11a
139
(K11a
139
)
A knot diagram
1
Linearized knot diagam
5 1 9 8 2 11 10 3 4 6 7
Solving Sequence
6,10
11 7 8
1,2
3 5 4 9
c
10
c
6
c
7
c
11
c
2
c
5
c
4
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1330328u
36
− 337157u
35
+ ··· + 3064546b − 5423429,
2108869u
36
− 5518964u
35
+ ··· + 1532273a + 24842943, u
37
− 2u
36
+ ··· + 13u + 1i
I
u
2
= hu
2
+ b, a − 1, u
15
− 5u
13
− u
12
+ 10u
11
+ 4u
10
− 8u
9
− 6u
8
− u
7
+ 3u
6
+ 5u
5
+ u
4
− u
3
− u
2
− u − 1i
I
u
3
= hb
2
+ 2b − 1, a − 1, u + 1i
I
u
4
= hb + 1, a − 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 55 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−1.33 × 10
6
u
36
− 3.37 × 10
5
u
35
+ · · · + 3.06 × 10
6
b − 5.42 × 10
6
, 2.11 ×
10
6
u
36
−5.52×10
6
u
35
+· · ·+1.53×10
6
a+2.48×10
7
, u
37
−2u
36
+· · ·+13u+1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−1.37630u
36
+ 3.60182u
35
+ ··· − 53.4414u − 16.2131
0.434103u
36
+ 0.110019u
35
+ ··· + 4.77936u + 1.76973
a
3
=
−1.61129u
36
+ 4.21702u
35
+ ··· − 52.0448u − 17.2627
−1.20630u
36
+ 0.913862u
35
+ ··· + 17.4922u + 2.71463
a
5
=
−1.84921u
36
+ 3.03426u
35
+ ··· − 28.6788u − 14.3763
−0.129011u
36
− 0.605251u
35
+ ··· + 4.55239u + 1.81040
a
4
=
−1.03926u
36
+ 2.83241u
35
+ ··· − 37.3538u − 14.7413
−0.817794u
36
+ 0.142729u
35
+ ··· + 14.2739u + 2.65174
a
9
=
1.35408u
36
− 3.76576u
35
+ ··· + 69.5409u + 23.2930
0.656314u
36
+ 0.203071u
35
+ ··· − 15.2619u − 3.27106
a
9
=
1.35408u
36
− 3.76576u
35
+ ··· + 69.5409u + 23.2930
0.656314u
36
+ 0.203071u
35
+ ··· − 15.2619u − 3.27106
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5839087
1532273
u
36
+
3620132
1532273
u
35
+ ··· +
36237593
1532273
u −
19224398
1532273
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
37
+ 2u
36
+ ··· + u + 1
c
2
u
37
+ 18u
36
+ ··· + 5u + 1
c
3
, c
8
, c
9
u
37
+ 2u
36
+ ··· + 2u
2
− 2
c
4
u
37
− 6u
36
+ ··· + 288u − 128
c
6
, c
10
, c
11
u
37
− 2u
36
+ ··· + 13u + 1
c
7
u
37
+ 6u
36
+ ··· − 224u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
37
− 18y
36
+ ··· + 5y −1
c
2
y
37
+ 6y
36
+ ··· + 21y −1
c
3
, c
8
, c
9
y
37
− 34y
36
+ ··· + 8y −4
c
4
y
37
− 10y
36
+ ··· + 156672y −16384
c
6
, c
10
, c
11
y
37
− 34y
36
+ ··· + 117y −1
c
7
y
37
+ 18y
36
+ ··· + 32256y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.013380 + 0.311874I
a = −0.007083 + 0.507321I
b = −0.911372 + 0.339991I
−3.23840 + 0.33679I −3.19033 + 0.85162I
u = −1.013380 − 0.311874I
a = −0.007083 − 0.507321I
b = −0.911372 − 0.339991I
−3.23840 − 0.33679I −3.19033 − 0.85162I
u = −0.148500 + 0.878352I
a = −0.35212 + 1.40071I
b = −0.17334 + 2.13411I
−8.84281 − 9.20717I −9.51764 + 6.62975I
u = −0.148500 − 0.878352I
a = −0.35212 − 1.40071I
b = −0.17334 − 2.13411I
−8.84281 + 9.20717I −9.51764 − 6.62975I
u = −1.15117
a = −0.432099
b = −1.94913
−3.47854 −0.910990
u = 0.165281 + 0.808869I
