11n
98
(K11n
98
)
A knot diagram
1
Linearized knot diagam
7 1 8 7 10 2 4 11 6 8 9
Solving Sequence
8,11
9
1,4
3 2 7 5 6 10
c
8
c
11
c
3
c
2
c
7
c
4
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−325810u
16
+ 546213u
15
+ ··· + 3637114b − 2536642,
− 877137u
16
+ 1987958u
15
+ ··· + 7274228a − 10784281, u
17
− 2u
16
+ ··· + 13u − 4i
I
u
2
= h−u
10
+ u
9
+ 4u
8
− 3u
7
− 6u
6
+ 2u
5
+ 2u
4
− u
2
a + 3u
3
+ 3u
2
+ b + a − 3u − 2, 2u
10
− 5u
9
+ ··· − 4a + 5,
u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1i
I
u
3
= hau + b + a + 2u + 3, a
2
+ 2au + 4a + 2u + 6, u
2
+ u − 1i
I
u
4
= hb − 1, 2a − 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 44 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−3.26 × 10
5
u
16
+ 5.46 × 10
5
u
15
+ · · · + 3.64 × 10
6
b − 2.54 × 10
6
, −8.77 ×
10
5
u
16
+1.99×10
6
u
15
+· · ·+7.27×10
6
a−1.08×10
7
, u
17
−2u
16
+· · ·+13u−4i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
0.120581u
16
− 0.273288u
15
+ ··· − 0.0580715u + 1.48253
0.0895793u
16
− 0.150178u
15
+ ··· + 0.0542218u + 0.697433
a
3
=
0.0310022u
16
− 0.123110u
15
+ ··· − 0.112293u + 0.785100
0.0895793u
16
− 0.150178u
15
+ ··· + 0.0542218u + 0.697433
a
2
=
0.239444u
16
− 0.304221u
15
+ ··· − 1.56094u + 1.51558
0.205575u
16
− 0.224465u
15
+ ··· − 0.728410u + 0.910041
a
7
=
0.235464u
16
− 0.270574u
15
+ ··· − 0.673677u + 2.19687
0.182621u
16
− 0.156800u
15
+ ··· − 1.28067u + 0.925424
a
5
=
0.360026u
16
− 0.577509u
15
+ ··· − 0.619016u + 2.99812
0.295154u
16
− 0.374642u
15
+ ··· − 1.67419u + 1.60747
a
6
=
0.474993u
16
− 0.539864u
15
+ ··· − 1.82912u + 3.29061
0.410121u
16
− 0.336997u
15
+ ··· − 2.88429u + 1.89997
a
10
=
u
u
a
10
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
9594931
7274228
u
16
−
15193461
7274228
u
15
+ ··· +
10670363
7274228
u +
21150807
1818557
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
u
17
− u
16
+ ··· − 4u
2
− 1
c
2
u
17
+ 5u
16
+ ··· − 8u − 1
c
5
, c
9
u
17
− 3u
16
+ ··· + 22u − 8
c
8
, c
10
, c
11
u
17
− 2u
16
+ ··· + 13u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
y
17
+ 5y
16
+ ··· − 8y −1
c
2
y
17
+ 13y
16
+ ··· − 12y −1
c
5
, c
9
y
17
+ 9y
16
+ ··· − 12y −64
c
8
, c
10
, c
11
y
17
− 16y
16
+ ··· + 209y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.240053 + 0.973100I
a = 0.644042 − 0.652010I
b = −0.678341 − 1.093890I
0.65577 + 8.75138I 0.84209 − 7.19652I
u = −0.240053 − 0.973100I
a = 0.644042 + 0.652010I
b = −0.678341 + 1.093890I
0.65577 − 8.75138I 0.84209 + 7.19652I
u = −0.911746 + 0.271963I
a = 0.521420 − 0.719384I
b = −0.187558 − 0.379982I
−1.69658 + 0.80451I −2.69480 − 2.52231I
u = −0.911746 − 0.271963I
