11a
36
(K11a
36
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 8 3 5 11 6 9
Solving Sequence
5,10
6
2,11
4 1 9 8 7 3
c
5
c
10
c
4
c
1
c
9
c
8
c
6
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
62
− u
61
+ ··· + b − 2u, −u
60
+ u
59
+ ··· + a − 2, u
63
− 2u
62
+ ··· − 10u
2
+ 1i
I
u
2
= hb + 1, a + u, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 66 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
= hu
62
−u
61
+· · ·+b−2u, −u
60
+u
59
+· · ·+a−2, u
63
−2u
62
+· · ·−10u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
u
60
− u
59
+ ··· − 4u + 2
−u
62
+ u
61
+ ··· − 6u
2
+ 2u
a
11
=
u
−u
3
+ u
a
4
=
−u
62
+ u
61
+ ··· − 4u + 3
−u
62
+ u
61
+ ··· − 7u
2
+ u
a
1
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
−u
5
− u
u
5
− u
3
+ u
a
7
=
−u
12
+ u
10
− 3u
8
+ 2u
6
− 2u
4
+ u
2
+ 1
u
12
− 2u
10
+ 4u
8
− 4u
6
+ 3u
4
− 2u
2
a
3
=
u
62
− u
61
+ ··· − 4u + 2
−u
62
+ u
61
+ ··· − 5u
2
+ 2u
a
3
=
u
62
− u
61
+ ··· − 4u + 2
−u
62
+ u
61
+ ··· − 5u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11u
62
+ 14u
61
+ ··· + 25u + 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
63
− 4u
62
+ ··· − 3u + 1
c
2
u
63
+ 34u
62
+ ··· + 5u + 1
c
3
, c
7
u
63
+ u
62
+ ··· + 12u + 8
c
5
, c
10
u
63
− 2u
62
+ ··· − 10u
2
+ 1
c
6
u
63
− 21u
62
+ ··· − 624u + 64
c
8
u
63
+ 2u
62
+ ··· − 18u + 9
c
9
, c
11
u
63
− 20u
62
+ ··· + 20u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
63
− 34y
62
+ ··· + 5y −1
c
2
y
63
− 6y
62
+ ··· − 27y −1
c
3
, c
7
y
63
+ 21y
62
+ ··· − 624y −64
c
5
, c
10
y
63
− 20y
62
+ ··· + 20y −1
c
6
y
63
+ 37y
62
+ ··· + 167168y −4096
c
8
y
63
+ 12y
62
+ ··· − 16272y −81
c
9
, c
11
y
63
+ 48y
62
+ ··· + 340y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986745 + 0.175564I
a = 0.61504 − 2.83433I
b = −1.081170 + 0.440014I
−0.60605 + 3.69700I 2.17014 − 4.90316I
u = 0.986745 − 0.175564I
a = 0.61504 + 2.83433I
b = −1.081170 − 0.440014I
−0.60605 − 3.69700I 2.17014 + 4.90316I
u = 0.874745 + 0.474777I
a = 0.286938 + 1.257720I
b = 0.415444 − 0.641775I
1.88400 + 1.11201I 5.93092 − 2.67876I
u = 0.874745 − 0.474777I
a = 0.286938 − 1.257720I
b = 0.415444 + 0.641775I
1.88400 − 1.11201I 5.93092 + 2.67876I
u = 0.964494 + 0.355493I
a = −0.902672 − 0.260134I
b = 1.089750 + 0.505160I
−0.13818 − 3.33082I 2.52685 + 2.17772I
u = 0.964494 − 0.355493I
a = −0.902672 + 0.260134I
b = 1.089750 − 0.505160I
−0.13818 + 3.33082I 2.52685 − 2.17772I
u = −0.812502 + 0.632834I
a = 0.90804 − 1.10283I
b = −0.817947 + 0.392240I
−2.19626 − 0.72911I 0
u = −0.812502 − 0.632834I
a = 0.90804 + 1.10283I
b = −0.817947 − 0.392240I
