11n
96
(K11n
96
)
A knot diagram
1
Linearized knot diagam
5 1 8 7 2 11 10 1 4 5 9
Solving Sequence
1,5
2 3
6,9
8 11 10 7 4
c
1
c
2
c
5
c
8
c
11
c
10
c
7
c
4
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−49163590906u
11
+ 107218013353u
10
+ ··· + 21229569666128b + 7549955391253,
− 3432579931219u
11
+ 9265624647069u
10
+ ··· + 891641925977376a + 779226085539559,
u
12
− 18u
10
− 3u
9
+ 95u
8
+ 104u
7
+ 172u
6
− 39u
5
− 97u
4
− 126u
3
+ 90u
2
+ 56u + 21i
I
u
2
= hu
4
+ 2u
3
+ b, 2u
4
+ 4u
3
+ u
2
+ a + 3u, u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 2u + 1i
I
u
3
= h−2a
3
− a
2
+ b − 5a + 3, a
4
+ 2a
2
− 3a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 21 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−4.92 × 10
10
u
11
+ 1.07 × 10
11
u
10
+ · · · + 2.12 × 10
13
b + 7.55 ×
10
12
, −3.43 × 10
12
u
11
+ 9.27 × 10
12
u
10
+ · · · + 8.92 × 10
14
a + 7.79 ×
10
14
, u
12
− 18u
10
+ · · · + 56u + 21i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
0.00384973u
11
− 0.0103916u
10
+ ··· + 0.0171393u − 0.873923
0.00231581u
11
− 0.00505041u
10
+ ··· + 0.944426u − 0.355634
a
8
=
0.00153392u
11
− 0.00534123u
10
+ ··· − 0.927287u − 0.518289
0.00231581u
11
− 0.00505041u
10
+ ··· + 0.944426u − 0.355634
a
11
=
−0.00463890u
11
+ 0.00727890u
10
+ ··· − 0.777940u + 1.33085
−0.00697735u
11
+ 0.00595506u
10
+ ··· − 0.776534u + 0.0957645
a
10
=
−0.00463890u
11
+ 0.00727890u
10
+ ··· − 0.777940u + 1.33085
−0.00382620u
11
+ 0.00729647u
10
+ ··· − 0.466333u + 0.248621
a
7
=
−0.0229677u
11
+ 0.00971661u
10
+ ··· − 4.00235u − 0.352817
−0.00186562u
11
− 0.00155113u
10
+ ··· + 0.277243u − 0.308445
a
4
=
−0.00384973u
11
+ 0.0103916u
10
+ ··· − 0.0171393u + 0.873923
0.00382620u
11
− 0.00729647u
10
+ ··· + 0.466333u − 0.248621
a
4
=
−0.00384973u
11
+ 0.0103916u
10
+ ··· − 0.0171393u + 0.873923
0.00382620u
11
− 0.00729647u
10
+ ··· + 0.466333u − 0.248621
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
6189983418965
84918278664512
u
11
+
1650234375373
84918278664512
u
10
+ ··· +
95722121856831
84918278664512
u +
414947504713599
84918278664512
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
12
− 18u
10
+ ··· − 56u + 21
c
2
u
12
+ 36u
11
+ ··· − 644u + 441
c
3
u
12
+ 43u
10
+ ··· − 242u + 713
c
4
u
12
− 3u
11
+ 4u
10
− u
9
+ u
8
− 6u
7
+ 8u
6
+ u
5
− 5u
4
− u
3
+ 4u
2
− 3u + 1
c
6
u
12
+ 2u
11
+ ··· + 211u + 199
c
7
u
12
+ 4u
11
+ ··· − 56u + 48
c
8
, c
11
u
12
+ 2u
11
+ ··· − 2u + 1
c
9
u
12
+ 9u
11
+ ··· + 32u + 8
c
10
u
12
− u
11
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
− 36y
11
+ ··· + 644y + 441
c
2
y
12
− 268y
11
+ ··· + 15582980y + 194481
c
3
y
12
+ 86y
11
+ ··· − 2050686y + 508369
c
4
y
12
− y
11
+ ··· − y + 1
c
6
y
12
− 50y
11
+ ··· − 181433y + 39601
c
7
y
12
+ 14y
11
+ ··· + 19136y + 2304
c
8
, c
11
y
12
+ 30y
11
+ ··· − 34y + 1
c
9
y
12
− 5y
11
+ ··· − 160y + 64
c
10
y
12
− 31y
11
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695715 + 0.738682I
a = 0.84389 − 1.18718I
b = −0.353721 − 0.071932I
0.40587 + 4.64089I 1.41872 − 4.81790I
u = −0.695715 − 0.738682I
a = 0.84389 + 1.18718I
b = −0.353721 + 0.071932I
0.40587 − 4.64089I 1.41872 + 4.81790I
