11a
94
(K11a
94
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 3 11 10 4 7 8
Solving Sequence
7,10
11 8
3,9
4 1 2 6 5
c
10
c
7
c
8
c
3
c
11
c
2
c
6
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−17u
55
+ 43u
54
+ ··· + 2b − 11, −3u
55
+ 7u
54
+ ··· + 4a + 3, u
56
− 4u
55
+ ··· − 2u − 1i
I
u
2
= hb, a
3
+ a
2
+ 2a + 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 59 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−17u
55
+ 43u
54
+ · · · + 2b − 11, −3u
55
+ 7u
54
+ · · · + 4a + 3, u
56
−
4u
55
+ · · · − 2u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
3
=
3
4
u
55
−
7
4
u
54
+ ··· +
13
4
u −
3
4
17
2
u
55
−
43
2
u
54
+ ··· +
31
2
u +
11
2
a
9
=
u
3
− 2u
−u
3
+ u
a
4
=
33
4
u
55
−
85
4
u
54
+ ··· +
71
4
u +
19
4
5
2
u
55
−
17
2
u
54
+ ··· +
17
2
u +
5
2
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
27
4
u
55
−
71
4
u
54
+ ··· +
57
4
u +
13
4
27
4
u
55
−
75
4
u
54
+ ··· +
61
4
u +
21
4
a
6
=
1
4
u
55
−
3
4
u
54
+ ··· −
13
4
u −
3
4
−u
10
+ 4u
8
+ 2u
7
− 5u
6
− 6u
5
+ 4u
3
+ 3u
2
+ 2u
a
5
=
4u
55
−
23
2
u
54
+ ··· + 5u +
3
2
−
9
4
u
55
+
25
4
u
54
+ ··· −
7
4
u −
7
4
a
5
=
4u
55
−
23
2
u
54
+ ··· + 5u +
3
2
−
9
4
u
55
+
25
4
u
54
+ ··· −
7
4
u −
7
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
55
+
15
2
u
54
+ ··· + 5u −
29
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
56
+ 2u
55
+ ··· − 5u − 1
c
2
, c
4
u
56
+ 18u
55
+ ··· + 5u + 1
c
3
, c
9
u
56
− u
55
+ ··· + 12u + 8
c
6
u
56
− 2u
55
+ ··· − 145u − 25
c
7
, c
10
, c
11
u
56
− 4u
55
+ ··· − 2u − 1
c
8
u
56
+ 21u
55
+ ··· + 592u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
56
− 18y
55
+ ··· − 5y + 1
c
2
, c
4
y
56
+ 42y
55
+ ··· − 77y + 1
c
3
, c
9
y
56
− 21y
55
+ ··· − 592y + 64
c
6
y
56
+ 6y
55
+ ··· + 7275y + 625
c
7
, c
10
, c
11
y
56
− 48y
55
+ ··· − 18y + 1
c
8
y
56
+ 23y
55
+ ··· − 85248y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866172 + 0.412104I
a = 0.716759 + 0.563360I
b = 0.408158 − 0.290046I
−3.84915 − 0.47402I −20.0517 + 1.8006I
u = −0.866172 − 0.412104I
a = 0.716759 − 0.563360I
b = 0.408158 + 0.290046I
−3.84915 + 0.47402I −20.0517 − 1.8006I
u = −0.188462 + 0.854305I
a = 1.56928 + 1.20703I
b = −1.35361 − 1.14786I
3.70616 + 10.08220I −9.08620 − 8.29722I
u = −0.188462 − 0.854305I
a = 1.56928 − 1.20703I
b = −1.35361 + 1.14786I
3.70616 − 10.08220I −9.08620 + 8.29722I
u = −0.165662 + 0.838312I
a = −1.65426 − 0.98689I
b = 1.41656 + 1.00950I
4.58143 + 4.28016I −7.26827 − 3.33660I
u = −0.165662 − 0.838312I
a = −1.65426 + 0.98689I
b = 1.41656 − 1.00950I
4.58143 − 4.28016I −7.26827 + 3.33660I
u = −1.050040 + 0.463708I
a = 0.479637 + 1.195890I
b = 0.907676 − 0.666506I
1.07406 − 5.37584I 0
u = −1.050040 − 0.463708I
a = 0.479637 − 1.195890I
b = 0.907676 + 0.666506I
1.07406 + 5.37584I 0
u = −1.078200 + 0.427394I
a = −0.272195 − 1.149050I
b = −1.066620 + 0.514728I
1.79919 + 0.26900I 0
u = −1.078200 − 0.427394I
a = −0.272195 + 1.149050I
b = −1.066620 − 0.514728I
1.79919 − 0.26900I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617027 + 0.535939I
a = 0.858761 − 0.032635I
b = 0.0856353 + 0.0708847I
−0.71189 + 4.42421I −14.7302 − 6.6620I
u = −0.617027 − 0.535939I
a = 0.858761 + 0.032635I