a = 0.521420 + 0.719384I
b = −0.187558 + 0.379982I
−1.69658 − 0.80451I −2.69480 + 2.52231I
u = 1.114510 + 0.218797I
a = 0.635665 + 0.251760I
b = 1.157790 + 0.487195I
0.354258 − 0.834124I 0.06498 + 5.84789I
u = 1.114510 − 0.218797I
a = 0.635665 − 0.251760I
b = 1.157790 − 0.487195I
0.354258 + 0.834124I 0.06498 − 5.84789I
u = −1.030910 + 0.649737I
a = −0.466920 + 0.601803I
b = −0.583285 + 0.914805I
−1.75655 − 3.15519I −1.08772 + 4.41422I
u = −1.030910 − 0.649737I
a = −0.466920 − 0.601803I
b = −0.583285 − 0.914805I
−1.75655 + 3.15519I −1.08772 − 4.41422I
u = 0.248382 + 0.709434I
a = −0.785996 − 0.998686I
b = 0.784905 − 0.787523I
2.78581 − 2.60100I 4.98680 + 3.49505I
u = 0.248382 − 0.709434I
a = −0.785996 + 0.998686I
b = 0.784905 + 0.787523I
2.78581 + 2.60100I 4.98680 − 3.49505I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44333 + 0.29962I
a = −0.27964 + 2.02194I
b = 0.606656 + 1.025000I
−2.68580 + 6.31167I −1.34813 − 5.64607I
u = −1.44333 − 0.29962I
a = −0.27964 − 2.02194I
b = 0.606656 − 1.025000I
−2.68580 − 6.31167I −1.34813 + 5.64607I
u = 1.43553 + 0.42213I
a = 0.59170 + 1.89308I
b = −0.678472 + 1.240020I
−4.6382 − 13.7590I −2.60534 + 8.09148I
u = 1.43553 − 0.42213I
a = 0.59170 − 1.89308I
b = −0.678472 − 1.240020I
−4.6382 + 13.7590I −2.60534 − 8.09148I
u = 1.67968 + 0.04846I
a = −0.20221 − 1.49330I
b = −0.239314 − 0.869369I
−11.59490 + 1.04318I −1.35194 − 7.04363I
u = 1.67968 − 0.04846I
a = −0.20221 + 1.49330I
b = −0.239314 + 0.869369I
−11.59490 − 1.04318I −1.35194 + 7.04363I
u = 0.295856
a = 1.43389
b = 0.635251
0.963952 10.6380
6
II.
I
u
2
= h−u
10
+u
9
+· · ·+a −2, 2u
10
−5u
9
+· · ·−4a +5, u
11
−u
10
+· · ·+2u +1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
u
10
− u
9
− 4u
8
+ 3u
7
+ 6u
6
− 2u
5
− 2u
4
+ u
2
a − 3u
3
− 3u
2
− a + 3u + 2
a
3
=
−u
10
+ u
9
+ ··· + 2a − 2
u
10
− u
9
− 4u
8
+ 3u
7
+ 6u
6
− 2u
5
− 2u
4
+ u
2
a − 3u
3
− 3u
2
− a + 3u + 2
a
2
=
−u
10
+ u
9
+ ··· + 2a − 2
u
10
− u
9
+ ··· − a + 2
a
7
=
−u
10
a + 2u
10
+ ··· − 2a + 3
−u
5
a − u
6
+ 2u
3
a + 2u
4
− au − 2
a
5
=
u
7
− 2u
5
+ 2u
u
9
− 3u
7
+ 3u
5
− u
a
6
=
u
10
− 3u
8
+ 2u
6
+ 3u
4
− 3u
2
− 1
u
10
+ u
9
− 3u
8
− 4u
7
+ 2u
6
+ 5u
5
+ 3u
4
− 3u
2
− 3u − 1
a
10
=
u
u
a
10
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
− 16u
7
− 4u
6
+ 20u
5
+ 12u
4
+ 4u
3
− 8u
2
− 20u − 6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
u
22
+ 3u
21
+ ··· + 24u + 9
c
2
u
22
+ 11u
21
+ ··· + 432u + 81
c
5
, c
9
(u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
2
c
8
, c
10
, c
11
(u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
y
22
+ 11y
21
+ ··· + 432y + 81
c
2
y
22
− y
21
