12n
0290
(K12n
0290
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 2 5 11 5 12 7 9 10
Solving Sequence
5,8 9,11
12 4 7 3 6 2 1 10
c
8
c
11
c
4
c
7
c
3
c
6
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.68465 × 10
94
u
40
− 9.84743 × 10
94
u
39
+ ··· + 1.38333 × 10
95
b − 5.11987 × 10
96
,
− 4.36327 × 10
94
u
40
− 1.61063 × 10
95
u
39
+ ··· + 2.76666 × 10
95
a − 8.27022 × 10
96
,
u
41
+ 4u
40
+ ··· + 544u + 64i
I
u
2
= hb, a − 1, u + 1i
I
v
1
= ha, 26v
5
+ 33v
4
+ 317v
3
+ 123v
2
+ 413b + 89v + 685, v
6
+ 3v
5
+ 15v
4
+ 24v
3
+ 11v
2
+ 6v + 1i
* 3 irreducible components of dim
C
= 0, with total 48 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−2.68 × 10
94
u
40
− 9.85 × 10
94
u
39
+ · · · + 1.38 × 10
95
b − 5.12 ×
10
96
, −4.36 × 10
94
u
40
− 1.61 × 10
95
u
39
+ · · · + 2.77 × 10
95
a − 8.27 ×
10
96
, u
41
+ 4u
40
+ · · · + 544u + 64i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
0.157709u
40
+ 0.582157u
39
+ ··· + 171.531u + 29.8924
0.194072u
40
+ 0.711864u
39
+ ··· + 205.306u + 37.0112
a
12
=
−0.0560706u
40
− 0.198690u
39
+ ··· − 50.1633u − 10.2342
0.220015u
40
+ 0.806259u
39
+ ··· + 232.028u + 41.7645
a
4
=
−u
u
a
7
=
−0.0860026u
40
− 0.314486u
39
+ ··· − 88.7056u − 16.8751
0.244795u
40
+ 0.889941u
39
+ ··· + 248.405u + 43.2805
a
3
=
−0.0998198u
40
− 0.360991u
39
+ ··· − 89.6766u − 14.8006
0.137856u
40
+ 0.501525u
39
+ ··· + 141.893u + 24.7433
a
6
=
−0.0860026u
40
− 0.314486u
39
+ ··· − 88.7056u − 16.8751
0.253986u
40
+ 0.923580u
39
+ ··· + 258.962u + 45.1700
a
2
=
−0.214458u
40
− 0.770687u
39
+ ··· − 201.880u − 34.5510
0.344343u
40
+ 1.25111u
39
+ ··· + 349.391u + 60.8829
a
1
=
−0.158792u
40
− 0.575454u
39
+ ··· − 159.700u − 26.4054
0.269010u
40
+ 0.976627u
39
+ ··· + 270.728u + 47.1022
a
10
=
0.357088u
40
+ 1.31046u
39
+ ··· + 376.594u + 66.5801
−0.262269u
40
− 0.954859u
39
+ ··· − 266.063u − 46.3657
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.16290u
40
− 7.86224u
39
+ ··· − 2195.29u − 401.897
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
41
+ 10u
40
+ ··· + 124u + 1
c
2
, c
5
u
41
+ 4u
40
+ ··· − 8u + 1
c
3
u
41
− 2u
40
+ ··· − 56802u + 4129
c
4
, c
8
u
41
+ 4u
40
+ ··· + 544u + 64
c
7
, c
10
u
41
+ 4u
40
+ ··· − 2u + 2
c
9
, c
11
, c
12
u
41
− 5u
40
+ ··· − 11u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
41
+ 46y
40
+ ··· + 12420y −1
c
2
, c
5
y
41
− 10y
40
+ ··· + 124y −1
c
3
y
41
+ 106y
40
+ ··· + 3427830276y −17048641
c
4
, c
