11a
20
(K11a
20
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 9 3 11 10 5 7 8
Solving Sequence
2,5
4 1
3,10
9 6 7 8 11
c
4
c
1
c
2
c
9
c
5
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.27448 × 10
21
u
63
+ 1.27056 × 10
22
u
62
+ ··· + 4.69870 × 10
20
b + 1.19330 × 10
21
,
− 5.52423 × 10
21
u
63
+ 2.53933 × 10
22
u
62
+ ··· + 9.39740 × 10
20
a + 2.28536 × 10
20
, u
64
− 7u
63
+ ··· + u + 1i
I
u
2
= h−a
4
+ a
3
− a
2
+ b + 2a − 1, a
5
− a
4
+ a
3
− 2a
2
+ a − 1, u + 1i
I
u
3
= hb, u
2
+ a − 2u + 1, u
3
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 72 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−2.27×10
21
u
63
+1.27×10
22
u
62
+· · ·+4.70×10
20
b+1.19×10
21
, −5.52×
10
21
u
63
+2.54×10
22
u
62
+· · ·+9.40×10
20
a+2.29×10
20
, u
64
−7u
63
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
10
=
5.87847u
63
− 27.0216u
62
+ ··· + 28.2191u − 0.243190
4.84066u
63
− 27.0407u
62
+ ··· + 0.696184u − 2.53964
a
9
=
1.03781u
63
+ 0.0190663u
62
+ ··· + 27.5230u + 2.29645
4.84066u
63
− 27.0407u
62
+ ··· + 0.696184u − 2.53964
a
6
=
10.4449u
63
− 79.7256u
62
+ ··· − 50.1840u − 25.9116
0.631883u
63
+ 8.05715u
62
+ ··· + 34.0330u + 11.6574
a
7
=
5.78835u
63
− 39.8513u
62
+ ··· − 14.9790u − 11.2988
−2.02198u
63
+ 22.2471u
62
+ ··· + 31.7864u + 11.7439
a
8
=
13.3094u
63
− 73.2209u
62
+ ··· + 17.5988u − 8.10092
−4.44093u
63
+ 37.8664u
62
+ ··· + 36.2343u + 13.7317
a
11
=
17.7393u
63
− 103.819u
62
+ ··· + 2.17710u − 17.2081
−2.67789u
63
+ 31.9650u
62
+ ··· + 50.1233u + 17.4101
a
11
=
17.7393u
63
− 103.819u
62
+ ··· + 2.17710u − 17.2081
−2.67789u
63
+ 31.9650u
62
+ ··· + 50.1233u + 17.4101
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2720935457231122035033
469870013462984070152
u
63
−
8461485863841657548067
469870013462984070152
u
62
+ ··· +
14151995465501805816563
469870013462984070152
u +
1148701840102396678745
117467503365746017538
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
64
− 7u
63
+ ··· + u + 1
c
2
u
64
+ 29u
63
+ ··· + 27u + 1
c
3
, c
6
u
64
− 2u
63
+ ··· + 64u − 32
c
5
, c
9
u
64
− 2u
63
+ ··· + 4u + 8
c
7
, c
10
, c
11
u
64
− 5u
63
+ ··· + 14u − 1
c
8
u
64
+ 24u
63
+ ··· − 464u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
64
− 29y
63
+ ··· − 27y + 1
c
2
y
64
+ 19y
63
+ ··· − 2587y + 1
c
3
, c
6
y
64
+ 36y
63
+ ··· + 7680y + 1024
c
5
, c
9
y
64
+ 24y
63
+ ··· − 464y + 64
c
7
, c
10
, c
11
y
64
− 55y
63
+ ··· − 294y + 1
c
8
y
64
+ 28y
63
+ ··· − 1248512y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.892738 + 0.448763I
a = −0.677948 − 0.577752I
b = −1.105160 + 0.138131I
−3.21351 − 1.80870I 0
u = 0.892738 − 0.448763I
a = −0.677948 + 0.577752I
b = −1.105160 − 0.138131I
−3.21351 + 1.80870I 0
u = 0.455631 + 0.904878I
a = −1.188140 − 0.429481I
b = −0.722344 − 0.983370I
5.23941 + 5.04408I 0
u = 0.455631 − 0.904878I
a = −1.188140 + 0.429481I
b = −0.722344 + 0.983370I
5.23941 − 5.04408I 0
u = 0.458581 + 0.849452I
a = 1.68790 − 0.08561I
b = 0.950572 − 0.661117I
1.85655 + 3.18076I −7.00000 + 0.I
u = 0.458581 − 0.849452I
a = 1.68790 + 0.08561I
b = 0.950572 + 0.661117I
1.85655 − 3.18076I −7.00000 + 0.I
