11a
142
(K11a
142
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 2 5 11 3 4 7 8
Solving Sequence
3,9
4 10 5
8,11
1 2 7 6
c
3
c
9
c
4
c
8
c
11
c
2
c
7
c
6
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.36795 × 10
16
u
34
− 7.90337 × 10
16
u
33
+ ··· + 3.65214 × 10
17
b − 1.06187 × 10
17
,
3.20846 × 10
16
u
34
+ 7.33609 × 10
16
u
33
+ ··· + 3.65214 × 10
17
a + 5.49062 × 10
17
, u
35
− u
34
+ ··· − 12u − 4i
I
u
2
= h2b + 2a + u, 2a
2
− 2au − 2a + u + 3, u
2
− 2i
I
v
1
= ha, b − v + 1, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 41 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−6.37×10
16
u
34
−7.90×10
16
u
33
+· · ·+3.65×10
17
b−1.06×10
17
, 3.21×
10
16
u
34
+7.34×10
16
u
33
+· · ·+3.65×10
17
a+5.49×10
17
, u
35
−u
34
+· · ·−12u−4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−u
u
a
11
=
−0.0878513u
34
− 0.200871u
33
+ ··· − 1.92802u − 1.50340
0.174362u
34
+ 0.216404u
33
+ ··· + 2.30563u + 0.290753
a
1
=
−0.0624444u
34
+ 0.0343900u
33
+ ··· − 0.357458u − 1.09522
0.148955u
34
− 0.0188573u
33
+ ··· + 0.735065u − 0.117420
a
2
=
0.00194352u
34
+ 0.344883u
33
+ ··· + 1.74022u + 2.04509
−0.0876840u
34
− 0.158849u
33
+ ··· − 1.60828u − 0.239291
a
7
=
0.0878513u
34
+ 0.200871u
33
+ ··· + 1.92802u + 1.50340
−0.268809u
34
− 0.150206u
33
+ ··· − 1.51044u − 0.864136
a
6
=
0.0328237u
34
− 0.0751277u
33
+ ··· + 0.506093u + 0.865585
0.00374850u
34
− 0.0472669u
33
+ ··· + 0.524988u − 0.0604220
a
6
=
0.0328237u
34
− 0.0751277u
33
+ ··· + 0.506093u + 0.865585
0.00374850u
34
− 0.0472669u
33
+ ··· + 0.524988u − 0.0604220
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
32902895900849614
91303571055107371
u
34
+
12004762532282944
91303571055107371
u
33
+···+
239783904823467776
91303571055107371
u+
1365844903778505204
91303571055107371
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
35
− 2u
34
+ ··· − 2u + 1
c
2
, c
6
u
35
+ 10u
34
+ ··· + 4u − 1
c
3
, c
4
, c
8
c
9
u
35
+ u
34
+ ··· − 12u + 4
c
7
, c
10
, c
11
u
35
− 3u
34
+ ··· + 7u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
35
+ 10y
34
+ ··· + 4y −1
c
2
, c
6
y
35
+ 34y
34
+ ··· + 108y −1
c
3
, c
4
, c
8
c
9
y
35
− 45y
34
+ ··· + 80y −16
c
7
, c
10
, c
11
y
35
− 39y
34
+ ··· + 749y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01124
a = 0.435017
b = −1.74489
5.84048 16.2440
u = 0.842940 + 0.301389I
a = 0.279499 + 1.063810I
b = 0.541332 − 0.560583I
3.15741 + 4.91553I 11.80461 − 7.26359I
u = 0.842940 − 0.301389I
a = 0.279499 − 1.063810I
b = 0.541332 + 0.560583I
3.15741 − 4.91553I 11.80461 + 7.26359I
u = −0.046502 + 0.876821I
a = −0.05406 − 1.61301I
b = 0.014495 − 0.143542I
7.57337 + 3.08858I 11.98726 − 2.45837I
u = −0.046502 − 0.876821I
a = −0.05406 + 1.61301I
b = 0.014495 + 0.143542I