8
y
41
− 36y
40
+ ··· + 46080y −4096
c
7
, c
10
y
41
+ 42y
39
+ ··· + 24y −4
c
9
, c
11
, c
12
y
41
− 29y
40
+ ··· + 141y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900371 + 0.275130I
a = −0.07966 − 1.47335I
b = 0.570501 + 0.849499I
−1.03538 + 3.10516I −9.19728 − 4.58914I
u = 0.900371 − 0.275130I
a = −0.07966 + 1.47335I
b = 0.570501 − 0.849499I
−1.03538 − 3.10516I −9.19728 + 4.58914I
u = −0.863117 + 0.163519I
a = 0.530392 − 1.038990I
b = 0.906841 + 0.441301I
−0.434343 − 0.606208I −8.36824 + 3.20718I
u = −0.863117 − 0.163519I
a = 0.530392 + 1.038990I
b = 0.906841 − 0.441301I
−0.434343 + 0.606208I −8.36824 − 3.20718I
u = −1.118190 + 0.134810I
a = 0.285482 + 1.154880I
b = −0.692354 − 0.679657I
2.14754 − 4.46827I −5.46325 + 6.31020I
u = −1.118190 − 0.134810I
a = 0.285482 − 1.154880I
b = −0.692354 + 0.679657I
2.14754 + 4.46827I −5.46325 − 6.31020I
u = −0.208887 + 0.817072I
a = 0.191298 − 0.000456I
b = −1.390780 + 0.124154I
−6.67711 + 2.45351I −15.2931 − 1.4222I
u = −0.208887 − 0.817072I
a = 0.191298 + 0.000456I
b = −1.390780 − 0.124154I
−6.67711 − 2.45351I −15.2931 + 1.4222I
u = −0.142298 + 0.686085I
a = 0.754137 − 0.156560I
b = 0.609820 − 0.257002I
−0.95163 + 1.08981I −8.28855 − 6.14268I
u = −0.142298 − 0.686085I
a = 0.754137 + 0.156560I
b = 0.609820 + 0.257002I
−0.95163 − 1.08981I −8.28855 + 6.14268I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.320790 + 0.205247I
a = 0.272392 + 0.830191I
b = −0.359803 − 0.924561I
3.58935 + 0.36497I 0
u = 1.320790 − 0.205247I
a = 0.272392 − 0.830191I
b = −0.359803 + 0.924561I
3.58935 − 0.36497I 0
u = −1.47758 + 0.08314I
a = −0.028558 + 0.821385I
b = 1.27898 − 1.15594I
7.32002 + 1.31400I 0
u = −1.47758 − 0.08314I
a = −0.028558 − 0.821385I
b = 1.27898 + 1.15594I
7.32002 − 1.31400I 0
u = 1.47211 + 0.17758I
a = −0.081855 − 0.839711I
b = 1.19530 + 1.24551I
7.22140 + 5.18811I 0
u = 1.47211 − 0.17758I
a = −0.081855 + 0.839711I
b = 1.19530 − 1.24551I
7.22140 − 5.18811I 0
u = −0.493631
a = 1.54896
b = −0.291712
−1.40989 −5.76550
u = 0.55563 + 1.40865I
a = 0.332513 + 0.052129I
b = −0.033282 − 0.910556I
4.81513 + 1.29204I 0
u = 0.55563 − 1.40865I
a = 0.332513 − 0.052129I
b = −0.033282 + 0.910556I
4.81513 − 1.29204I 0
u = 0.279316 + 0.386457I
a = −3.05813 − 4.36695I
b = −0.098053 + 0.379909I
−2.86863 − 0.30349I 1.29089 − 11.45256I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279316 − 0.386457I
a = −3.05813 + 4.36695I
b = −0.098053 − 0.379909I
