26032 − 2.20716I
u = 1.61124 + 0.53845I
a = 1.041830 − 0.051732I
b = −1.70649 − 0.47762I
−2.13858 − 8.47484I −10.02725 + 6.22402I
u = 1.61124 − 0.53845I
a = 1.041830 + 0.051732I
b = −1.70649 + 0.47762I
−2.13858 + 8.47484I −10.02725 − 6.22402I
u = 1.68493 + 0.47840I
a = −1.090820 − 0.055715I
b = 1.81129 + 0.61572I
−7.9978 − 12.6965I −13.6924 + 6.6132I
u = 1.68493 − 0.47840I
a = −1.090820 + 0.055715I
b = 1.81129 − 0.61572I
−7.9978 + 12.6965I −13.6924 − 6.6132I
u = −0.215621
a = 1.31222
b = 0.282943
−0.531160 −18.6230
6
II. I
u
2
= hu
8
+ 2u
7
+ 3u
2
+ b + 1, −u
8
− 2u
7
+ · · · + a + u, u
9
+ 3u
8
+ u
7
−
2u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
−u
2
a
8
=
u
8
+ 2u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
+ 2u
2
− u
−u
8
− 2u
7
− 3u
2
− 1
a
2
=
−u
8
− 3u
7
− u
6
+ 2u
5
− u
4
− 2u
3
− 2u
2
− 2u + 1
−u
2
+ 1
a
9
=
u
8
+ 3u
7
+ 2u
6
− u
5
− 2u
4
+ u
3
+ 4u
2
+ u + 1
u
7
+ 2u
6
− u
5
− u
4
+ 2u
3
+ u
a
7
=
−u
6
− 2u
5
+ u
4
+ 2u
3
− u
2
− u − 1
−u
8
− 2u
7
− 3u
2
− 1
a
6
=
−u
6
− 2u
5
+ u
4
+ 2u
3
− u
2
− u − 1
−u
6
− 2u
5
+ u
4
+ u
3
− 2u
2
− 1
a
11
=
u
7
+ 2u
6
− u
5
− u
4
+ 2u
3
+ 2u
u
8
+ 2u
7
− u
6
− u
5
+ 2u
4
+ 2u
2
+ u
a
10
=
u
8
+ 3u
7
+ u
6
− 2u
5
+ u
4
+ 2u
3
+ 2u
2
+ 3u
u
8
+ 2u
7
− u
6
− u
5
+ 2u
4
+ 2u
2
+ u
a
5
=
−u
8
− 2u
7
+ u
6
+ u
5
− 2u
4
+ u
3
− u
u
8
+ 2u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
+ 2u
2
− u + 1
a
5
=
−u
8
− 2u
7
+ u
6
+ u
5
− 2u
4
+ u
3
− u
u
8
+ 2u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
+ 2u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
8
− 9u
7
+ 3u
6
+ 10u
5
− 5u
4
− 5u
3
− 4u
2
− 2u − 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
9
+ 3u
7
+ u
6
+ 2u
5
+ 2u
4
− u
3
+ u
2
− u − 1
c
2
, c
6
u
9
+ 3u
7
− u
6
+ 2u
5
− 2u
4
− u
3
− u
2
− u + 1
c
3
u
9
+ 3u
8
+ u
7
− 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 1
c
4
, c
5
u
9
− 5u
7
+ 8u
5
+ u
4
− 3u
3
− 2u
2
− 2u + 1
c
7
, c
11
u
9
− u
8
− u
7
− u
6
− 2u
5
+ 2u
4
− u
3
+ 3u
2
+ 1
c
9
u
9
− 5u
7
+ 8u
5
− u
4
− 3u
3
+ 2u
2
− 2u − 1
c
10
u
9
− u
7
+ 8u
6
− 4u
5
+ 5u
4
− 2u
3
+ 3u
2
− 2u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
9
+ 6y
8
+ 13y
7
+ 9y
6
− 8y
5
− 16y
4
− 5y
3
+ 5y
2
+ 3y −1
c
3
y
9
− 7y
8
+ 15y
7
− 10y
6
+ y
5
+ 2y
4
− 8y
2
− 4y −1
c
4
, c
5
, c
9
y
9
− 10y
8
+ 41y
7
− 86y
6
+ 90y
5
− 29y
4
− 19y
3
+ 6y
2
+ 8y −1
c
7
, c
11
y
9
− 3y
8
− 5y
7
+ 5y
6
+ 16y
5
+ 8y
4
− 9y
3
− 13y
2
− 6y −1
c
10
y
9
− 2y
8
− 7y
7
− 60y
6
− 64y
5
− 53y
4
+ 6y
3
+ 9y
2
+ 10y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.901563 + 0.564856I
a = 0.432004 + 0.508675I
b = 0.102151 + 0.702622I
1.79239 − 1.81153I −9.80943 + 3.54546I
u = 0.901563 − 0.564856I
a = 0.432004 − 0.508675I
b = 0.102151 − 0.702622I
1.79239 + 1.81153I −9.80943 − 3.54546I
u = −0.291663 + 0.753926I
a = 0.866867 − 0.853127I
b = 0.390361 + 0.902380I
−0.28529 + 4.77597I −8.22483 − 4.15931I
u = −0.291663 − 0.753926I
a = 0.866867 + 0.853127I
b = 0.390361 − 0.902380I
−0.28529 − 4.77597I −8.22483 + 4.15931I
u = −1.27478
a = 1.49648
b = −1.90768
−11.1241 −11.2460
u = 0.233182 + 0.559961I
a = −1.39335 − 0.25566I
b = −0.181746 − 0.839836I
4.84522 + 1.19732I −2.35469 − 1.53706I
u = 0.233182 − 0.559961I
a = −1.39335 + 0.25566I
b = −0.181746 + 0.839836I
4.84522 − 1.19732I −2.35469 + 1.53706I
u = −1.54182
a = −0.881123
b = 1.35854
−4.17989 −9.50990
u = −1.86956
a = 0.573604
b = −1.07239
−7.27021 −22.4660
10
III.