−2.19626 + 0.72911I 0
u = −1.028670 + 0.156882I
a = −1.00602 + 1.41426I
b = 0.264864 − 0.800811I
3.55985 − 4.49777I 7.47027 + 4.85592I
u = −1.028670 − 0.156882I
a = −1.00602 − 1.41426I
b = 0.264864 + 0.800811I
3.55985 + 4.49777I 7.47027 − 4.85592I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.042190 + 0.029758I
a = −1.18918 − 2.02036I
b = 0.778473 + 0.655233I
6.20929 − 2.51179I 9.63450 + 3.63863I
u = −1.042190 − 0.029758I
a = −1.18918 + 2.02036I
b = 0.778473 − 0.655233I
6.20929 + 2.51179I 9.63450 − 3.63863I
u = −0.935551 + 0.179164I
a = 0.853660 − 0.118464I
b = −1.182530 + 0.257010I
−1.01619 − 1.23564I 2.18804 + 4.79371I
u = −0.935551 − 0.179164I
a = 0.853660 + 0.118464I
b = −1.182530 − 0.257010I
−1.01619 + 1.23564I 2.18804 − 4.79371I
u = −1.052700 + 0.191629I
a = −0.51296 − 2.42316I
b = 1.157220 + 0.552536I
0.91945 − 9.52832I 0. + 8.35881I
u = −1.052700 − 0.191629I
a = −0.51296 + 2.42316I
b = 1.157220 − 0.552536I
0.91945 + 9.52832I 0. − 8.35881I
u = 0.708953 + 0.814144I
a = −0.019906 + 0.202917I
b = 0.178721 − 0.848670I
−2.92774 − 4.17173I 0
u = 0.708953 − 0.814144I
a = −0.019906 − 0.202917I
b = 0.178721 + 0.848670I
−2.92774 + 4.17173I 0
u = 0.607392 + 0.688668I
a = 0.119031 − 0.627685I
b = 0.881881 + 0.575730I
0.93068 − 3.11451I 1.81708 + 3.79797I
u = 0.607392 − 0.688668I
a = 0.119031 + 0.627685I
b = 0.881881 − 0.575730I
0.93068 + 3.11451I 1.81708 − 3.79797I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730831 + 0.812085I
a = −1.03790 − 0.99175I
b = −1.158560 + 0.468666I
−7.07861 + 2.97979I 0
u = −0.730831 − 0.812085I
a = −1.03790 + 0.99175I
b = −1.158560 − 0.468666I
−7.07861 − 2.97979I 0
u = 0.866834 + 0.666035I
a = −0.97074 − 1.07449I
b = −1.210370 + 0.030629I
−3.42806 + 2.58129I 0
u = 0.866834 − 0.666035I
a = −0.97074 + 1.07449I
b = −1.210370 − 0.030629I
−3.42806 − 2.58129I 0
u = −0.766973 + 0.785827I
a = 0.238443 + 0.199801I
b = −0.074618 − 0.675215I
−4.03831 − 1.31004I 0
u = −0.766973 − 0.785827I
a = 0.238443 − 0.199801I
b = −0.074618 + 0.675215I
−4.03831 + 1.31004I 0
u = 0.746245 + 0.806063I
a = −1.32268 − 0.61068I
b = −1.246680 + 0.342536I
−7.36657 − 0.17993I 0
u = 0.746245 − 0.806063I
a = −1.32268 + 0.61068I
b = −1.246680 − 0.342536I
−7.36657 + 0.17993I 0
u = 0.709456 + 0.839598I
a = 1.007390 − 0.709259I
b = 1.198760 + 0.538883I
−5.96644 − 9.24715I 0
u = 0.709456 − 0.839598I
a = 1.007390 + 0.709259I
b = 1.198760 − 0.538883I
−5.96644 + 9.24715I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896870 + 0.059236I
a = 1.60096 + 0.91476I
b = −0.331068 − 0.319832I
1.55408 + 0.10582I 6.26556 + 0.58371I
u = 0.896870 − 0.059236I
