11n
33
(K11n
33
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 9 4 11 6 1 8 10
Solving Sequence
8,11 4,7
3 6 10 1 2 5 9
c
7
c
3
c
6
c
10
c
11
c
2
c
4
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−37402427u
28
+ 81134437u
27
+ ··· + 95729774b + 19128061,
18654994u
28
− 22307356u
27
+ ··· + 47864887a + 114512378, u
29
− 2u
28
+ ··· + 3u − 1i
I
u
2
= h−u
2
+ b + u − 1, −u
3
+ 2u
2
+ a − 2u, u
4
− u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 33 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−3.74 × 10
7
u
28
+ 8.11 × 10
7
u
27
+ · · · + 9.57 × 10
7
b + 1.91 × 10
7
, 1.87 ×
10
7
u
28
−2.23×10
7
u
27
+· · ·+4.79×10
7
a+1.15×10
8
, u
29
−2u
28
+· · ·+3u −1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−0.389743u
28
+ 0.466048u
27
+ ··· − 0.0720082u − 2.39241
0.390708u
28
− 0.847536u
27
+ ··· + 1.96725u − 0.199813
a
7
=
1
u
2
a
3
=
−0.301913u
28
+ 0.291851u
27
+ ··· − 1.48869u − 2.50603
0.301774u
28
− 0.697679u
27
+ ··· + 2.05069u − 0.198352
a
6
=
−0.387941u
28
+ 0.329624u
27
+ ··· − 1.28229u − 0.468247
−0.00769895u
28
+ 0.202551u
27
+ ··· − 0.868360u + 0.400024
a
10
=
−u
u
a
1
=
−u
3
u
3
+ u
a
2
=
−0.613206u
28
+ 0.567015u
27
+ ··· − 1.46731u − 2.44550
0.410088u
28
− 0.627420u
27
+ ··· + 2.11495u − 0.000268506
a
5
=
0.380897u
28
+ 0.633142u
27
+ ··· + 3.45405u − 0.121313
0.0116806u
28
− 0.577333u
27
+ ··· + 0.279345u − 0.400432
a
9
=
−u
5
− u
u
5
+ u
3
+ u
a
9
=
−u
5
− u
u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
65937967
47864887
u
28
−
91712198
47864887
u
27
+ ··· +
129153968
47864887
u −
217380957
47864887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
29
− 5u
28
+ ··· + 11u + 1
c
2
u
29
+ 33u
28
+ ··· + 5u + 1
c
3
, c
6
u
29
+ 5u
28
+ ··· − 72u + 16
c
5
, c
8
u
29
− 2u
28
+ ··· + u − 1
c
7
, c
10
u
29
+ 2u
28
+ ··· + 3u + 1
c
9
, c
11
u
29
+ 12u
28
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
29
− 33y
28
+ ··· + 5y −1
c
2
y
29
− 69y
28
+ ··· − 1359y −1
c
3
, c
6
y
29
+ 27y
28
+ ··· − 2240y −256
c
5
, c
8
y
29
+ 30y
27
+ ··· − y −1
c
7
, c
10
y
29
+ 12y
28
+ ··· − y −1
c
9
, c
11
y
29
+ 12y
28
+ ··· + 35y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.430937 + 0.875588I
a = 2.46856 + 2.58292I
b = 0.13985 − 3.12093I
−1.94857 − 1.79081I 9.7159 + 22.2862I
u = −0.430937 − 0.875588I
a = 2.46856 − 2.58292I
b = 0.13985 + 3.12093I
−1.94857 + 1.79081I 9.7159 − 22.2862I
u = 0.251301 + 0.941534I
a = −1.04299 + 2.34476I
b = 0.283465 − 0.998451I
−3.57724 − 0.66247I −10.09352 + 1.94504I
u = 0.251301 − 0.941534I
a = −1.04299 − 2.34476I
b = 0.283465 + 0.998451I
−3.57724 + 0.66247I −10.09352 − 1.94504I
u = 0.932586 + 0.472277I
a = −0.0835356 + 0.0913296I
b = 0.58205 − 1.50292I
−6.37168 − 6.75282I −3.69355 + 3.15214I
u = 0.932586 − 0.472277I
a = −0.0835356 − 0.0913296I
b = 0.58205 + 1.50292I
−6.37168 + 6.75282I −3.69355 − 3.15214I
u = −0.953647 + 0.505885I
a = −0.0879207 + 0.0911589I
b = 0.085199 − 1.281550I
−6.12495 − 1.71894I −4.74605 + 1.89417I
u = −0.953647 − 0.505885I
a = −0.0879207 − 0.0911589I
b = 0.085199 + 1.281550I
−6.12495 + 1.71894I −4.74605 − 1.89417I
u = −0.547094 + 0.958808I
a = −1.29758 − 1.42753I
b = −0.64604 + 1.52374I
−0.84435 − 2.90824I −4.00553 + 0.79959I
u = −0.547094 − 0.958808I
a = −1.29758 + 1.42753I
b = −0.64604 − 1.52374I
−0.84435 + 2.90824I −4.00553 − 0.79959I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.429919 + 1.019430I
a = 1.079660 + 0.824021I
b = 0.147997 − 0.384192I
−4.75773 + 3.16768I −10.84320 − 4.60951I
u = 0.429919 − 1.019430I
a = 1.079660 − 0.824021I
b = 0.147997 + 0.384192I
−4.75773 − 3.16768I −10.84320 + 4.60951I
u = −0.493784 + 0.719618I
a = −0.524927 + 0.358431I
b = 0.543180 + 0.690761I
0.00011 − 1.41557I −1.83013 + 4.50450I
u = −0.493784 − 0.719618I
a = −0.524927 − 0.358431I
b = 0.543180 − 0.690761I
0.00011 + 1.41557I −1.83013 − 4.50450I
u = 0.559884 + 1.035720I
a = 1.24254 − 1.84489I