a = −0.30320 − 1.46229I
b = −0.11222 − 1.95034I
−3.03568 + 5.84417I −5.83954 − 7.10655I
u = 0.165281 − 0.808869I
a = −0.30320 + 1.46229I
b = −0.11222 + 1.95034I
−3.03568 − 5.84417I −5.83954 + 7.10655I
u = −0.471583 + 0.599168I
a = 0.162338 + 1.262080I
b = −0.480709 + 1.121580I
−2.94289 − 4.00123I −5.31382 + 7.13651I
u = −0.471583 − 0.599168I
a = 0.162338 − 1.262080I
b = −0.480709 − 1.121580I
−2.94289 + 4.00123I −5.31382 − 7.13651I
u = −0.022041 + 0.744033I
a = −0.53343 − 1.59774I
b = 0.42055 − 2.05462I
−9.93818 − 0.58603I −11.65035 − 0.12880I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.022041 − 0.744033I
a = −0.53343 + 1.59774I
b = 0.42055 + 2.05462I
−9.93818 + 0.58603I −11.65035 + 0.12880I
u = −0.099912 + 0.709675I
a = −0.33485 + 1.62744I
b = 0.17353 + 1.80893I
−3.65380 − 1.92705I −8.13048 + 0.55620I
u = −0.099912 − 0.709675I
a = −0.33485 − 1.62744I
b = 0.17353 − 1.80893I
−3.65380 + 1.92705I −8.13048 − 0.55620I
u = −1.253160 + 0.303469I
a = −0.759003 − 0.531242I
b = 1.10971 − 2.91416I
−6.13830 − 3.19514I −6.64446 + 4.28023I
u = −1.253160 − 0.303469I
a = −0.759003 + 0.531242I
b = 1.10971 + 2.91416I
−6.13830 + 3.19514I −6.64446 − 4.28023I
u = 1.296560 + 0.177192I
a = −0.331390 − 0.464636I
b = −0.683956 − 0.483013I
3.08964 + 0.95760I − 60.10 + 1.305195I
u = 1.296560 − 0.177192I
a = −0.331390 + 0.464636I
b = −0.683956 + 0.483013I
3.08964 − 0.95760I − 60.10 − 1.305195I
u = 0.568431 + 0.375314I
a = 0.520054 − 0.971540I
b = −0.443456 − 0.641882I
0.89372 + 1.45212I 2.19487 − 5.36999I
u = 0.568431 − 0.375314I
a = 0.520054 + 0.971540I
b = −0.443456 + 0.641882I
0.89372 − 1.45212I 2.19487 + 5.36999I
u = 1.332640 + 0.298347I
a = −0.706159 + 0.554504I
b = 1.13989 + 2.44217I
0.86122 + 5.58916I −3.00000 − 3.15563I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.332640 − 0.298347I
a = −0.706159 − 0.554504I
b = 1.13989 − 2.44217I
0.86122 − 5.58916I −3.00000 + 3.15563I
u = −1.350860 + 0.271610I
a = −0.313821 + 0.546709I
b = −0.634567 + 0.232909I
4.43467 − 4.86040I 0. + 4.57417I
u = −1.350860 − 0.271610I
a = −0.313821 − 0.546709I
b = −0.634567 − 0.232909I
4.43467 + 4.86040I 0. − 4.57417I
u = 1.361180 + 0.332115I
a = −0.298381 − 0.581807I
b = −0.695184 − 0.117059I
−1.06880 + 8.43099I 0. − 5.07593I
u = 1.361180 − 0.332115I
a = −0.298381 + 0.581807I
b = −0.695184 + 0.117059I
−1.06880 − 8.43099I 0. + 5.07593I
u = 1.400590 + 0.045310I
a = −0.466611 − 0.492889I
b = −0.170732 − 0.843883I
3.96621 + 1.16950I 0
u = 1.400590 − 0.045310I
a = −0.466611 + 0.492889I
b = −0.170732 + 0.843883I
3.96621 − 1.16950I 0
u = −1.366970 + 0.343185I
a = −0.701831 − 0.589074I
b = 1.41347 − 2.32983I
1.80064 − 9.99903I 0. + 8.15131I
u = −1.366970 − 0.343185I
a = −0.701831 + 0.589074I
b = 1.41347 + 2.32983I
1.80064 + 9.99903I 0. − 8.15131I
u = −1.411670 + 0.052360I
a = −0.537001 − 0.501630I
b = 0.155713 − 1.234020I