a = 1.60096 − 0.91476I
b = −0.331068 + 0.319832I
1.55408 − 0.10582I 6.26556 − 0.58371I
u = −0.915129 + 0.657239I
a = 0.50428 + 2.10750I
b = −0.706877 − 0.424114I
−1.85739 − 4.32227I 0
u = −0.915129 − 0.657239I
a = 0.50428 − 2.10750I
b = −0.706877 + 0.424114I
−1.85739 + 4.32227I 0
u = −0.788679 + 0.828583I
a = 1.248600 − 0.560983I
b = 1.153780 + 0.425567I
−7.38822 − 5.19388I 0
u = −0.788679 − 0.828583I
a = 1.248600 + 0.560983I
b = 1.153780 − 0.425567I
−7.38822 + 5.19388I 0
u = 0.972413 + 0.616521I
a = −1.155960 − 0.419026I
b = 0.638145 + 0.682574I
2.75209 + 3.26890I 0
u = 0.972413 − 0.616521I
a = −1.155960 + 0.419026I
b = 0.638145 − 0.682574I
2.75209 − 3.26890I 0
u = −0.880612 + 0.777007I
a = 0.870304 − 0.514339I
b = 0.742658 + 0.034260I
−3.99010 − 2.92514I 0
u = −0.880612 − 0.777007I
a = 0.870304 + 0.514339I
b = 0.742658 − 0.034260I
−3.99010 + 2.92514I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.995425 + 0.656387I
a = 0.43151 + 2.20348I
b = 0.892480 − 0.637862I
2.02729 + 8.31052I 0
u = 0.995425 − 0.656387I
a = 0.43151 − 2.20348I
b = 0.892480 + 0.637862I
2.02729 − 8.31052I 0
u = −0.963455 + 0.732228I
a = 1.199630 − 0.298215I
b = −0.136404 + 0.659647I
−3.43377 − 4.42046I 0
u = −0.963455 − 0.732228I
a = 1.199630 + 0.298215I
b = −0.136404 − 0.659647I
−3.43377 + 4.42046I 0
u = 0.982283 + 0.738862I
a = −0.457935 − 0.943864I
b = −1.260650 − 0.325376I
−6.64299 + 5.98946I 0
u = 0.982283 − 0.738862I
a = −0.457935 + 0.943864I
b = −1.260650 + 0.325376I
−6.64299 − 5.98946I 0
u = −0.965072 + 0.771283I
a = 0.443626 − 0.814250I
b = 1.141120 − 0.407113I
−6.84424 − 0.78588I 0
u = −0.965072 − 0.771283I
a = 0.443626 + 0.814250I
b = 1.141120 + 0.407113I
−6.84424 + 0.78588I 0
u = −0.992955 + 0.736861I
a = −1.15889 + 2.64082I
b = −1.148080 − 0.485998I
−6.27660 − 8.79934I 0
u = −0.992955 − 0.736861I
a = −1.15889 − 2.64082I
b = −1.148080 + 0.485998I
−6.27660 + 8.79934I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004710 + 0.730240I
a = −1.188500 − 0.320665I
b = 0.198021 + 0.868774I
−2.02603 + 9.97382I 0
u = 1.004710 − 0.730240I
a = −1.188500 + 0.320665I
b = 0.198021 − 0.868774I
−2.02603 − 9.97382I 0
u = 1.014130 + 0.742144I
a = 1.18770 + 2.38163I
b = 1.201630 − 0.551168I
−5.0319 + 15.1597I 0
u = 1.014130 − 0.742144I
a = 1.18770 − 2.38163I
b = 1.201630 + 0.551168I
−5.0319 − 15.1597I 0
u = 0.467397 + 0.552241I
a = 0.336545 + 0.777590I
b = 0.656494 − 0.538703I
1.61397 + 1.37996I 3.33026 − 3.84355I
u = 0.467397 − 0.552241I
a = 0.336545 − 0.777590I
b = 0.656494 + 0.538703I
1.61397 − 1.37996I 3.33026 + 3.84355I
u = 0.100658 + 0.672094I
a = 1.138600 + 0.751362I