b = 0.620348 + 1.095660I
−1.53843 + 6.72020I −5.08320 − 8.59362I
u = 0.559884 − 1.035720I
a = 1.24254 + 1.84489I
b = 0.620348 − 1.095660I
−1.53843 − 6.72020I −5.08320 + 8.59362I
u = 0.819034 + 0.903920I
a = 0.003538 − 0.368412I
b = −0.0535027 + 0.0855444I
5.64977 + 3.06577I 7.92754 − 1.40495I
u = 0.819034 − 0.903920I
a = 0.003538 + 0.368412I
b = −0.0535027 − 0.0855444I
5.64977 − 3.06577I 7.92754 + 1.40495I
u = 0.591123 + 0.479483I
a = −0.544559 − 0.113805I
b = −0.539946 + 0.901812I
0.05591 − 2.10154I −1.15823 + 3.97516I
u = 0.591123 − 0.479483I
a = −0.544559 + 0.113805I
b = −0.539946 − 0.901812I
0.05591 + 2.10154I −1.15823 − 3.97516I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.011422 + 1.270990I
a = 0.43345 − 2.08872I
b = −0.25247 + 1.62101I
−12.90150 − 4.17591I −8.75836 + 2.29339I
u = 0.011422 − 1.270990I
a = 0.43345 + 2.08872I
b = −0.25247 − 1.62101I
−12.90150 + 4.17591I −8.75836 − 2.29339I
u = 0.672968 + 1.141060I
a = −1.17654 + 1.68782I
b = −0.69150 − 1.64363I
−8.4308 + 12.6362I −5.52931 − 7.07301I
u = 0.672968 − 1.141060I
a = −1.17654 − 1.68782I
b = −0.69150 + 1.64363I
−8.4308 − 12.6362I −5.52931 + 7.07301I
u = −0.692012 + 1.147210I
a = 1.31632 + 0.88452I
b = 0.117471 − 1.304600I
−8.11998 − 4.31757I −6.45074 + 2.65761I
u = −0.692012 − 1.147210I
a = 1.31632 − 0.88452I
b = 0.117471 + 1.304600I
−8.11998 + 4.31757I −6.45074 − 2.65761I
u = −0.332179 + 0.485836I
a = −0.663603 + 0.306233I
b = −0.103350 + 0.657057I
0.002667 − 1.254980I −0.07638 + 5.17093I
u = −0.332179 − 0.485836I
a = −0.663603 − 0.306233I
b = −0.103350 − 0.657057I
0.002667 + 1.254980I −0.07638 − 5.17093I
u = 0.362835
a = −3.24481
b = 0.534503
−2.52742 −3.75050
7
II. I
u
2
= h−u
2
+ b + u − 1, −u
3
+ 2u
2
+ a − 2u, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
u
3
− 2u
2
+ 2u
u
2
− u + 1
a
7
=
1
u
2
a
3
=
u
3
− 2u
2
+ 2u
u
2
− u + 1
a
6
=
1
u
2
a
10
=
−u
u
a
1
=
−u
3
u
3
+ u
a
2
=
−2u
2
+ 2u
u
3
+ u
2
+ 1
a
5
=
u
3
−u
3
− u
a
9
=
u
2
+ 1
u
3
− u
2
− 1
a
9
=
u
2
+ 1
u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 5u
2
− 4
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
6
u
4
c
5
, c
9
u
4
− u
3
+ 3u
2
− 2u + 1
c
7
u
4
− u
3
+ u
2
+ 1
c
8
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
10
u
4
+ u
3
+ u
2
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
7
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = 0.59074 + 2.34806I
b = 0.95668 − 1.22719I
−1.85594 − 1.41510I −0.51206 + 2.21528I
u = −0.351808 − 0.720342I
a = 0.59074 − 2.34806I
b = 0.95668 + 1.22719I
−1.85594 + 1.41510I −0.51206 − 2.21528I
u = 0.851808 + 0.911292I
a = 0.409261 − 0.055548I
b = 0.043315 + 0.641200I
5.14581 + 3.16396I −7.98794 − 4.08190I
u = 0.851808 − 0.911292I
a = 0.409261 + 0.055548I
b = 0.043315 − 0.641200I
5.14581 − 3.16396I −7.98794 + 4.08190I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
29
− 5u
28
+ ··· + 11u + 1)
c
2
((u + 1)
4
)(u
29
+ 33u
28
+ ··· + 5u + 1)
c
3
, c
6
u
4
(u
29
+ 5u
28
+ ··· − 72u + 16)
c
4
((u + 1)
4
)(u
29
− 5u
28
+ ··· + 11u + 1)
c
5
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
29
− 2u
28
+ ··· + u − 1)
c
7
(u
4
− u
3
+ u
2
+ 1)(u
29
+ 2u
28
+ ··· + 3u + 1)
c
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
29
− 2u
28
+ ··· + u − 1)
c
9
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
29
+ 12u
28
+ ··· − u − 1)
c
10
(u
4
+ u
3
+ u
2
+ 1)(u
29
+ 2u
28
+ ··· + 3u + 1)
c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
29
+ 12u
28
+ ··· − u − 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
29
− 33y
28
+ ··· + 5y −1)
c
2
((y −1)
4
)(y
29
− 69y
28
+ ··· − 1359y −1)
c
3
, c
6
y
4
(y
29
+ 27y
28
+ ··· − 2240y −256)
c
5
, c
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
29
+ 30y
27
+ ··· − y −1)
c
7
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
29
+ 12y
28
+ ··· − y −1)
c
9
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
29
+ 12y
28
+ ··· + 35y −1)
13