7.20025 − 2.58398I 4.12642 + 3.46228I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.411670 − 0.052360I
a = −0.537001 + 0.501630I
b = 0.155713 + 1.234020I
7.20025 + 2.58398I 4.12642 − 3.46228I
u = 1.37052 + 0.38186I
a = −0.709680 + 0.609188I
b = 1.59214 + 2.36282I
−4.0535 + 13.7305I 0. − 8.23789I
u = 1.37052 − 0.38186I
a = −0.709680 − 0.609188I
b = 1.59214 − 2.36282I
−4.0535 − 13.7305I 0. + 8.23789I
u = 1.41824 + 0.13440I
a = −0.588434 + 0.523307I
b = 0.51535 + 1.54249I
3.18948 + 6.36871I 0. − 6.27419I
u = 1.41824 − 0.13440I
a = −0.588434 − 0.523307I
b = 0.51535 − 1.54249I
3.18948 − 6.36871I 0. + 6.27419I
u = −0.302230
a = 2.69339
b = 0.212469
−1.08012 −10.9510
u = −0.0973082
a = −10.7401
b = 1.30703
−6.54639 −13.9600
8
II. I
u
2
= hu
2
+ b, a − 1, u
15
− 5u
13
+ · · · − u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
1
−u
2
a
3
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
5
=
u
−u
3
+ u
a
4
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
9
=
u
13
− 4u
11
+ 7u
9
− 6u
7
+ 2u
5
+ u
−u
12
+ 4u
10
+ u
9
− 6u
8
− 3u
7
+ 3u
6
+ 3u
5
+ u
4
− u
3
− u
2
− 1
a
9
=
u
13
− 4u
11
+ 7u
9
− 6u
7
+ 2u
5
+ u
−u
12
+ 4u
10
+ u
9
− 6u
8
− 3u
7
+ 3u
6
+ 3u
5
+ u
4
− u
3
− u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
− 12u
7
− 4u
6
+ 12u
5
+ 8u
4
− 4u
2
− 4u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
u
15
− 5u
13
+ ··· − u − 1
c
2
u
15
+ 10u
14
+ ··· − u + 1
c
3
, c
8
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
c
4
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
c
7
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
, c
11
y
15
− 10y
14
+ ··· − y −1
c
2
y
15
− 10y
14
+ ··· + 7y −1
c
3
, c
8
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
3
c
4
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
3
c
7
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051760 + 0.377982I
a = 1.00000
b = −0.963319 − 0.795090I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 1.051760 − 0.377982I
a = 1.00000
b = −0.963319 + 0.795090I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.162112 + 0.782578I
a = 1.00000
b = 0.586148 + 0.253730I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.162112 − 0.782578I
a = 1.00000
b = 0.586148 − 0.253730I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.121390 + 0.470419I
a = 1.00000
b = −1.03622 + 1.05504I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.121390 − 0.470419I
a = 1.00000
b = −1.03622 − 1.05504I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.633490 + 0.451585I
a = 1.00000
b = −0.197381 + 0.572150I
−2.40108 −3.48114 + 0.I
u = −0.633490 − 0.451585I
a = 1.00000
b = −0.197381 − 0.572150I
−2.40108 −3.48114 + 0.I
u = −1.209710 + 0.247023I
a = 1.00000
b = −1.40237 + 0.59765I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −1.209710 − 0.247023I
a = 1.00000
b = −1.40237 − 0.59765I
