12n
0477
(K12n
0477
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 12 11 3 4 6 7 8
Solving Sequence
6,12 3,7
2 1 5 11 8 10 4 9
c
6
c
2
c
1
c
5
c
11
c
7
c
10
c
3
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2225017u
29
+ 4505754u
28
+ ··· + 4816957b − 1955093,
− 2648086u
29
− 9433003u
28
+ ··· + 28901742a + 37209631, u
30
− 2u
29
+ ··· + 5u − 3i
I
u
2
= hb − 1, −2u
2
a + a
2
− 2au + 4u
2
− 4a + 3u + 7, u
3
+ u
2
+ 2u + 1i
I
u
3
= hb + 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 39 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−2.23 × 10
6
u
29
+ 4.51 × 10
6
u
28
+ · · · + 4.82 × 10
6
b − 1.96 × 10
6
, −2.65 ×
10
6
u
29
−9.43×10
6
u
28
+· · ·+2.89×10
7
a+3.72×10
7
, u
30
−2u
29
+· · ·+5u −3i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
0.0916238u
29
+ 0.326382u
28
+ ··· − 0.0897393u − 1.28745
0.461913u
29
− 0.935394u
28
+ ··· + 0.0723297u + 0.405877
a
7
=
1
u
2
a
2
=
0.553537u
29
− 0.609012u
28
+ ··· − 0.0174096u − 0.881576
0.461913u
29
− 0.935394u
28
+ ··· + 0.0723297u + 0.405877
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
0.847386u
29
− 1.24384u
28
+ ··· − 1.07511u + 1.57925
0.551237u
29
− 1.21563u
28
+ ··· − 1.81025u + 0.917412
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
u
3
+ 2u
u
3
+ u
a
4
=
−0.0573861u
29
+ 0.274952u
28
+ ··· + 0.731599u − 2.38174
0.0837160u
29
− 0.147522u
28
+ ··· + 1.77910u − 0.712657
a
9
=
0.348620u
29
− 1.11181u
28
+ ··· − 3.98425u + 2.17901
0.0392597u
29
− 0.428436u
28
+ ··· − 1.44021u + 0.962791
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4602334
4816957
u
29
+
5525451
4816957
u
28
+ ··· −
80618534
4816957
u −
73845258
4816957
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 42u
29
+ ··· + 4660u + 289
c
2
, c
5
u
30
+ 4u
29
+ ··· + 28u − 17
c
3
, c
4
, c
9
u
30
− u
29
+ ··· + 16u + 8
c
6
, c
7
, c
11
u
30
+ 2u
29
+ ··· − 5u − 3
c
8
u
30
+ u
29
+ ··· − 48u + 488
c
10
, c
12
u
30
− 2u
29
+ ··· − 17u − 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 98y
29
+ ··· − 20560756y + 83521
c
2
, c
5
y
30
− 42y
29
+ ··· − 4660y + 289
c
3
, c
4
, c
9
y
30
+ 23y
29
+ ··· − 2304y
2
+ 64
c
6
, c
7
, c
11
y
30
+ 24y
29
+ ··· − 121y + 9
c
8
y
30
− 61y
29
+ ··· + 989312y + 238144
c
10
, c
12
y
30
− 40y
29
+ ··· − 265y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999114
a = −2.25143
b = −1.90174
−15.9829 −16.7010
u = 0.966560 + 0.100179I
a = 2.26552 − 0.36955I
b = 1.79997 + 0.26406I
−11.56980 − 6.42747I −14.4599 + 3.2280I
u = 0.966560 − 0.100179I
a = 2.26552 + 0.36955I
b = 1.79997 − 0.26406I
−11.56980 + 6.42747I −14.4599 − 3.2280I
u = −0.067362 + 1.069610I
a = −0.93060 + 1.33467I
b = −1.167500 − 0.308385I
5.15569 + 0.50722I −9.61314 + 0.41907I
u = −0.067362 − 1.069610I
a = −0.93060 − 1.33467I
b = −1.167500 + 0.308385I
5.15569 − 0.50722I −9.61314 − 0.41907I
u = −0.293578 + 1.051070I
a = 0.782550 + 1.067670I
b = 1.113160 − 0.513139I
−0.78564 + 2.16545I −13.74695 − 1.34185I