u = 0.513790 + 0.814105I
a = 1.137550 + 0.030043I
b = 0.641399 + 0.876706I
2.25186 + 0.42541I −7.00000 + 0.I
u = 0.513790 − 0.814105I
a = 1.137550 − 0.030043I
b = 0.641399 − 0.876706I
2.25186 − 0.42541I −7.00000 + 0.I
u = 0.575812 + 0.867424I
a = −1.40928 + 0.24972I
b = −0.808864 + 0.726024I
6.03567 − 0.70423I 0
u = 0.575812 − 0.867424I
a = −1.40928 − 0.24972I
b = −0.808864 − 0.726024I
6.03567 + 0.70423I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404010 + 0.961178I
a = 1.161090 + 0.684160I
b = 0.751183 + 1.083290I
0.50492 + 9.42816I 0
u = 0.404010 − 0.961178I
a = 1.161090 − 0.684160I
b = 0.751183 − 1.083290I
0.50492 − 9.42816I 0
u = −0.926583 + 0.484056I
a = −1.11157 + 1.26592I
b = −0.870442 + 0.528800I
−2.88218 + 3.00440I 0
u = −0.926583 − 0.484056I
a = −1.11157 − 1.26592I
b = −0.870442 − 0.528800I
−2.88218 − 3.00440I 0
u = −1.043140 + 0.195913I
a = −0.91468 + 1.70928I
b = 0.025861 − 0.692002I
−2.98471 + 0.79780I 0
u = −1.043140 − 0.195913I
a = −0.91468 − 1.70928I
b = 0.025861 + 0.692002I
−2.98471 − 0.79780I 0
u = 0.942735 + 0.500566I
a = 0.607864 + 1.224530I
b = 0.012514 − 1.072630I
−1.51825 − 4.24420I 0
u = 0.942735 − 0.500566I
a = 0.607864 − 1.224530I
b = 0.012514 + 1.072630I
−1.51825 + 4.24420I 0
u = −0.842329 + 0.399836I
a = −2.62253 + 0.97033I
b = −0.487811 − 0.667717I
−2.41667 + 0.68003I −10.70240 − 3.97154I
u = −0.842329 − 0.399836I
a = −2.62253 − 0.97033I
b = −0.487811 + 0.667717I
−2.41667 − 0.68003I −10.70240 + 3.97154I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643524 + 0.662505I
a = −0.81928 + 1.53795I
b = −0.573528 + 0.999433I
−3.53655 − 3.75839I −9.90897 + 2.47413I
u = −0.643524 − 0.662505I
a = −0.81928 − 1.53795I
b = −0.573528 − 0.999433I
−3.53655 + 3.75839I −9.90897 − 2.47413I
u = −0.924487 + 0.552399I
a = 2.35170 − 0.32648I
b = 0.638310 + 0.930488I
0.23940 + 4.71266I 0
u = −0.924487 − 0.552399I
a = 2.35170 + 0.32648I
b = 0.638310 − 0.930488I
0.23940 − 4.71266I 0
u = −0.750013 + 0.530556I
a = 0.92021 − 1.37826I
b = 0.649111 − 0.745774I
0.803950 − 0.315255I −4.55635 + 0.I
u = −0.750013 − 0.530556I
a = 0.92021 + 1.37826I
b = 0.649111 + 0.745774I
0.803950 + 0.315255I −4.55635 + 0.I
u = 0.813121 + 0.418560I
a = −0.127255 − 1.035700I
b = 0.284466 + 1.063420I
−0.924060 + 0.442031I −7.00000 + 0.I
u = 0.813121 − 0.418560I
a = −0.127255 + 1.035700I
b = 0.284466 − 1.063420I
−0.924060 − 0.442031I −7.00000 + 0.I
u = 0.861442 + 0.662767I
a = 0.499053 + 0.320374I
b = 0.602748 − 0.054842I
2.28792 − 2.57835I 0
u = 0.861442 − 0.662767I
a = 0.499053 − 0.320374I
b = 0.602748 + 0.054842I
2.28792 + 2.57835I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841966 + 0.249603I
a = 0.106480 + 0.758428I
b = −0.493505 − 1.278120I
−7.08020 + 3.75832I −7.89460 + 2.35018I
u = 0.841966 − 0.249603I
a = 0.106480 − 0.758428I
b = −0.493505 + 1.278120I
−7.08020 − 3.75832I −7.89460 − 2.35018I
u = 0.692342 + 0.906468I
a = 1.135280 − 0.491124I
b = 0.613430 − 0.823572I
2.43022 − 4.49300I 0
u = 0.692342 − 0.906468I
a = 1.135280 + 0.491124I
b = 0.613430 + 0.823572I
2.43022 + 4.49300I 0
u = −0.988405 + 0.608854I
a = −2.21838 + 0.08688I