−2.86863 + 0.30349I 1.29089 + 11.45256I
u = −0.012640 + 0.387805I
a = −8.88584 + 0.60443I
b = −0.500213 + 0.034819I
1.80837 − 2.87388I −39.8656 + 3.3819I
u = −0.012640 − 0.387805I
a = −8.88584 − 0.60443I
b = −0.500213 − 0.034819I
1.80837 + 2.87388I −39.8656 − 3.3819I
u = −0.64609 + 1.49909I
a = 0.280505 − 0.050822I
b = −0.227266 + 0.902339I
4.34862 + 5.20839I 0
u = −0.64609 − 1.49909I
a = 0.280505 + 0.050822I
b = −0.227266 − 0.902339I
4.34862 − 5.20839I 0
u = −0.353952
a = 0.190811
b = −1.66327
−9.84381 14.6310
u = −1.50019 + 0.69974I
a = −0.107163 − 0.866028I
b = 0.797327 + 0.867883I
−1.34409 − 8.57415I 0
u = −1.50019 − 0.69974I
a = −0.107163 + 0.866028I
b = 0.797327 − 0.867883I
−1.34409 + 8.57415I 0
u = −0.305001
a = 1.67143
b = 0.580690
−1.10346 −8.70760
u = −1.63935 + 0.45660I
a = −0.069974 + 0.912206I
b = −1.19023 − 1.18604I
11.66750 − 7.74036I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63935 − 0.45660I
a = −0.069974 − 0.912206I
b = −1.19023 + 1.18604I
11.66750 + 7.74036I 0
u = 1.56194 + 0.67841I
a = 0.009027 + 0.726408I
b = 0.492906 − 0.964772I
1.69219 + 4.01190I 0
u = 1.56194 − 0.67841I
a = 0.009027 − 0.726408I
b = 0.492906 + 0.964772I
1.69219 − 4.01190I 0
u = 1.67787 + 0.37565I
a = −0.035629 − 0.893097I
b = −1.10249 + 1.25882I
11.97710 + 1.09300I 0
u = 1.67787 − 0.37565I
a = −0.035629 + 0.893097I
b = −1.10249 − 1.25882I
11.97710 − 1.09300I 0
u = −1.49517 + 0.90641I
a = 0.139383 − 0.997291I
b = 1.11424 + 1.19188I
7.3447 − 13.9917I 0
u = −1.49517 − 0.90641I
a = 0.139383 + 0.997291I
b = 1.11424 − 1.19188I
7.3447 + 13.9917I 0
u = 1.54232 + 0.88599I
a = 0.131039 + 0.948244I
b = 1.03138 − 1.24212I
8.03425 + 7.41571I 0
u = 1.54232 − 0.88599I
a = 0.131039 − 0.948244I
b = 1.03138 + 1.24212I
8.03425 − 7.41571I 0
u = −1.63054 + 0.83010I
a = −0.034959 − 0.425949I
b = 0.284331 + 0.549059I
−3.12842 − 0.82148I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63054 − 0.83010I
a = −0.034959 + 0.425949I
b = 0.284331 − 0.549059I
−3.12842 + 0.82148I 0
9
II. I
u
2
= hb, a − 1, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
8
=
1
0
a
9
=
1
−1
a
11
=
1
0
a
12
=
0
1
a
4
=
1
−1
a
7
=
1
0
a
3
=
0
−1
a
6
=
1
−1
a
2
=
−1
0
a
1
=
−1
1
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
9
u − 1
c
5
, c
6
, c
8
c
11
, c
12
u + 1
c
7
, c
10
u
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
11
c
12
y −1
c
7
, c
10
y
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
−3.28987 −12.0000
13
III.