u = −0.293578 − 1.051070I
a = 0.782550 − 1.067670I
b = 1.113160 + 0.513139I
−0.78564 − 2.16545I −13.74695 + 1.34185I
u = 0.151469 + 1.144510I
a = −0.115008 − 0.375373I
b = −0.123274 + 0.591027I
2.57428 − 1.65013I −8.15669 + 3.84589I
u = 0.151469 − 1.144510I
a = −0.115008 + 0.375373I
b = −0.123274 − 0.591027I
2.57428 + 1.65013I −8.15669 − 3.84589I
u = 0.809755 + 0.043993I
a = −1.114310 + 0.426209I
b = −0.855875 + 0.695414I
−2.25326 + 2.17999I −13.9404 − 3.4735I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.809755 − 0.043993I
a = −1.114310 − 0.426209I
b = −0.855875 − 0.695414I
−2.25326 − 2.17999I −13.9404 + 3.4735I
u = −0.636663 + 0.315952I
a = 1.41716 + 0.84138I
b = 1.344600 + 0.179052I
−2.86347 + 1.34973I −14.1130 − 4.7512I
u = −0.636663 − 0.315952I
a = 1.41716 − 0.84138I
b = 1.344600 − 0.179052I
−2.86347 − 1.34973I −14.1130 + 4.7512I
u = 0.397857 + 1.242680I
a = −0.883299 + 0.876579I
b = −0.772590 − 0.869650I
1.43546 − 6.54686I −9.76473 + 6.27179I
u = 0.397857 − 1.242680I
a = −0.883299 − 0.876579I
b = −0.772590 + 0.869650I
1.43546 + 6.54686I −9.76473 − 6.27179I
u = 0.308606 + 1.287910I
a = 0.045483 + 0.304042I
b = −0.835858 + 0.482328I
1.90752 − 1.82850I −9.06320 − 1.31557I
u = 0.308606 − 1.287910I
a = 0.045483 − 0.304042I
b = −0.835858 − 0.482328I
1.90752 + 1.82850I −9.06320 + 1.31557I
u = −0.153332 + 1.323030I
a = 0.841526 − 0.802993I
b = −0.200009 + 0.363871I
8.24471 + 3.12382I −2.39878 − 3.89363I
u = −0.153332 − 1.323030I
a = 0.841526 + 0.802993I
b = −0.200009 − 0.363871I
8.24471 − 3.12382I −2.39878 + 3.89363I
u = 0.525666 + 1.225010I
a = 0.922843 − 0.837941I
b = 1.82392 − 0.14447I
−8.11797 + 1.14335I −11.97314 − 0.02421I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.525666 − 1.225010I
a = 0.922843 + 0.837941I
b = 1.82392 + 0.14447I
−8.11797 − 1.14335I −11.97314 + 0.02421I
u = −0.502067 + 1.320010I
a = −0.90661 − 1.20129I
b = −1.86679 + 0.13017I
−11.88350 + 5.33435I −13.75533 − 3.00902I
u = −0.502067 − 1.320010I
a = −0.90661 + 1.20129I
b = −1.86679 − 0.13017I
−11.88350 − 5.33435I −13.75533 + 3.00902I
u = −0.19285 + 1.42513I
a = −0.285158 + 0.831272I
b = 1.394710 + 0.010800I
2.84039 + 4.26517I −9.12872 − 4.11003I
u = −0.19285 − 1.42513I
a = −0.285158 − 0.831272I
b = 1.394710 − 0.010800I
2.84039 − 4.26517I −9.12872 + 4.11003I
u = 0.44395 + 1.37034I
a = 0.92880 − 1.52502I
b = 1.73382 + 0.33968I
−6.95106 − 11.46670I −10.90832 + 5.56525I
u = 0.44395 − 1.37034I
a = 0.92880 + 1.52502I
b = 1.73382 − 0.33968I
−6.95106 + 11.46670I −10.90832 − 5.56525I
u = −0.399508 + 0.267149I
a = 0.62991 − 1.27405I
b = −0.560771 + 0.285755I
3.37415 + 1.14100I −8.01557 − 6.01383I
u = −0.399508 − 0.267149I
a = 0.62991 + 1.27405I
b = −0.560771 − 0.285755I
3.37415 − 1.14100I −8.01557 + 6.01383I
u = 0.282112
a = −0.612831
b = 0.246723
−0.514940 −19.2240
7
II. I
u
2
= hb − 1, −2u
2
a + a
2
− 2au + 4u
2
− 4a + 3u + 7, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