7.57337 − 3.08858I 11.98726 + 2.45837I
u = −0.924843 + 0.638045I
a = −0.377611 + 0.218222I
b = 1.63025 + 0.42363I
10.22050 − 8.11783I 13.7681 + 6.1510I
u = −0.924843 − 0.638045I
a = −0.377611 − 0.218222I
b = 1.63025 − 0.42363I
10.22050 + 8.11783I 13.7681 − 6.1510I
u = −0.855744 + 0.143816I
a = −0.530278 + 1.121980I
b = −0.261867 − 0.584427I
3.37741 + 0.53913I 12.96867 + 0.98562I
u = −0.855744 − 0.143816I
a = −0.530278 − 1.121980I
b = −0.261867 + 0.584427I
3.37741 − 0.53913I 12.96867 − 0.98562I
u = 1.002070 + 0.587960I
a = 0.398952 + 0.208816I
b = −1.62413 + 0.38544I
10.76680 + 1.81479I 14.8433 − 1.1672I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002070 − 0.587960I
a = 0.398952 − 0.208816I
b = −1.62413 − 0.38544I
10.76680 − 1.81479I 14.8433 + 1.1672I
u = −0.746503 + 0.235179I
a = −0.327678 + 0.089960I
b = 1.94693 + 0.30523I
2.70500 − 3.34459I 11.31994 + 5.51487I
u = −0.746503 − 0.235179I
a = −0.327678 − 0.089960I
b = 1.94693 − 0.30523I
2.70500 + 3.34459I 11.31994 − 5.51487I
u = 0.418462 + 0.378689I
a = 0.176733 + 0.515354I
b = 0.541640 + 0.031955I
−1.54201 + 1.37506I 2.61836 − 5.92080I
u = 0.418462 − 0.378689I
a = 0.176733 − 0.515354I
b = 0.541640 − 0.031955I
−1.54201 − 1.37506I 2.61836 + 5.92080I
u = 1.45544 + 0.05665I
a = 0.731751 + 0.109995I
b = −1.382100 + 0.064187I
6.70444 + 0.15451I 13.90887 + 0.I
u = 1.45544 − 0.05665I
a = 0.731751 − 0.109995I
b = −1.382100 − 0.064187I
6.70444 − 0.15451I 13.90887 + 0.I
u = −1.48918 + 0.04339I
a = −1.030150 − 0.268681I
b = 1.268110 + 0.012077I
4.71864 − 2.64789I 7.00000 + 4.86854I
u = −1.48918 − 0.04339I
a = −1.030150 + 0.268681I
b = 1.268110 − 0.012077I
4.71864 + 2.64789I 7.00000 − 4.86854I
u = −0.267965 + 0.386180I
a = −1.06586 − 2.12149I
b = 0.0421102 − 0.0027654I
1.31539 + 1.16539I 7.47416 + 2.51618I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267965 − 0.386180I
a = −1.06586 + 2.12149I
b = 0.0421102 + 0.0027654I
1.31539 − 1.16539I 7.47416 − 2.51618I
u = 0.026938 + 0.426896I
a = −0.010788 + 0.289994I
b = 0.286121 + 0.820389I
0.70287 − 2.35372I 3.69812 + 3.90292I
u = 0.026938 − 0.426896I
a = −0.010788 − 0.289994I
b = 0.286121 − 0.820389I
0.70287 + 2.35372I 3.69812 − 3.90292I
u = −0.410201
a = −0.632763
b = −0.224697
0.605164 16.5250
u = 1.65775 + 0.05997I
a = −2.99916 + 0.53570I
b = 3.92472 − 0.49978I
11.20700 + 4.43486I 0
u = 1.65775 − 0.05997I
a = −2.99916 − 0.53570I
b = 3.92472 + 0.49978I
11.20700 − 4.43486I 0
u = −1.67466 + 0.07865I
a = −0.776181 − 0.438183I
b = 1.157350 − 0.141346I
12.00650 − 6.36730I 0
u = −1.67466 − 0.07865I
a = −0.776181 + 0.438183I
b = 1.157350 + 0.141346I
12.00650 + 6.36730I 0
u = 1.67898 + 0.03136I
a = 0.756308 − 0.404108I
b = −1.189480 − 0.156593I
12.35470 + 0.09189I 0