b = 0.0856353 − 0.0708847I
−0.71189 − 4.42421I −14.7302 + 6.6620I
u = −1.168010 + 0.209136I
a = 0.247139 − 0.431048I
b = −1.026800 − 0.591291I
−1.37028 + 0.97595I 0
u = −1.168010 − 0.209136I
a = 0.247139 + 0.431048I
b = −1.026800 + 0.591291I
−1.37028 − 0.97595I 0
u = −0.241002 + 0.768489I
a = 0.882963 + 0.837698I
b = −0.943312 − 0.875499I
−1.88523 + 4.71954I −14.7264 − 6.6425I
u = −0.241002 − 0.768489I
a = 0.882963 − 0.837698I
b = −0.943312 + 0.875499I
−1.88523 − 4.71954I −14.7264 + 6.6425I
u = 1.225830 + 0.232995I
a = 0.37066 − 1.43650I
b = 0.872612 − 0.365716I
1.47062 + 1.23708I 0
u = 1.225830 − 0.232995I
a = 0.37066 + 1.43650I
b = 0.872612 + 0.365716I
1.47062 − 1.23708I 0
u = 1.240870 + 0.261920I
a = −0.09120 + 1.42966I
b = −1.006580 + 0.465327I
1.86713 − 4.74693I 0
u = 1.240870 − 0.261920I
a = −0.09120 − 1.42966I
b = −1.006580 − 0.465327I
1.86713 + 4.74693I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140644 + 0.703431I
a = −1.178460 − 0.095442I
b = 1.155670 + 0.456832I
1.60637 + 2.37356I −6.13877 − 4.17137I
u = −0.140644 − 0.703431I
a = −1.178460 + 0.095442I
b = 1.155670 − 0.456832I
1.60637 − 2.37356I −6.13877 + 4.17137I
u = 0.048164 + 0.710249I
a = −2.01204 + 0.89303I
b = 1.59325 − 0.13231I
5.50599 + 1.24032I −5.23066 − 2.33484I
u = 0.048164 − 0.710249I
a = −2.01204 − 0.89303I
b = 1.59325 + 0.13231I
5.50599 − 1.24032I −5.23066 + 2.33484I
u = −0.448607 + 0.542572I
a = −0.438992 + 0.149521I
b = −0.297929 − 0.283370I
−0.279032 − 0.387064I −13.17728 − 1.08778I
u = −0.448607 − 0.542572I
a = −0.438992 − 0.149521I
b = −0.297929 + 0.283370I
−0.279032 + 0.387064I −13.17728 + 1.08778I
u = 0.086804 + 0.689503I
a = 2.00700 − 1.20329I
b = −1.55835 + 0.31132I
4.89165 − 4.55526I −6.35177 + 3.19659I
u = 0.086804 − 0.689503I
a = 2.00700 + 1.20329I
b = −1.55835 − 0.31132I
4.89165 + 4.55526I −6.35177 − 3.19659I
u = −1.305330 + 0.049118I
a = −0.193950 − 0.243423I
b = 0.39449 + 1.81061I
−2.36775 − 2.29859I 0
u = −1.305330 − 0.049118I
a = −0.193950 + 0.243423I
b = 0.39449 − 1.81061I
−2.36775 + 2.29859I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.302410 + 0.198734I
a = −0.712631 + 0.159499I
b = 1.50723 + 1.35120I
−4.77983 + 2.82843I 0
u = −1.302410 − 0.198734I
a = −0.712631 − 0.159499I
b = 1.50723 − 1.35120I
−4.77983 − 2.82843I 0
u = −1.296500 + 0.293943I
a = 0.904976 − 0.648287I
b = −2.05274 − 0.77370I
1.30531 + 2.39964I 0
u = −1.296500 − 0.293943I
a = 0.904976 + 0.648287I
b = −2.05274 + 0.77370I
1.30531 − 2.39964I 0
u = −1.322480 + 0.285611I
a = −1.042770 + 0.548589I
b = 2.18268 + 0.97725I
0.45930 + 8.10035I 0
u = −1.322480 − 0.285611I
a = −1.042770 − 0.548589I
b = 2.18268 − 0.97725I
0.45930 − 8.10035I 0
u = 1.350790 + 0.293586I
a = 0.501547 + 0.644493I
b = −1.03042 + 1.22757I
−3.10733 − 6.00225I 0
u = 1.350790 − 0.293586I
a = 0.501547 − 0.644493I
b = −1.03042 − 1.22757I
−3.10733 + 6.00225I 0
u = 1.372070 + 0.235523I
a = −0.076585 − 0.360451I
b = 0.548336 − 1.187110I
−5.59879 − 2.28336I 0
u = 1.372070 − 0.235523I
a = −0.076585 + 0.360451I
b = 0.548336 + 1.187110I
−5.59879 + 2.28336I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.403150 + 0.062138I
a = 0.772974 − 0.030882I
b = −0.360419 − 0.400109I