+ ··· + 35640y + 6561
c
5
, c
9
(y
11
+ 3y
10
+ ··· − 2y −1)
2
c
8
, c
10
, c
11
(y
11
− 9y
10
+ ··· − 2y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14725
a = −2.18308 + 3.31504I
b = 0.181376 + 1.048190I
−5.48524 0.376260
u = −1.14725
a = −2.18308 − 3.31504I
b = 0.181376 − 1.048190I
−5.48524 0.376260
u = −0.044199 + 0.849205I
a = 0.547434 + 0.348829I
b = −0.853835 + 0.533591I
2.35273 + 3.04152I 4.06121 − 2.82242I
u = −0.044199 + 0.849205I
a = −0.372720 + 0.162477I
b = 0.714099 + 0.923041I
2.35273 + 3.04152I 4.06121 − 2.82242I
u = −0.044199 − 0.849205I
a = 0.547434 − 0.348829I
b = −0.853835 − 0.533591I
2.35273 − 3.04152I 4.06121 + 2.82242I
u = −0.044199 − 0.849205I
a = −0.372720 − 0.162477I
b = 0.714099 − 0.923041I
2.35273 − 3.04152I 4.06121 + 2.82242I
u = −1.232090 + 0.392876I
a = 0.674566 − 0.370203I
b = 0.623653 − 0.552777I
−1.31282 + 1.41699I 0.791306 − 0.633731I
u = −1.232090 + 0.392876I
a = 0.48177 − 1.51619I
b = −0.555909 − 0.782909I
−1.31282 + 1.41699I 0.791306 − 0.633731I
u = −1.232090 − 0.392876I
a = 0.674566 + 0.370203I
b = 0.623653 + 0.552777I
−1.31282 − 1.41699I 0.791306 + 0.633731I
u = −1.232090 − 0.392876I
a = 0.48177 + 1.51619I
b = −0.555909 + 0.782909I
−1.31282 − 1.41699I 0.791306 + 0.633731I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.317220 + 0.129556I
a = 0.469425 + 0.990105I
b = −0.752651 + 0.945347I
−8.47148 − 2.94672I −5.79937 + 4.11787I
u = 1.317220 + 0.129556I
a = −0.15850 − 2.09923I
b = −0.14927 − 1.48798I
−8.47148 − 2.94672I −5.79937 + 4.11787I
u = 1.317220 − 0.129556I
a = 0.469425 − 0.990105I
b = −0.752651 − 0.945347I
−8.47148 + 2.94672I −5.79937 − 4.11787I
u = 1.317220 − 0.129556I
a = −0.15850 + 2.09923I
b = −0.14927 + 1.48798I
−8.47148 + 2.94672I −5.79937 − 4.11787I
u = 1.304640 + 0.385413I
a = −0.579828 + 0.055525I
b = −1.081770 − 0.344108I
−1.85809 − 7.47524I −0.22908 + 5.55460I
u = 1.304640 + 0.385413I
a = −0.45041 − 1.69192I
b = 0.747184 − 1.181250I
−1.85809 − 7.47524I −0.22908 + 5.55460I
u = 1.304640 − 0.385413I
a = −0.579828 − 0.055525I
b = −1.081770 + 0.344108I
−1.85809 + 7.47524I −0.22908 − 5.55460I
u = 1.304640 − 0.385413I
a = −0.45041 + 1.69192I
b = 0.747184 + 1.181250I
−1.85809 + 7.47524I −0.22908 − 5.55460I
u = −0.271947 + 0.385187I
a = 1.270550 + 0.259399I
b = −0.087548 + 1.187670I
−3.59460 + 1.13130I −0.01220 − 6.05785I
u = −0.271947 + 0.385187I
a = 1.80079 + 2.03466I
b = −0.285332 − 0.830788I
−3.59460 + 1.13130I −0.01220 − 6.05785I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271947 − 0.385187I
a = 1.270550 − 0.259399I
b = −0.087548 − 1.187670I
−3.59460 − 1.13130I −0.01220 + 6.05785I
u = −0.271947 − 0.385187I