u = 0.778147 + 0.299444I
a = −0.811194 − 0.475700I
b = 0.333912 − 0.014682I
−1.39285 − 0.48352I −6.04456 + 0.14475I
u = 0.778147 − 0.299444I
a = −0.811194 + 0.475700I
b = 0.333912 + 0.014682I
−1.39285 + 0.48352I −6.04456 − 0.14475I
u = −0.182826 + 1.285270I
a = 0.012072 + 0.419952I
b = −0.18796 + 1.60199I
−4.09909 − 2.92553I −6.51732 + 0.13616I
u = −0.182826 − 1.285270I
a = 0.012072 − 0.419952I
b = −0.18796 − 1.60199I
−4.09909 + 2.92553I −6.51732 − 0.13616I
u = −0.246048 + 0.302553I
a = −0.835828 − 0.015119I
b = −0.578983 + 0.267705I
1.34063 − 0.78648I 4.38906 + 1.25430I
u = −0.246048 − 0.302553I
a = −0.835828 + 0.015119I
b = −0.578983 − 0.267705I
1.34063 + 0.78648I 4.38906 − 1.25430I
u = −3.01586 + 0.46060I
a = −0.161563 + 0.704724I
b = 0.81768 + 2.58567I
18.0497 + 1.3274I −3.03771 + 0.06650I
u = −3.01586 − 0.46060I
a = −0.161563 − 0.704724I
b = 0.81768 − 2.58567I
18.0497 − 1.3274I −3.03771 − 0.06650I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 3.36230 + 0.99651I
a = −0.214046 − 0.589764I
b = 0.96907 − 2.80816I
17.7719 − 9.0470I −3.20819 + 3.73893I
u = 3.36230 − 0.99651I
a = −0.214046 + 0.589764I
b = 0.96907 + 2.80816I
17.7719 + 9.0470I −3.20819 − 3.73893I
6
II.
I
u
2
= hu
4
+ 2u
3
+ b, 2u
4
+ 4u
3
+ u
2
+ a + 3u, u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
−2u
4
− 4u
3
− u
2
− 3u
−u
4
− 2u
3
a
8
=
−u
4
− 2u
3
− u
2
− 3u
−u
4
− 2u
3
a
11
=
−u
4
− 3u
3
− 2u
2
− u − 1
u
4
+ 3u
3
+ 3u
2
+ 2u
a
10
=
−u
4
− 3u
3
− 2u
2
− u − 1
u
3
+ 2u
2
+ u
a
7
=
u
3
+ 2u
2
+ u + 2
u
4
+ 3u
3
+ 4u
2
+ 2u
a
4
=
2u
4
+ 4u
3
+ u
2
+ 3u
−u
3
− 2u
2
− u
a
4
=
2u
4
+ 4u
3
+ u
2
+ 3u
−u
3
− 2u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
4
− 25u
3
− 19u
2
− 24u − 15
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
2
u
5
+ 3u
4
− 5u
3
+ 3u
2
− 2u + 1
c
3
u
5
− u
4
− 2u
3
+ 9u
2
− 17u + 11
c
4
u
5
− 2u
4
+ 2u
3
+ u
2
− 2u + 1
c
5
u
5
− 3u
4
+ 3u
3
− 3u
2
+ 2u − 1
c
6
u
5
+ 3u
4
− 5u
3
− 8u
2
+ 9u + 11
c
7
u
5
+ u
4
− 2u
3
+ 3u
2
+ 7u + 13
c
8
u
5
− u
4
+ 3u
3
− 3u
2
+ 2u − 1
c
9
u
5
− u
3
+ u
2
+ u − 1
c
10
u
5
+ u
4
− u
3
− u
2
+ 1
c
11
u
5
+ u
4
+ 3u
3
+ 3u
2
+ 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
5
− 3y
4
− 5y
3
− 3y
2
− 2y −1
c
2
y
5
− 19y
4
+ 3y
3
+ 5y
2
− 2y −1
c
3
y
5
− 5y
4
− 12y
3
+ 9y
2
+ 91y −121
c
4
y
5
+ 4y
3
− 5y
2
+ 2y −1
c
6
y
5
− 19y
4
+ 91y
3
− 220y
2
+ 257y −121
c
7
y
5
− 5y
4
+ 12y
3
− 63y
2
− 29y −169
c
8
, c
11
y
5
+ 5y
4
+ 7y
3
+ y
2
− 2y −1
c
9
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1
c
10
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128506 + 0.862169I
a = 0.520756 + 0.228796I
b = 0.08973 + 1.51845I
−3.58220 + 3.70382I −1.95503 − 6.72693I
u = 0.128506 − 0.862169I
a = 0.520756 − 0.228796I
b = 0.08973 − 1.51845I
−3.58220 − 3.70382I −1.95503 + 6.72693I
u = −0.586994 + 0.535944I
a = 1.27460 − 2.43458I
b = −0.214528 − 0.727972I
−0.27969 + 5.17259I −5.66442 − 10.18801I
u = −0.586994 − 0.535944I
a = 1.27460 + 2.43458I
b = −0.214528 + 0.727972I
−0.27969 − 5.17259I −5.66442 + 10.18801I
u = −2.08302
a = 0.409288
b = −0.750397
−5.43570 −9.76110
10
III. I
u
3
= h−2a
3
− a
2
+ b − 5a + 3, a
4
+ 2a
2