I
u
3
= h39a
9
u−16a
8
u+· · ·+108a+311, a
9
u+8a
8
u+· · ·−58a+53, u
2
+u−1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
3
=
1
u − 1
a
8
=
a
−7.80000a
9
u + 3.20000a
8
u + ··· − 21.6000a − 62.2000
a
2
=
−5.40000a
9
u + 5.60000a
8
u + ··· + 18.2000a + 40.4000
−a
2
u + a
2
+ 2u
a
9
=
−14a
9
u + 3a
8
u + ··· + 24a + 48
−12.8000a
9
u + 2.20000a
8
u + ··· + 13.4000a + 22.8000
a
7
=
−7.80000a
9
u + 3.20000a
8
u + ··· − 20.6000a − 62.2000
−7.80000a
9
u + 3.20000a
8
u + ··· − 21.6000a − 62.2000
a
6
=
−7.80000a
9
u + 3.20000a
8
u + ··· − 20.6000a − 62.2000
13.4000a
9
u − 2.60000a
8
u + ··· − 19.2000a − 35.4000
a
11
=
a
2
u
−8.20000a
9
u + 10.8000a
8
u + ··· − 5.40000a − 28.8000
a
10
=
−8.20000a
9
u + 10.8000a
8
u + ··· − 5.40000a − 28.8000
−8.20000a
9
u + 10.8000a
8
u + ··· − 5.40000a − 28.8000
a
5
=
−3.20000a
9
u + 4.80000a
8
u + ··· − 13.4000a − 30.8000
−1.60000a
9
u + 2.40000a
8
u + ··· − 7.20000a − 14.4000
a
5
=
−3.20000a
9
u + 4.80000a
8
u + ··· − 13.4000a − 30.8000
−1.60000a
9
u + 2.40000a
8
u + ··· − 7.20000a − 14.4000
(ii) Obstruction class = −1
(iii) Cusp Shapes =
92
5
a
9
u +
172
5
a
8
u + ··· −
376
5
a −
1102
5
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
20
− u
19
+ ··· − 42u − 1
c
3
(u
2
+ u − 1)
10
c
4
, c
5
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
4
c
7
, c
11
u
20
+ u
19
+ ··· + 40u − 29
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
20
+ 7y
19
+ ··· − 1772y + 1
c
3
(y
2
− 3y + 1)
10
c
4
, c
5
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
4
c
7
, c
11
y
20
− 13y
19
+ ··· − 12736y + 841
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.677607 + 0.002824I
b = −0.129907 + 1.332380I
3.61874 − 1.53058I −10.51511 + 4.43065I
u = 0.618034
a = 0.677607 − 0.002824I
b = −0.129907 − 1.332380I
3.61874 + 1.53058I −10.51511 − 4.43065I
u = 0.618034
a = −1.147360 + 0.672981I
b = 0.02823 − 1.52596I
−1.92472 − 4.40083I −14.7443 + 3.4986I
u = 0.618034
a = −1.147360 − 0.672981I
b = 0.02823 + 1.52596I
−1.92472 + 4.40083I −14.7443 − 3.4986I
u = 0.618034
a = −1.00379 + 1.46626I
b = 0.620375 + 0.906196I
1.54676 −11.48114 + 0.I
u = 0.618034
a = −1.00379 − 1.46626I
b = 0.620375 − 0.906196I
1.54676 −11.48114 + 0.I
u = 0.618034
a = 0.21019 + 2.15583I
b = −0.418784 + 0.001745I
3.61874 + 1.53058I −10.51511 − 4.43065I
u = 0.618034
a = 0.21019 − 2.15583I
b = −0.418784 − 0.001745I
3.61874 − 1.53058I −10.51511 + 4.43065I
u = 0.618034
a = −0.04567 + 2.46906I
b = 0.709108 − 0.415925I
−1.92472 − 4.40083I −14.7443 + 3.4986I
u = 0.618034
a = −0.04567 − 2.46906I
b = 0.709108 + 0.415925I
−1.92472 + 4.40083I −14.7443 − 3.4986I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61803
