11n
5
(K11n
5
)
A knot diagram
1
Linearized knot diagam
5 1 7 2 3 10 4 11 7 8 10
Solving Sequence
4,8
7
3,11
10 1 2 6 5 9
c
7
c
3
c
10
c
11
c
2
c
6
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.93438 × 10
39
u
39
+ 3.89993 × 10
39
u
38
+ ··· + 9.67095 × 10
39
b − 1.11354 × 10
40
,
− 5.08844 × 10
39
u
39
+ 9.58525 × 10
38
u
38
+ ··· + 9.67095 × 10
39
a − 1.38422 × 10
40
, u
40
+ 2u
39
+ ··· − u − 1i
I
u
2
= hb − 1, u
4
− 2u
3
− u
2
+ a + 3u + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 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
= h2.93×10
39
u
39
+3.90×10
39
u
38
+· · ·+9.67×10
39
b−1.11×10
40
, −5.09×
10
39
u
39
+9.59×10
38
u
38
+· · ·+9.67×10
39
a−1.38×10
40
, u
40
+2u
39
+· · ·−u−1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
0.526157u
39
− 0.0991139u
38
+ ··· + 1.57286u + 1.43132
−0.303422u
39
− 0.403263u
38
+ ··· + 0.625271u + 1.15143
a
10
=
0.222735u
39
− 0.502377u
38
+ ··· + 2.19813u + 2.58275
−0.303422u
39
− 0.403263u
38
+ ··· + 0.625271u + 1.15143
a
1
=
0.290241u
39
+ 0.200008u
38
+ ··· − 1.21785u − 0.612287
−0.120227u
39
− 0.159505u
38
+ ··· + 0.237926u + 0.0802655
a
2
=
−0.578068u
39
− 1.17622u
38
+ ··· + 2.15345u + 1.24641
−0.0185294u
39
− 0.0980063u
38
+ ··· + 1.25512u − 0.0172308
a
6
=
0.410467u
39
+ 0.359513u
38
+ ··· − 1.45577u − 0.692552
−0.101647u
39
− 0.257991u
38
+ ··· − 0.186972u + 0.381156
a
5
=
0.218303u
39
+ 0.00140845u
38
+ ··· − 1.36554u − 0.312079
−0.337234u
39
− 0.662090u
38
+ ··· + 0.0692011u + 0.735406
a
9
=
0.278749u
39
− 0.364781u
38
+ ··· + 2.29798u + 2.37917
−0.264706u
39
− 0.351837u
38
+ ··· + 0.543689u + 1.12586
a
9
=
0.278749u
39
− 0.364781u
38
+ ··· + 2.29798u + 2.37917
−0.264706u
39
− 0.351837u
38
+ ··· + 0.543689u + 1.12586
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.625380u
39
− 2.23284u
38
+ ··· + 22.1362u − 1.81055
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
40
+ 2u
39
+ ··· + 5u + 1
c
2
u
40
+ 18u
39
+ ··· − u + 1
c
3
, c
7
u
40
+ 2u
39
+ ··· − u − 1
c
5
u
40
− 2u
39
+ ··· + 61u + 17
c
6
, c
9
u
40
+ 5u
39
+ ··· + 64u + 32
c
8
, c
10
u
40
− 6u
39
+ ··· − 5u − 1
c
11
u
40
+ 14u
39
+ ··· + 23u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
40
+ 18y
39
+ ··· − y + 1
c
2
y
40
+ 10y
39
+ ··· − 101y + 1
c
3
, c
7
y
40
− 10y
39
+ ··· − y + 1
c
5
y
40
+ 2y
39
+ ··· + 223y + 289
c
6
, c
9
y
40
− 33y
39
+ ··· − 8704y + 1024
c
8
, c
10
y
40
− 14y
39
+ ··· − 23y + 1
c
11
y
40
+ 30y
39
+ ··· + 89y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752901 + 0.442189I
a = −0.604966 + 0.350008I
b = 0.829023 + 0.938697I
−1.98806 − 6.13047I −7.04352 + 9.47962I
u = 0.752901 − 0.442189I
a = −0.604966 − 0.350008I
b = 0.829023 − 0.938697I
−1.98806 + 6.13047I −7.04352 − 9.47962I
u = −0.655458 + 0.476008I
a = −0.318936 − 0.554304I
b = 0.613689 − 0.710479I
−0.42554 + 1.82346I −2.95478 − 4.65601I
u = −0.655458 − 0.476008I
a = −0.318936 + 0.554304I
b = 0.613689 + 0.710479I
−0.42554 − 1.82346I −2.95478 + 4.65601I
u = −0.810417 + 0.872688I
a = 0.140090 + 0.325947I
b = −0.551174 − 1.182170I
4.57008 + 7.07850I −2.02910 − 5.97329I
u = −0.810417 − 0.872688I