u = 1.67898 − 0.03136I
a = 0.756308 + 0.404108I
b = −1.189480 + 0.156593I
12.35470 − 0.09189I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70626
a = 2.73816
b = −3.68944
15.4583 0
u = 1.70118 + 0.18976I
a = −2.19546 + 0.94563I
b = 3.16027 − 0.84490I
19.2288 + 11.4138I 0
u = 1.70118 − 0.18976I
a = −2.19546 − 0.94563I
b = 3.16027 + 0.84490I
19.2288 − 11.4138I 0
u = −1.72576 + 0.15889I
a = 2.25378 + 0.76495I
b = −3.22623 − 0.68282I
−19.2201 − 4.8251I 0
u = −1.72576 − 0.15889I
a = 2.25378 − 0.76495I
b = −3.22623 + 0.68282I
−19.2201 + 4.8251I 0
8
II. I
u
2
= h2b + 2a + u, 2a
2
− 2au − 2a + u + 3, u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−2
a
10
=
u
−u
a
5
=
−1
0
a
8
=
−u
u
a
11
=
a
−a −
1
2
u
a
1
=
a − u
−a +
1
2
u
a
2
=
−
1
2
au + a −
1
2
u +
1
2
−a +
1
2
u + 1
a
7
=
a − u
−a +
1
2
u
a
6
=
−
1
2
u
−a +
1
2
u
a
6
=
−
1
2
u
−a +
1
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 2u + 12
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
5
, c
6
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
7
(u − 1)
4
c
10
, c
11
(u + 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
c
7
, c
10
, c
11
(y −1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 1.20711 + 0.86603I
b = −1.91421 − 0.86603I
6.57974 − 2.02988I 14.0000 + 3.4641I
u = 1.41421
a = 1.20711 − 0.86603I
b = −1.91421 + 0.86603I
6.57974 + 2.02988I 14.0000 − 3.4641I
u = −1.41421
a = −0.207107 + 0.866025I
b = 0.914214 − 0.866025I
6.57974 − 2.02988I 14.0000 + 3.4641I
u = −1.41421
a = −0.207107 − 0.866025I
b = 0.914214 + 0.866025I
6.57974 + 2.02988I 14.0000 − 3.4641I
12
III. I
v
1
= ha, b − v + 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
10
=
v
0
a
5
=
1
0
a
8
=
v
0
a
11
=
0
v − 1
a
1
=
−v
v − 1
a
2
=
0
v
a
7
=
v
−v + 1
a
6
=
1
−v + 1
a
6
=
1
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u + 1)
2
c
10
, c
11
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
1.64493 + 2.02988I 12.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
1.64493 − 2.02988I 12.00000 + 3.46410I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
35
− 2u
34
+ ··· − 2u + 1)
c
2
, c
6
((u
2
+ u + 1)
3
)(u
35
+ 10u
34
+ ··· + 4u − 1)
c
3
, c
4
, c
8
c
9
u
2
(u
2
− 2)
2
(u
35
+ u
34
+ ··· − 12u + 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
35
− 2u
34
+ ··· − 2u + 1)
c
7
((u − 1)
4
)(u + 1)
2
(u
35
− 3u
34
+ ··· + 7u + 7)
c
10
, c
11
((u − 1)
2
)(u + 1)
4
(u
35
− 3u
34
+ ··· + 7u + 7)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
35
+ 10y
34
+ ··· + 4y − 1)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
35
+ 34y
34
+ ··· + 108y − 1)
c
3
, c
4
, c
8
c
9
y
2
(y − 2)
4
(y
35
− 45y
34
+ ··· + 80y − 16)
c
7
, c
10
, c
11
((y − 1)
6
)(y
35
− 39y
34
+ ··· + 749y − 49)
18