−6.13819 − 1.16533I 0
u = 1.403150 − 0.062138I
a = 0.772974 + 0.030882I
b = −0.360419 + 0.400109I
−6.13819 + 1.16533I 0
u = 1.37282 + 0.35653I
a = 1.134610 + 0.597959I
b = −1.51941 + 1.55952I
−0.27805 − 8.58003I 0
u = 1.37282 − 0.35653I
a = 1.134610 − 0.597959I
b = −1.51941 − 1.55952I
−0.27805 + 8.58003I 0
u = 1.39495 + 0.31342I
a = −0.767957 − 0.290710I
b = 1.06397 − 1.65056I
−7.07159 − 8.63297I 0
u = 1.39495 − 0.31342I
a = −0.767957 + 0.290710I
b = 1.06397 + 1.65056I
−7.07159 + 8.63297I 0
u = 1.38707 + 0.36194I
a = −1.225820 − 0.469271I
b = 1.54315 − 1.70908I
−1.2781 − 14.4580I 0
u = 1.38707 − 0.36194I
a = −1.225820 + 0.469271I
b = 1.54315 + 1.70908I
−1.2781 + 14.4580I 0
u = 1.45135 + 0.08180I
a = −0.739121 − 0.103503I
b = 0.656296 + 0.649639I
−7.50796 − 6.20957I 0
u = 1.45135 − 0.08180I
a = −0.739121 + 0.103503I
b = 0.656296 − 0.649639I
−7.50796 + 6.20957I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45795
a = −0.872262
b = 0.821275
−11.3625 0
u = −0.035406 + 0.444835I
a = 0.396342 − 1.248670I
b = −0.772381 + 0.172570I
−0.691494 − 0.342390I −11.27142 + 0.66679I
u = −0.035406 − 0.444835I
a = 0.396342 + 1.248670I
b = −0.772381 − 0.172570I
−0.691494 + 0.342390I −11.27142 − 0.66679I
u = 0.316601 + 0.055324I
a = 0.04721 − 3.30384I
b = −0.067426 + 0.690981I
2.47292 + 2.72146I −4.00548 − 3.04642I
u = 0.316601 − 0.055324I
a = 0.04721 + 3.30384I
b = −0.067426 − 0.690981I
2.47292 − 2.72146I −4.00548 + 3.04642I
u = −0.306961
a = −1.09551
b = −0.380686
−0.701749 −14.3130
10
II. I
u
2
= hb, a
3
+ a
2
+ 2a + 1, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
8
=
1
0
a
3
=
a
0
a
9
=
1
0
a
4
=
a
0
a
1
=
0
1
a
2
=
a
−a
a
6
=
−a
2
−1
a
5
=
−a
2
− a − 1
a
a
5
=
−a
2
− a − 1
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
− 3a − 15
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
, c
8
, c
9
u
3
c
4
u
3
− u
2
+ 2u − 1
c
5
u
3
− u
2
+ 1
c
7
(u − 1)
3
c
10
, c
11
(u + 1)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y − 1
c
2
, c
4
, c
6
y
3
+ 3y
2
+ 2y − 1
c
3
, c
8
, c
9
y
3
c
7
, c
10
, c
11
(y − 1)
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.215080 + 1.307140I
b = 0
1.37919 + 2.82812I −12.69240 − 3.35914I
u = −1.00000
a = −0.215080 − 1.307140I
b = 0
1.37919 − 2.82812I −12.69240 + 3.35914I
u = −1.00000
a = −0.569840
b = 0
−2.75839 −13.6150
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)(u
56
+ 2u
55
+ ··· − 5u − 1)
c
2
(u
3
+ u
2
+ 2u + 1)(u
56
+ 18u
55
+ ··· + 5u + 1)
c
3
, c
9
u
3
(u
56
− u
55
+ ··· + 12u + 8)
c
4
(u
3
− u
2
+ 2u − 1)(u
56
+ 18u
55
+ ··· + 5u + 1)
c
5
(u
3
− u
2
+ 1)(u
56
+ 2u
55
+ ··· − 5u − 1)
c
6
(u
3
+ u
2
+ 2u + 1)(u
56
− 2u
55
+ ··· − 145u − 25)
c
7
((u − 1)
3
)(u
56
− 4u
55
+ ··· − 2u − 1)
c
8
u
3
(u
56
+ 21u
55
+ ··· + 592u + 64)
c
10
, c
11
((u + 1)
3
)(u
56
− 4u
55
+ ··· − 2u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
− y
2
+ 2y − 1)(y
56
− 18y
55
+ ··· − 5y + 1)
c
2
, c
4
(y
3
+ 3y
2
+ 2y − 1)(y
56
+ 42y
55
+ ··· − 77y + 1)
c
3
, c
9
y
3
(y
56
− 21y
55
+ ··· − 592y + 64)
c
6
(y
3
+ 3y
2
+ 2y − 1)(y
56
+ 6y
55
+ ··· + 7275y + 625)
c
7
, c
10
, c
11
((y − 1)
3
)(y
56
− 48y
55
+ ··· − 18y + 1)
c
8
y
3
(y
56
+ 23y
55
+ ··· − 85248y + 4096)
16