a = 0.140090 − 0.325947I
b = −0.551174 + 1.182170I
4.57008 − 7.07850I −2.02910 + 5.97329I
u = −0.643082 + 1.012100I
a = 0.398027 + 0.191743I
b = −0.617281 − 0.666490I
0.145121 + 0.763133I −4.51767 − 0.23788I
u = −0.643082 − 1.012100I
a = 0.398027 − 0.191743I
b = −0.617281 + 0.666490I
0.145121 − 0.763133I −4.51767 + 0.23788I
u = 0.799783 + 0.916888I
a = 0.215570 − 0.335982I
b = −0.650453 + 1.082920I
6.09690 − 1.71389I 0.373315 + 0.701321I
u = 0.799783 − 0.916888I
a = 0.215570 + 0.335982I
b = −0.650453 − 1.082920I
6.09690 + 1.71389I 0.373315 − 0.701321I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.711514 + 0.271124I
a = −1.148250 + 0.635421I
b = 1.174800 + 0.553857I
−3.56782 − 0.26795I −11.60981 + 1.69985I
u = 0.711514 − 0.271124I
a = −1.148250 − 0.635421I
b = 1.174800 − 0.553857I
−3.56782 + 0.26795I −11.60981 − 1.69985I
u = −0.753278 + 0.081360I
a = −1.63901 − 0.21826I
b = 1.50673 − 0.20107I
−4.40562 + 3.00647I −12.14909 − 4.76014I
u = −0.753278 − 0.081360I
a = −1.63901 + 0.21826I
b = 1.50673 + 0.20107I
−4.40562 − 3.00647I −12.14909 + 4.76014I
u = −1.028320 + 0.763633I
a = 1.61875 + 0.32346I
b = −0.801483 + 0.818338I
3.86288 − 0.92225I −2.44177 − 0.36369I
u = −1.028320 − 0.763633I
a = 1.61875 − 0.32346I
b = −0.801483 − 0.818338I
3.86288 + 0.92225I −2.44177 + 0.36369I
u = 0.797251 + 1.038720I
a = 0.390573 − 0.367350I
b = −0.878605 + 0.846502I
5.41673 + 1.52162I − 60.10 − 0.682803I
u = 0.797251 − 1.038720I
a = 0.390573 + 0.367350I
b = −0.878605 − 0.846502I
5.41673 − 1.52162I − 60.10 + 0.682803I
u = −0.422420 + 0.531130I
a = 0.580600 − 0.488478I
b = 0.175715 − 0.238829I
−0.196422 + 1.363410I −2.16894 − 4.86353I
u = −0.422420 − 0.531130I
a = 0.580600 + 0.488478I
b = 0.175715 + 0.238829I
−0.196422 − 1.363410I −2.16894 + 4.86353I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.054050 + 0.808417I
a = 1.58951 − 0.38241I
b = −0.921400 − 0.829719I
5.28266 − 4.71026I 0. + 5.00895I
u = 1.054050 − 0.808417I
a = 1.58951 + 0.38241I
b = −0.921400 + 0.829719I
5.28266 + 4.71026I 0. − 5.00895I
u = −1.35764
a = 1.36371
b = −0.670384
−3.32615 1.98010
u = −0.816149 + 1.085630I
a = 0.451733 + 0.389885I
b = −0.971878 − 0.771756I
3.33510 − 6.89323I −3.00000 + 5.25790I
u = −0.816149 − 1.085630I
a = 0.451733 − 0.389885I
b = −0.971878 + 0.771756I
3.33510 + 6.89323I −3.00000 − 5.25790I
u = −0.460095 + 0.445935I
a = 1.143080 − 0.772133I
b = 0.315005 + 0.068617I
−0.154276 + 1.379410I −2.57505 − 4.68653I
u = −0.460095 − 0.445935I
a = 1.143080 + 0.772133I
b = 0.315005 − 0.068617I
−0.154276 − 1.379410I −2.57505 + 4.68653I
u = 0.392808 + 0.498293I
a = 1.96044 + 1.55878I
b = 0.700490 − 0.229460I
−1.02172 + 2.83866I −5.26921 + 0.34131I
u = 0.392808 − 0.498293I
a = 1.96044 − 1.55878I
b = 0.700490 + 0.229460I
−1.02172 − 2.83866I −5.26921 − 0.34131I
u = 1.093020 + 0.888850I
a = 1.51810 − 0.48663I
b = −1.155200 − 0.809789I
4.47319 − 8.54344I 0. + 4.74667I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093020 − 0.888850I
a = 1.51810 + 0.48663I
b = −1.155200 + 0.809789I
4.47319 + 8.54344I 0. − 4.74667I
u = 0.577742
a = −2.60696
b = 1.20395
−2.39024 −2.93570