a = 1.80079 − 2.03466I
b = −0.285332 + 0.830788I
−3.59460 − 1.13130I −0.01220 + 6.05785I
12
III. I
u
3
= hau + b + a + 2u + 3, a
2
+ 2au + 4a + 2u + 6, u
2
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u + 1
a
1
=
−u
−u + 1
a
4
=
a
−au − a − 2u − 3
a
3
=
au + 2a + 2u + 3
−au − a − 2u − 3
a
2
=
au + 2a + u + 3
−au − a − 3u − 2
a
7
=
2au + 3a + 6u + 9
−1
a
5
=
−au − a − 2u − 3
0
a
6
=
−a − u − 2
au + u + 1
a
10
=
u
u
a
10
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
2
c
2
(u + 1)
4
c
5
, c
9
u
4
+ 3u
2
+ 1
c
8
(u
2
+ u − 1)
2
c
10
, c
11
(u
2
− u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(y + 1)
4
c
2
(y −1)
4
c
5
, c
9
(y
2
+ 3y + 1)
2
c
8
, c
10
, c
11
(y
2
− 3y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.61803 + 0.61803I
b = − 1.000000I
−4.27683 −8.00000
u = 0.618034
a = −2.61803 − 0.61803I
b = 1.000000I
−4.27683 −8.00000
u = −1.61803
a = −0.38197 + 1.61803I
b = 1.000000I
−12.1725 −8.00000
u = −1.61803
a = −0.38197 − 1.61803I
b = − 1.000000I
−12.1725 −8.00000
16
IV. I
u
4
= hb − 1, 2a − 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
4
=
0.5
1
a
3
=
−0.5
1
a
2
=
0.5
1
a
7
=
1.5
1
a
5
=
2
2
a
6
=
2
2
a
10
=
1
1
a
10
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2.25
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
10
, c
11
u + 1
c
2
, c
6
, c
7
c
8
u − 1
c
5
, c
9
u
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
10
, c
11
y −1
c
5
, c
9
y
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000
b = 1.00000
0 −2.25000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
(u + 1)(u
2
+ 1)
2
(u
17
− u
16
+ ··· − 4u
2
− 1)(u
22
+ 3u
21
+ ··· + 24u + 9)
c
2
(u − 1)(u + 1)
4
(u
17
+ 5u
16
+ ··· − 8u − 1)
· (u
22
+ 11u
21
+ ··· + 432u + 81)
c
5
, c
9
u(u
4
+ 3u
2
+ 1)
· (u
11
+ u
10
+ 2u
9
+ u
8
+ 4u
7
+ 2u
6
+ 4u
5
+ u
4
+ 3u
3
− u
2
− 1)
2
· (u
17
− 3u
16
+ ··· + 22u − 8)
c
6
, c
7
(u − 1)(u
2
+ 1)
2
(u
17
− u
16
+ ··· − 4u
2
− 1)(u
22
+ 3u
21
+ ··· + 24u + 9)
c
8
(u − 1)(u
2
+ u − 1)
2
· (u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
2
· (u
17
− 2u
16
+ ··· + 13u − 4)
c
10
, c
11
(u + 1)(u
2
− u − 1)
2
· (u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
2
· (u
17
− 2u
16
+ ··· + 13u − 4)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
(y −1)(y + 1)
4
(y
17
+ 5y
16
+ ··· − 8y −1)
· (y
22
+ 11y
21
+ ··· + 432y + 81)
c
2
((y −1)
5
)(y
17
+ 13y
16
+ ··· − 12y −1)
· (y
22
− y
21
+ ··· + 35640y + 6561)
c
5
, c
9
y(y
2
+ 3y + 1)
2
(y
11
+ 3y
10
+ ··· − 2y −1)
2
· (y
17
+ 9y
16
+ ··· − 12y −64)
c
8
, c
10
, c
11
(y −1)(y
2
− 3y + 1)
2
(y
11
− 9y
10
+ ··· − 2y −1)
2
· (y
17
− 16y
16
+ ··· + 209y −16)
22