−0.32910 + 1.53058I −2.51511 − 4.43065I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26698
a = 1.00000
b = −1.60524
−2.40108 −3.48110
u = 1.283500 + 0.312159I
a = 1.00000
b = −1.54993 − 0.80131I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 1.283500 − 0.312159I
a = 1.00000
b = −1.54993 + 0.80131I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 0.157950 + 0.625006I
a = 1.00000
b = 0.365684 − 0.197439I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.157950 − 0.625006I
a = 1.00000
b = 0.365684 + 0.197439I
−0.32910 − 1.53058I −2.51511 + 4.43065I
13
III. I
u
3
= hb
2
+ 2b − 1, a − 1, u + 1i
(i) Arc colorings
a
6
=
0
−1
a
10
=
1
0
a
11
=
1
−1
a
7
=
−1
0
a
8
=
−1
0
a
1
=
0
−1
a
2
=
1
b
a
3
=
1
b + 1
a
5
=
−1
−b − 1
a
4
=
−b − 2
−b − 1
a
9
=
−b − 2
−2
a
9
=
−b − 2
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
11
(u + 1)
2
c
3
, c
4
, c
8
c
9
u
2
− 2
c
5
, c
6
(u − 1)
2
c
7
u
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
(y −1)
2
c
3
, c
4
, c
8
c
9
(y −2)
2
c
7
y
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0.414214
−4.93480 −8.00000
u = −1.00000
a = 1.00000
b = −2.41421
−4.93480 −8.00000
17
IV. I
u
4
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
6
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
7
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
2
=
1
−1
a
3
=
1
0
a
5
=
1
0
a
4
=
1
0
a
9
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
u − 1
c
2
, c
5
, c
6
u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
y −1
c
3
, c
4
, c
7
c
8
, c
9
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
0 0
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u + 1)
2
(u
15
− 5u
13
+ ··· − u − 1)(u
37
+ 2u
36
+ ··· + u + 1)
c
2
((u + 1)
3
)(u
15
+ 10u
14
+ ··· − u + 1)(u
37
+ 18u
36
+ ··· + 5u + 1)
c
3
, c
8
, c
9
u(u
2
− 2)(u
5
− u
4
+ ··· + u + 1)
3
(u
37
+ 2u
36
+ ··· + 2u
2
− 2)
c
4
u(u
2
− 2)(u
5
+ 3u
4
+ ··· − u − 1)
3
(u
37
− 6u
36
+ ··· + 288u − 128)
c
5
((u − 1)
2
)(u + 1)(u
15
− 5u
13
+ ··· − u − 1)(u
37
+ 2u
36
+ ··· + u + 1)
c
6
((u − 1)
2
)(u + 1)(u
15
− 5u
13
+ ··· − u − 1)(u
37
− 2u
36
+ ··· + 13u + 1)
c
7
u
3
(u
5
+ u
4
+ ··· + u + 1)
3
(u
37
+ 6u
36
+ ··· − 224u − 16)
c
10
, c
11
(u − 1)(u + 1)
2
(u
15
− 5u
13
+ ··· − u − 1)(u
37
− 2u
36
+ ··· + 13u + 1)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y −1)
3
)(y
15
− 10y
14
+ ··· − y −1)(y
37
− 18y
36
+ ··· + 5y −1)
c
2
((y −1)
3
)(y
15
− 10y
14
+ ··· + 7y −1)(y
37
+ 6y
36
+ ··· + 21y −1)
c
3
, c
8
, c
9
y(y −2)
2
(y
5
− 5y
4
+ ··· − y −1)
3
(y
37
− 34y
36
+ ··· + 8y −4)
c
4
y(y −2)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
3
· (y
37
− 10y
36
+ ··· + 156672y −16384)
c
6
, c
10
, c
11
((y −1)
3
)(y
15
− 10y
14
+ ··· − y −1)(y
37
− 34y
36
+ ··· + 117y −1)
c
7
y
3
(y
5
+ 3y
4
+ ··· − y −1)
3
(y
37
+ 18y
36
+ ··· + 32256y −256)
23