u = −1.14394 + 0.85054I
a = 1.46853 + 0.41523I
b = −1.082180 + 0.668751I
−1.33633 + 6.06144I 0
u = −1.14394 − 0.85054I
a = 1.46853 − 0.41523I
b = −1.082180 − 0.668751I
−1.33633 − 6.06144I 0
u = −1.10053 + 0.91184I
a = 1.49517 + 0.51717I
b = −1.22599 + 0.79743I
2.4064 + 14.1156I 0. − 8.71801I
u = −1.10053 − 0.91184I
a = 1.49517 − 0.51717I
b = −1.22599 − 0.79743I
2.4064 − 14.1156I 0. + 8.71801I
u = 1.51868 + 0.20012I
a = 1.325660 − 0.048656I
b = −0.767634 − 0.087671I
−7.01606 − 4.59273I 0
u = 1.51868 − 0.20012I
a = 1.325660 + 0.048656I
b = −0.767634 + 0.087671I
−7.01606 + 4.59273I 0
u = 0.103618 + 0.421336I
a = 6.03694 + 2.30128I
b = 1.041040 − 0.055984I
−1.92691 − 1.82552I 15.7454 + 26.9436I
u = 0.103618 − 0.421336I
a = 6.03694 − 2.30128I
b = 1.041040 + 0.055984I
−1.92691 + 1.82552I 15.7454 − 26.9436I
8
II. I
u
2
= hb − 1, u
4
− 2u
3
− u
2
+ a + 3u + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
−u
4
+ 2u
3
+ u
2
− 3u − 1
1
a
10
=
−u
4
+ 2u
3
+ u
2
− 3u
1
a
1
=
−1
0
a
2
=
−u
3
+ 2u
−u
3
+ u
a
6
=
1
−u
2
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
4
+ 2u
3
+ u
2
− 3u
1
a
9
=
−u
4
+ 2u
3
+ u
2
− 3u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
+ u
3
− 7u
2
− 3u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
, c
9
u
5
c
8
(u − 1)
5
c
10
, c
11
(u + 1)
5
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
5
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
9
y
5
c
8
, c
10
, c
11
(y −1)
5
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −1.67436
b = 1.00000
−4.04602 −10.1350
u = −0.309916 + 0.549911I
a = 0.29977 − 2.14694I
b = 1.00000
−1.97403 + 1.53058I −3.52158 + 1.00973I
u = −0.309916 − 0.549911I
a = 0.29977 + 2.14694I
b = 1.00000
−1.97403 − 1.53058I −3.52158 − 1.00973I
u = 1.41878 + 0.21917I
a = −1.46259 + 0.14641I
b = 1.00000
−7.51750 − 4.40083I −14.4110 + 1.1901I
u = 1.41878 − 0.21917I
a = −1.46259 − 0.14641I
b = 1.00000
−7.51750 + 4.40083I −14.4110 − 1.1901I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
40
+ 2u
39
+ ··· + 5u + 1)
c
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
40
+ 18u
39
+ ··· − u + 1)
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
40
+ 2u
39
+ ··· − u − 1)
c
4
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
40
+ 2u
39
+ ··· + 5u + 1)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
40
− 2u
39
+ ··· + 61u + 17)
c
6
, c
9
u
5
(u
40
+ 5u
39
+ ··· + 64u + 32)
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
40
+ 2u
39
+ ··· − u − 1)
c
8
((u − 1)
5
)(u
40
− 6u
39
+ ··· − 5u − 1)
c
10
((u + 1)
5
)(u
40
− 6u
39
+ ··· − 5u − 1)
c
11
((u + 1)
5
)(u
40
+ 14u
39
+ ··· + 23u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
40
+ 18y
39
+ ··· − y + 1)
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
40
+ 10y
39
+ ··· − 101y + 1)
c
3
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
40
− 10y
39
+ ··· − y + 1)
c
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
40
+ 2y
39
+ ··· + 223y + 289)
c
6
, c
9
y
5
(y
40
− 33y
39
+ ··· − 8704y + 1024)
c
8
, c
10
((y −1)
5
)(y
40
− 14y
39
+ ··· − 23y + 1)
c
11
((y −1)
5
)(y
40
+ 30y
39
+ ··· + 89y + 1)
14