b = 1.149530 − 0.509940I
−2.82669 + 6.78405I −3.37376 − 6.18383I
u = 0.100658 − 0.672094I
a = 1.138600 − 0.751362I
b = 1.149530 + 0.509940I
−2.82669 − 6.78405I −3.37376 + 6.18383I
u = 0.126664 + 0.583968I
a = 0.0087736 − 0.0534979I
b = 0.195316 + 0.700814I
−0.08935 + 2.18002I −0.08533 − 3.20984I
u = 0.126664 − 0.583968I
a = 0.0087736 + 0.0534979I
b = 0.195316 − 0.700814I
−0.08935 − 2.18002I −0.08533 + 3.20984I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032116 + 0.576226I
a = −1.38838 + 1.00826I
b = −1.143910 − 0.371905I
−3.80293 − 1.26646I −5.80106 + 0.80985I
u = −0.032116 − 0.576226I
a = −1.38838 − 1.00826I
b = −1.143910 + 0.371905I
−3.80293 + 1.26646I −5.80106 − 0.80985I
u = −0.235960
a = 2.62532
b = −0.870881
−1.26098 −8.95540
11
II. I
u
2
= hb + 1, a + u, u
3
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
−u
−1
a
11
=
u
−u
2
+ u + 1
a
4
=
−u + 1
−1
a
1
=
−1
0
a
9
=
−u
2
+ 1
−u
2
a
8
=
1
−u
2
a
7
=
1
−u
2
a
3
=
−u + 1
−1
a
3
=
−u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
− 7u − 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
c
2
, c
4
(u + 1)
3
c
3
, c
6
, c
7
u
3
c
5
u
3
− u
2
+ 1
c
8
, c
11
u
3
− u
2
+ 2u − 1
c
9
u
3
+ u
2
+ 2u + 1
c
10
u
3
+ u
2
− 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
, c
7
y
3
c
5
, c
10
y
3
− y
2
+ 2y −1
c
8
, c
9
, c
11
y
3
+ 3y
2
+ 2y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.877439 − 0.744862I
b = −1.00000
−4.66906 + 2.82812I −7.71191 − 2.59975I
u = 0.877439 − 0.744862I
a = −0.877439 + 0.744862I
b = −1.00000
−4.66906 − 2.82812I −7.71191 + 2.59975I
u = −0.754878
a = 0.754878
b = −1.00000
−0.531480 4.42380
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
63
− 4u
62
+ ··· − 3u + 1)
c
2
((u + 1)
3
)(u
63
+ 34u
62
+ ··· + 5u + 1)
c
3
, c
7
u
3
(u
63
+ u
62
+ ··· + 12u + 8)
c
4
((u + 1)
3
)(u
63
− 4u
62
+ ··· − 3u + 1)
c
5
(u
3
− u
2
+ 1)(u
63
− 2u
62
+ ··· − 10u
2
+ 1)
c
6
u
3
(u
63
− 21u
62
+ ··· − 624u + 64)
c
8
(u
3
− u
2
+ 2u − 1)(u
63
+ 2u
62
+ ··· − 18u + 9)
c
9
(u
3
+ u
2
+ 2u + 1)(u
63
− 20u
62
+ ··· + 20u − 1)
c
10
(u
3
+ u
2
− 1)(u
63
− 2u
62
+ ··· − 10u
2
+ 1)
c
11
(u
3
− u
2
+ 2u − 1)(u
63
− 20u
62
+ ··· + 20u − 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
63
− 34y
62
+ ··· + 5y −1)
c
2
((y −1)
3
)(y
63
− 6y
62
+ ··· − 27y −1)
c
3
, c
7
y
3
(y
63
+ 21y
62
+ ··· − 624y −64)
c
5
, c
10
(y
3
− y
2
+ 2y −1)(y
63
− 20y
62
+ ··· + 20y −1)
c
6
y
3
(y
63
+ 37y
62
+ ··· + 167168y −4096)
c
8
(y
3
+ 3y
2
+ 2y −1)(y
63
+ 12y
62
+ ··· − 16272y −81)
c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)(y
63
+ 48y
62
+ ··· + 340y −1)
17