a
1
a
7
=
1
u
2
a
2
=
a + 1
1
a
1
=
1
0
a
5
=
−a
−1
a
11
=
u
−u
2
− u − 1
a
8
=
u
2
+ 1
u
2
+ u + 1
a
10
=
−u
2
− 1
−u
2
− u − 1
a
4
=
−u
2
+ 2a − u − 2
−au
a
9
=
−u
2
a + 4u
2
− a + 5
−u
2
a − au + 2u
2
− a + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4u − 16
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
3
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
, c
12
(u
3
+ u
2
− 1)
2
c
11
(u
3
− u
2
+ 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y + 2)
6
c
6
, c
7
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
10
, c
12
(y
3
− y
2
+ 2y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.917744 − 0.191855I
b = 1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = −0.67262 + 1.68158I
b = 1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.917744 + 0.191855I
b = 1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = −0.67262 − 1.68158I
b = 1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = −0.569840
a = 1.75488 + 1.87343I
b = 1.00000
2.17641 −15.0200
u = −0.569840
a = 1.75488 − 1.87343I
b = 1.00000
2.17641 −15.0200
11
III. I
u
3
= hb + 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−u
2
+ u − 2
−1
a
7
=
1
u
2
a
2
=
−u
2
+ u − 3
−1
a
1
=
−1
0
a
5
=
−u
2
+ u − 2
−1
a
11
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
10
=
u
2
+ 1
u
2
− u + 1
a
4
=
−u
2
+ u − 2
−1
a
9
=
u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 4u − 16
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
7
u
3
− u
2
+ 2u − 1
c
10
, c
12
u
3
− u
2
+ 1
c
11
u
3
+ u
2
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
7
, c
11
y
3
+ 3y
2
+ 2y −1
c
10
, c
12
y
3
− y
2
+ 2y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −11.81496 + 4.10401I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −11.81496 − 4.10401I
u = 0.569840
a = −1.75488
b = −1.00000
−2.75839 −14.3700
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
30
+ 42u
29
+ ··· + 4660u + 289)
c
2
((u − 1)
3
)(u + 1)
6
(u
30
+ 4u
29
+ ··· + 28u − 17)
c
3
, c
4
, c
9
u
3
(u
2
+ 2)
3
(u
30
− u
29
+ ··· + 16u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
30
+ 4u
29
+ ··· + 28u − 17)
c
6
, c
7
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
30
+ 2u
29
+ ··· − 5u − 3)
c
8
u
3
(u
2
+ 2)
3
(u
30
+ u
29
+ ··· − 48u + 488)
c
10
, c
12
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
30
− 2u
29
+ ··· − 17u − 3)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
30
+ 2u
29
+ ··· − 5u − 3)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
30
− 98y
29
+ ··· − 2.05608 × 10
7
y + 83521)
c
2
, c
5
((y −1)
9
)(y
30
− 42y
29
+ ··· − 4660y + 289)
c
3
, c
4
, c
9
y
3
(y + 2)
6
(y
30
+ 23y
29
+ ··· − 2304y
2
+ 64)
c
6
, c
7
, c
11
((y
3
+ 3y
2
+ 2y −1)
3
)(y
30
+ 24y
29
+ ··· − 121y + 9)
c
8
y
3
(y + 2)
6
(y
30
− 61y
29
+ ··· + 989312y + 238144)
c
10
, c
12
((y
3
− y
2
+ 2y −1)
3
)(y
30
− 40y
29
+ ··· − 265y + 9)
17