I
v
1
= ha, 26v
5
+33v
4
+· · · +413b + 685, v
6
+3v
5
+15v
4
+24v
3
+11v
2
+6v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−0.0629540v
5
− 0.0799031v
4
+ ··· − 0.215496v −1.65860
a
12
=
0.0629540v
5
+ 0.0799031v
4
+ ··· + 0.215496v + 1.65860
−0.0629540v
5
− 0.0799031v
4
+ ··· − 0.215496v −1.65860
a
4
=
v
0
a
7
=
1
−0.0629540v
5
− 0.0799031v
4
+ ··· − 0.215496v −2.65860
a
3
=
−0.108959v
5
− 0.176755v
4
+ ··· + 3.28087v −0.0629540
0.326877v
5
+ 0.530266v
4
+ ··· − 5.84262v + 0.188862
a
6
=
−0.150121v
5
− 0.421308v
4
+ ··· − 0.590799v + 0.891041
−0.0629540v
5
− 0.0799031v
4
+ ··· − 0.215496v −2.65860
a
2
=
−0.600484v
5
− 1.68523v
4
+ ··· − 2.36320v −1.43584
1.26392v
5
+ 3.45036v
4
+ ··· + 4.94189v + 3.53027
a
1
=
−1
0.0629540v
5
+ 0.0799031v
4
+ ··· + 0.215496v + 2.65860
a
10
=
−0.0629540v
5
− 0.0799031v
4
+ ··· − 0.215496v −1.65860
0.0629540v
5
+ 0.0799031v
4
+ ··· + 0.215496v + 2.65860
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3042
413
v
5
−
8817
413
v
4
−
44523
413
v
3
−
68494
413
v
2
−
24042
413
v −
18195
413
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
, c
8
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
(u
2
+ u − 1)
3
c
10
, c
11
, c
12
(u
2
− u − 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
y
6
c
7
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.49186
a = 0
b = 0.618034
−2.10041 −19.6940
v = −0.082153 + 0.499284I
a = 0
b = −1.61803
−5.85852 + 2.82812I −6.54788 − 4.14885I
v = −0.082153 − 0.499284I
a = 0
b = −1.61803
−5.85852 − 2.82812I −6.54788 + 4.14885I
v = −0.217660
a = 0
b = −1.61803
−9.99610 −38.1750
v = −0.56309 + 3.42214I
a = 0
b = 0.618034
2.03717 + 2.82812I 0.982489 + 0.847836I
v = −0.56309 − 3.42214I
a = 0
b = 0.618034
2.03717 − 2.82812I 0.982489 − 0.847836I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
41
+ 10u
40
+ ··· + 124u + 1)
c
2
(u − 1)(u
3
+ u
2
− 1)
2
(u
41
+ 4u
40
+ ··· − 8u + 1)
c
3
(u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
41
− 2u
40
+ ··· − 56802u + 4129)
c
4
u
6
(u − 1)(u
41
+ 4u
40
+ ··· + 544u + 64)
c
5
(u + 1)(u
3
− u
2
+ 1)
2
(u
41
+ 4u
40
+ ··· − 8u + 1)
c
6
(u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
41
+ 10u
40
+ ··· + 124u + 1)
c
7
u(u
2
+ u − 1)
3
(u
41
+ 4u
40
+ ··· − 2u + 2)
c
8
u
6
(u + 1)(u
41
+ 4u
40
+ ··· + 544u + 64)
c
9
(u − 1)(u
2
+ u − 1)
3
(u
41
− 5u
40
+ ··· − 11u − 1)
c
10
u(u
2
− u − 1)
3
(u
41
+ 4u
40
+ ··· − 2u + 2)
c
11
, c
12
(u + 1)(u
2
− u − 1)
3
(u
41
− 5u
40
+ ··· − 11u − 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
3
+ 3y
2
+ 2y −1)
2
(y
41
+ 46y
40
+ ··· + 12420y −1)
c
2
, c
5
(y −1)(y
3
− y
2
+ 2y −1)
2
(y
41
− 10y
40
+ ··· + 124y −1)
c
3
(y −1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
41
+ 106y
40
+ ··· + 3427830276y −17048641)
c
4
, c
8
y
6
(y −1)(y
41
− 36y
40
+ ··· + 46080y −4096)
c
7
, c
10
y(y
2
− 3y + 1)
3
(y
41
+ 42y
39
+ ··· + 24y −4)
c
9
, c
11
, c
12
(y −1)(y
2
− 3y + 1)
3
(y
41
− 29y
40
+ ··· + 141y −1)
19