b = −0.675315 − 1.087940I
−4.58177 + 8.71812I 0
u = −0.988405 − 0.608854I
a = −2.21838 − 0.08688I
b = −0.675315 + 1.087940I
−4.58177 − 8.71812I 0
u = 1.083340 + 0.462764I
a = −0.909615 − 0.728843I
b = −0.220258 + 1.351590I
−8.76429 − 6.48628I 0
u = 1.083340 − 0.462764I
a = −0.909615 + 0.728843I
b = −0.220258 − 1.351590I
−8.76429 + 6.48628I 0
u = −0.814631
a = −0.747058
b = −0.242726
−1.19032 −8.27220
u = −1.188330 + 0.101883I
a = 0.944463 − 1.011510I
b = 0.755044 + 0.405276I
−3.86010 − 0.85522I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.188330 − 0.101883I
a = 0.944463 + 1.011510I
b = 0.755044 − 0.405276I
−3.86010 + 0.85522I 0
u = −1.190870 + 0.376705I
a = 1.075110 − 0.386024I
b = 0.047966 + 1.176860I
−9.32581 + 1.34639I 0
u = −1.190870 − 0.376705I
a = 1.075110 + 0.386024I
b = 0.047966 − 1.176860I
−9.32581 − 1.34639I 0
u = 1.081320 + 0.644153I
a = 1.66629 + 1.06042I
b = 0.541565 − 0.991647I
0.54026 − 5.89102I 0
u = 1.081320 − 0.644153I
a = 1.66629 − 1.06042I
b = 0.541565 + 0.991647I
0.54026 + 5.89102I 0
u = 1.062570 + 0.695609I
a = −0.374719 − 0.834857I
b = −0.838497 − 0.611622I
4.55904 − 5.08051I 0
u = 1.062570 − 0.695609I
a = −0.374719 + 0.834857I
b = −0.838497 + 0.611622I
4.55904 + 5.08051I 0
u = −1.272150 + 0.077417I
a = −0.289723 − 0.748311I
b = −0.589111 + 0.855580I
−0.94885 − 2.33285I 0
u = −1.272150 − 0.077417I
a = −0.289723 + 0.748311I
b = −0.589111 − 0.855580I
−0.94885 + 2.33285I 0
u = 1.007050 + 0.790636I
a = 0.061235 + 0.831316I
b = 0.477046 + 0.732746I
1.48618 − 1.70443I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.007050 − 0.790636I
a = 0.061235 − 0.831316I
b = 0.477046 − 0.732746I
1.48618 + 1.70443I 0
u = 1.114390 + 0.645519I
a = 0.525778 + 0.875080I
b = 1.057350 + 0.612780I
−0.11555 − 8.73931I 0
u = 1.114390 − 0.645519I
a = 0.525778 − 0.875080I
b = 1.057350 − 0.612780I
−0.11555 + 8.73931I 0
u = −0.043869 + 0.693831I
a = 0.223595 − 1.043440I
b = −0.179019 − 1.111590I
−5.83041 + 2.67272I −11.08007 − 3.60014I
u = −0.043869 − 0.693831I
a = 0.223595 + 1.043440I
b = −0.179019 + 1.111590I
−5.83041 − 2.67272I −11.08007 + 3.60014I
u = 1.134300 + 0.665213I
a = −1.79581 − 0.80258I
b = −0.694107 + 1.060630I
3.18001 − 10.81860I 0
u = 1.134300 − 0.665213I
a = −1.79581 + 0.80258I
b = −0.694107 − 1.060630I
3.18001 + 10.81860I 0
u = 1.174860 + 0.664654I
a = 1.79983 + 0.62712I
b = 0.769782 − 1.149600I
−1.8513 − 15.3455I 0
u = 1.174860 − 0.664654I
a = 1.79983 − 0.62712I
b = 0.769782 + 1.149600I
−1.8513 + 15.3455I 0
u = −1.344220 + 0.130440I
a = 0.177278 + 0.405955I
b = 0.617471 − 1.071230I
−5.71689 − 6.00573I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.344220 − 0.130440I
a = 0.177278 − 0.405955I
b = 0.617471 + 1.071230I
−5.71689 + 6.00573I 0
u = 0.029039 + 0.244733I
a = −1.77560 + 0.47939I
b = 0.227592 + 0.697212I
−0.369684 + 1.136730I −4.87497 − 6.04552I
u = 0.029039 − 0.244733I
a = −1.77560 − 0.47939I
b = 0.227592 − 0.697212I
−0.369684 − 1.136730I −4.87497 + 6.04552I
u = −0.147593
a = −6.94526
b = −0.568177
−2.17596 −2.85460
11
II. I
u
2
= h−a
4
+ a
3
− a
2
+ b + 2a − 1, a
5
− a
4
+ a
3
− 2a
2