a = 0.972088 + 0.050869I
b = −1.36329 + 0.42595I
−4.27694 + 1.53058I −10.51511 − 4.43065I
u = −1.61803
a = 0.972088 − 0.050869I
b = −1.36329 − 0.42595I
−4.27694 − 1.53058I −10.51511 + 4.43065I
u = −1.61803
a = 0.950790 + 0.411274I
b = −1.82005 + 0.07628I
−9.82040 − 4.40083I −14.7443 + 3.4986I
u = −1.61803
a = 0.950790 − 0.411274I
b = −1.82005 − 0.07628I
−9.82040 + 4.40083I −14.7443 − 3.4986I
u = −1.61803
a = −0.842560 + 0.263250I
b = 1.57287 + 0.08231I
−4.27694 + 1.53058I −10.51511 − 4.43065I
u = −1.61803
a = −0.842560 − 0.263250I
b = 1.57287 − 0.08231I
−4.27694 − 1.53058I −10.51511 + 4.43065I
u = −1.61803
a = −1.124850 + 0.047143I
b = 1.53841 + 0.66546I
−9.82040 − 4.40083I −14.7443 + 3.4986I
u = −1.61803
a = −1.124850 − 0.047143I
b = 1.53841 − 0.66546I
−9.82040 + 4.40083I −14.7443 − 3.4986I
u = −1.61803
a = −0.790561
b = 0.805229
−6.34892 −11.4810
u = −1.61803
a = 0.497659
b = −1.27915
−6.34892 −11.4810
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
9
+ 3u
7
+ ··· − u − 1)(u
16
+ 3u
14
+ ··· − 3u − 1)
· (u
20
− u
19
+ ··· − 42u − 1)
c
2
, c
6
(u
9
+ 3u
7
+ ··· − u + 1)(u
16
+ 3u
14
+ ··· − 3u − 1)
· (u
20
− u
19
+ ··· − 42u − 1)
c
3
(u
2
+ u − 1)
10
(u
9
+ 3u
8
+ u
7
− 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 1)
· (u
16
− 12u
15
+ ··· − 360u
2
+ 32)
c
4
, c
5
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
4
)(u
9
− 5u
7
+ ··· − 2u + 1)
· (u
16
− 5u
15
+ ··· − 10u − 4)
c
7
, c
11
(u
9
− u
8
+ ··· + 3u
2
+ 1)(u
16
+ u
15
+ ··· − 4u − 1)
· (u
20
+ u
19
+ ··· + 40u − 29)
c
9
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
4
)(u
9
− 5u
7
+ ··· − 2u − 1)
· (u
16
− 5u
15
+ ··· − 10u − 4)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
4
· (u
9
− u
7
+ 8u
6
− 4u
5
+ 5u
4
− 2u
3
+ 3u
2
− 2u − 1)
· (u
16
+ 15u
15
+ ··· + 1722u + 196)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
9
+ 6y
8
+ 13y
7
+ 9y
6
− 8y
5
− 16y
4
− 5y
3
+ 5y
2
+ 3y −1)
· (y
16
+ 6y
15
+ ··· − 5y + 1)(y
20
+ 7y
19
+ ··· − 1772y + 1)
c
3
(y
2
− 3y + 1)
10
(y
9
− 7y
8
+ 15y
7
− 10y
6
+ y
5
+ 2y
4
− 8y
2
− 4y −1)
· (y
16
− 10y
15
+ ··· − 23040y + 1024)
c
4
, c
5
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
4
· (y
9
− 10y
8
+ 41y
7
− 86y
6
+ 90y
5
− 29y
4
− 19y
3
+ 6y
2
+ 8y −1)
· (y
16
− 15y
15
+ ··· − 140y + 16)
c
7
, c
11
(y
9
− 3y
8
− 5y
7
+ 5y
6
+ 16y
5
+ 8y
4
− 9y
3
− 13y
2
− 6y −1)
· (y
16
− 27y
15
+ ··· − 36y + 1)(y
20
− 13y
19
+ ··· − 12736y + 841)
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
4
· (y
9
− 2y
8
− 7y
7
− 60y
6
− 64y
5
− 53y
4
+ 6y
3
+ 9y
2
+ 10y −1)
· (y
16
− 3y
15
+ ··· − 394156y + 38416)
17