− 3a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
−1
0
a
9
=
a
2a
3
+ a
2
+ 5a − 3
a
8
=
−2a
3
− a
2
− 4a + 3
2a
3
+ a
2
+ 5a − 3
a
11
=
a
3
+ a
2
+ 3a − 1
2a
3
+ a
2
+ 5a − 4
a
10
=
a
3
+ a
2
+ 3a − 1
a
3
+ 2a − 3
a
7
=
−2a
3
− a
2
− 4a + 3
2a
3
+ a
2
+ 5a − 3
a
4
=
−a
−a
3
− 2a + 3
a
4
=
−a
−a
3
− 2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
3
− a
2
− 11a + 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
5
(u + 1)
4
c
3
, c
4
u
4
− 2u
3
+ 2u
2
− u + 1
c
6
, c
11
(u
2
− u + 1)
2
c
7
u
4
c
8
(u
2
+ u + 1)
2
c
9
, c
10
u
4
− u
3
− u
2
+ u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
y
4
+ 2y
2
+ 3y + 1
c
6
, c
8
, c
11
(y
2
+ y + 1)
2
c
7
y
4
c
9
, c
10
y
4
− 3y
3
+ 5y
2
− 3y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.570696 + 0.107280I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −1.42268 − 1.82047I
u = 1.00000
a = 0.570696 − 0.107280I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −1.42268 + 1.82047I
u = 1.00000
a = −0.57070 + 1.62477I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −7.07732 − 2.50966I
u = 1.00000
a = −0.57070 − 1.62477I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −7.07732 + 2.50966I
14
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
5
+ 3u
4
+ ··· + 2u + 1)(u
12
− 18u
10
+ ··· − 56u + 21)
c
2
(u + 1)
4
(u
5
+ 3u
4
− 5u
3
+ 3u
2
− 2u + 1)
· (u
12
+ 36u
11
+ ··· − 644u + 441)
c
3
(u
4
− 2u
3
+ 2u
2
− u + 1)(u
5
− u
4
− 2u
3
+ 9u
2
− 17u + 11)
· (u
12
+ 43u
10
+ ··· − 242u + 713)
c
4
(u
4
− 2u
3
+ 2u
2
− u + 1)(u
5
− 2u
4
+ 2u
3
+ u
2
− 2u + 1)
· (u
12
− 3u
11
+ 4u
10
− u
9
+ u
8
− 6u
7
+ 8u
6
+ u
5
− 5u
4
− u
3
+ 4u
2
− 3u + 1)
c
5
((u + 1)
4
)(u
5
− 3u
4
+ ··· + 2u − 1)(u
12
− 18u
10
+ ··· − 56u + 21)
c
6
(u
2
− u + 1)
2
(u
5
+ 3u
4
− 5u
3
− 8u
2
+ 9u + 11)
· (u
12
+ 2u
11
+ ··· + 211u + 199)
c
7
u
4
(u
5
+ u
4
+ ··· + 7u + 13)(u
12
+ 4u
11
+ ··· − 56u + 48)
c
8
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + 2u − 1)(u
12
+ 2u
11
+ ··· − 2u + 1)
c
9
(u
4
− u
3
− u
2
+ u + 1)(u
5
− u
3
+ u
2
+ u − 1)(u
12
+ 9u
11
+ ··· + 32u + 8)
c
10
(u
4
− u
3
− u
2
+ u + 1)(u
5
+ u
4
− u
3
− u
2
+ 1)(u
12
− u
11
+ ··· − u + 1)
c
11
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + 2u + 1)(u
12
+ 2u
11
+ ··· − 2u + 1)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
(y
5
− 3y
4
− 5y
3
− 3y
2
− 2y −1)
· (y
12
− 36y
11
+ ··· + 644y + 441)
c
2
(y −1)
4
(y
5
− 19y
4
+ 3y
3
+ 5y
2
− 2y −1)
· (y
12
− 268y
11
+ ··· + 15582980y + 194481)
c
3
(y
4
+ 2y
2
+ 3y + 1)(y
5
− 5y
4
− 12y
3
+ 9y
2
+ 91y −121)
· (y
12
+ 86y
11
+ ··· − 2050686y + 508369)
c
4
(y
4
+ 2y
2
+ 3y + 1)(y
5
+ 4y
3
+ ··· + 2y −1)(y
12
− y
11
+ ··· − y + 1)
c
6
(y
2
+ y + 1)
2
(y
5
− 19y
4
+ 91y
3
− 220y
2
+ 257y −121)
· (y
12
− 50y
11
+ ··· − 181433y + 39601)
c
7
y
4
(y
5
− 5y
4
+ 12y
3
− 63y
2
− 29y −169)
· (y
12
+ 14y
11
+ ··· + 19136y + 2304)
c
8
, c
11
(y
2
+ y + 1)
2
(y
5
+ 5y
4
+ 7y
3
+ y
2
− 2y −1)
· (y
12
+ 30y
11
+ ··· − 34y + 1)
c
9
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)
· (y
12
− 5y
11
+ ··· − 160y + 64)
c
10
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)
· (y
12
− 31y
11
+ ··· + 5y + 1)
16