+ a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
1
=
−1
0
a
3
=
1
−1
a
10
=
a
a
4
− a
3
+ a
2
− 2a + 1
a
9
=
−a
4
+ a
3
− a
2
+ 3a − 1
a
4
− a
3
+ a
2
− 2a + 1
a
6
=
a
4
− a − 1
−a
4
+ a + 1
a
7
=
a
4
− a − 1
−a
4
+ a + 1
a
8
=
a
a
3
− 1
a
11
=
a
4
− a − 1
−a
3
+ a
2
+ 2
a
11
=
a
4
− a − 1
−a
3
+ a
2
+ 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
4
+ 5a
3
+ 7a − 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
6
u
5
c
5
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
10
, c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
7
, c
10
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.428550 + 1.039280I
b = −0.339110 − 0.822375I
−1.97403 + 1.53058I −10.50099 − 3.45976I
u = −1.00000
a = −0.428550 − 1.039280I
b = −0.339110 + 0.822375I
−1.97403 − 1.53058I −10.50099 + 3.45976I
u = −1.00000
a = 0.276511 + 0.728237I
b = 0.455697 − 1.200150I
−7.51750 − 4.40083I −14.3774 + 5.8297I
u = −1.00000
a = 0.276511 − 0.728237I
b = 0.455697 + 1.200150I
−7.51750 + 4.40083I −14.3774 − 5.8297I
u = −1.00000
a = 1.30408
b = 0.766826
−4.04602 −8.24330
15
III. I
u
3
= hb, u
2
+ a − 2u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
2
+ u + 1
a
3
=
−u
2
+ 1
−u
2
a
10
=
−u
2
+ 2u − 1
0
a
9
=
−u
2
+ 2u − 1
0
a
6
=
1
0
a
7
=
−u
u
2
− u − 1
a
8
=
−u
2
+ 2u − 1
0
a
11
=
−u
2
+ 3u − 1
−u
2
+ u + 1
a
11
=
−u
2
+ 3u − 1
−u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
+ 8u − 16
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
, c
8
, c
9
u
3
c
7
(u − 1)
3
c
10
, c
11
(u + 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− y
2
+ 2y −1
c
2
, c
3
, c
6
y
3
+ 3y
2
+ 2y −1
c
5
, c
8
, c
9
y
3
c
7
, c
10
, c
11
(y −1)
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.539798 + 0.182582I
b = 0
1.37919 − 2.82812I −9.19557 + 4.65175I
u = 0.877439 − 0.744862I
a = 0.539798 − 0.182582I
b = 0
1.37919 + 2.82812I −9.19557 − 4.65175I
u = −0.754878
a = −3.07960
b = 0
−2.75839 −22.6090
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
+ u
2
− 1)(u
64
− 7u
63
+ ··· + u + 1)
c
2
((u + 1)
5
)(u
3
+ u
2
+ 2u + 1)(u
64
+ 29u
63
+ ··· + 27u + 1)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
64
− 2u
63
+ ··· + 64u − 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)(u
64
− 7u
63
+ ··· + u + 1)
c
5
u
3
(u
5
− u
4
+ ··· + u − 1)(u
64
− 2u
63
+ ··· + 4u + 8)
c
6
u
5
(u
3
+ u
2
+ 2u + 1)(u
64
− 2u
63
+ ··· + 64u − 32)
c
7
((u − 1)
3
)(u
5
+ u
4
+ ··· + u − 1)(u
64
− 5u
63
+ ··· + 14u − 1)
c
8
u
3
(u
5
− 3u
4
+ ··· − u + 1)(u
64
+ 24u
63
+ ··· − 464u + 64)
c
9
u
3
(u
5
+ u
4
+ ··· + u + 1)(u
64
− 2u
63
+ ··· + 4u + 8)
c
10
, c
11
((u + 1)
3
)(u
5
− u
4
+ ··· + u + 1)(u
64
− 5u
63
+ ··· + 14u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
3
− y
2
+ 2y −1)(y
64
− 29y
63
+ ··· − 27y + 1)
c
2
((y −1)
5
)(y
3
+ 3y
2
+ 2y −1)(y
64
+ 19y
63
+ ··· − 2587y + 1)
c
3
, c
6
y
5
(y
3
+ 3y
2
+ 2y −1)(y
64
+ 36y
63
+ ··· + 7680y + 1024)
c
5
, c
9
y
3
(y
5
+ 3y
4
+ ··· − y −1)(y
64
+ 24y
63
+ ··· − 464y + 64)
c
7
, c
10
, c
11
((y −1)
3
)(y
5
− 5y
4
+ ··· − y −1)(y
64
− 55y
63
+ ··· − 294y + 1)
c
8
y
3
(y
5
− y
4
+ ··· + 3y −1)(y
64
+ 28y
63
+ ··· − 1248512y + 4096)
21
