12n
0189
(K12n
0189
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 12 7 6 8 11
Solving Sequence
8,11
12 9
1,4
3 2 7 6 10 5
c
11
c
8
c
12
c
3
c
1
c
7
c
6
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.49444 × 10
61
u
47
+ 5.42508 × 10
61
u
46
+ ··· + 2.55281 × 10
62
b − 1.56879 × 10
62
,
− 4.23145 × 10
61
u
47
− 5.04595 × 10
62
u
46
+ ··· + 3.57394 × 10
63
a − 9.28768 × 10
63
,
u
48
+ 4u
47
+ ··· + 59u − 7i
I
u
2
= h−2a
2
b + b
2
− 2ba − 2a
2
− 4b − a − 3, a
3
+ a
2
+ 2a + 1, u − 1i
I
u
3
= h−a
2
+ b − a − 2, a
3
+ a
2
+ 2a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 57 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
= h2.49 × 10
61
u
47
+ 5.43 × 10
61
u
46
+ · · · + 2.55 × 10
62
b − 1.57 ×
10
62
, −4.23 × 10
61
u
47
− 5.05 × 10
62
u
46
+ · · · + 3.57 × 10
63
a − 9.29 ×
10
63
, u
48
+ 4u
47
+ · · · + 59u − 7i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
u
2
a
4
=
0.0118397u
47
+ 0.141187u
46
+ ··· + 28.4662u + 2.59872
−0.0977134u
47
− 0.212514u
46
+ ··· − 12.5106u + 0.614532
a
3
=
0.0118397u
47
+ 0.141187u
46
+ ··· + 28.4662u + 2.59872
−0.0177507u
47
+ 0.0119124u
46
+ ··· − 7.05758u − 0.0422666
a
2
=
−0.0759396u
47
− 0.266607u
46
+ ··· − 5.41635u − 1.07005
−0.0304639u
47
− 0.113488u
46
+ ··· + 3.98647u + 0.0378137
a
7
=
−0.135632u
47
− 0.469213u
46
+ ··· + 8.97335u + 2.53780
−0.0896845u
47
− 0.258891u
46
+ ··· + 1.36877u − 0.441443
a
6
=
−0.0459476u
47
− 0.210322u
46
+ ··· + 7.60458u + 2.97924
−0.0896845u
47
− 0.258891u
46
+ ··· + 1.36877u − 0.441443
a
10
=
0.157505u
47
+ 0.559805u
46
+ ··· + 0.744089u − 1.23298
0.0268891u
47
− 0.0213891u
46
+ ··· + 0.825649u − 0.103367
a
5
=
0.0759396u
47
+ 0.266607u
46
+ ··· + 5.41635u + 1.07005
0.0604385u
47
+ 0.190773u
46
+ ··· − 4.38559u + 0.332492
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.523196u
47
− 1.69630u
46
+ ··· − 33.3905u − 3.88072
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 28u
47
+ ··· + 2u + 1
c
2
, c
4
u
48
− 4u
47
+ ··· + 2u + 1
c
3
, c
7
u
48
+ 2u
47
+ ··· + 8u − 1
c
5
, c
6
, c
10
u
48
− 3u
47
+ ··· − 8u − 8
c
8
, c
11
u
48
+ 4u
47
+ ··· + 59u − 7
c
9
u
48
+ 9u
47
+ ··· − 6632u − 1192
c
12
u
48
+ 54u
47
+ ··· + 4853u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
− 12y
47
+ ··· − 250y + 1
c
2
, c
4
y
48
− 28y
47
+ ··· − 2y + 1
c
3
, c
7
y
48
+ 12y
47
+ ··· − 42y + 1
c
5
, c
6
, c
10
y
48
− 41y
47
+ ··· − 1984y + 64
c
8
, c
11
y
48
− 54y
47
+ ··· − 4853y + 49
c
9
y
48
+ 43y
47
+ ··· − 58172992y + 1420864
c
12
y
48
− 110y
47
+ ··· − 30351829y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03474
a = −0.149518
b = 15.9108
1.67136 −181.820
u = −1.10270
a = 0.558674
b = −1.21115
−2.51979 7.01870
u = 0.402947 + 0.795966I
a = −1.253190 + 0.172447I
b = 1.24412 − 0.98353I
4.33668 − 4.44228I 2.15682 + 4.76767I
u = 0.402947 − 0.795966I
a = −1.253190 − 0.172447I
b = 1.24412 + 0.98353I
4.33668 + 4.44228I 2.15682 − 4.76767I
u = 0.549733 + 0.682678I
a = 0.009774 − 1.180920I
b = 1.026340 − 0.304021I
0.44919 − 3.43575I −2.94781 + 4.14151I
u = 0.549733 − 0.682678I
a = 0.009774 + 1.180920I
b = 1.026340 + 0.304021I
0.44919 + 3.43575I −2.94781 − 4.14151I
u = 0.607419 + 0.971287I
a = −0.314066 − 0.576245I
b = 0.709420 + 0.166838I
0.79074 + 2.62631I 0. − 8.02541I
u = 0.607419 − 0.971287I
a = −0.314066 + 0.576245I
b = 0.709420 − 0.166838I
0.79074 − 2.62631I 0. + 8.02541I
u = 0.529099 + 1.030160I
a = 1.023660 − 0.202973I
b = −1.33032 + 0.89512I
1.27119 − 9.09207I 0. + 7.97032I
u = 0.529099 − 1.030160I
a = 1.023660 + 0.202973I
b = −1.33032 − 0.89512I
1.27119 + 9.09207I 0. − 7.97032I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606029 + 0.575291I
a = 1.095020 + 0.107629I
b = −1.62264 + 1.09670I
0.227251 − 0.982213I −2.97456 + 4.05134I
u = 0.606029 − 0.575291I
a = 1.095020 − 0.107629I
b = −1.62264 − 1.09670I
0.227251 + 0.982213I −2.97456 − 4.05134I
u = 0.717418 + 0.339614I
a = −0.411980 + 0.676361I
b = −1.010750 − 0.101614I
3.05609 + 0.03450I 1.61725 − 0.04014I
u = 0.717418 − 0.339614I
a = −0.411980 − 0.676361I
b = −1.010750 + 0.101614I
3.05609 − 0.03450I 1.61725 + 0.04014I
u = 0.774869 + 0.143809I
a = 0.06554 − 1.56635I
b = 0.115818 − 0.297169I
1.81458 + 2.58829I 4.64199 + 0.62738I
u = 0.774869 − 0.143809I
a = 0.06554 + 1.56635I
b = 0.115818 + 0.297169I
1.81458 − 2.58829I 4.64199 − 0.62738I
u = −0.705342 + 0.225017I
a = 0.374486 + 0.783406I
b = −0.02299 + 1.57993I
−2.89686 + 0.77640I −12.15233 + 3.40612I
u = −0.705342 − 0.225017I
a = 0.374486 − 0.783406I
b = −0.02299 − 1.57993I
−2.89686 − 0.77640I −12.15233 − 3.40612I
u = 0.701884
a = −0.734892
b = −1.24205
3.11349 3.07850
u = −0.856659 + 0.985459I
a = 0.636632 + 0.001328I
b = −0.672001 − 0.732654I
−2.80642 + 4.10771I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856659 − 0.985459I
a = 0.636632 − 0.001328I
b = −0.672001 + 0.732654I
−2.80642 − 4.10771I 0
u = −1.312340 + 0.022176I
a = 0.159774 − 1.198270I
b = −0.14705 − 1.53594I
3.83816 + 3.33221I 0
u = −1.312340 − 0.022176I
a = 0.159774 + 1.198270I
b = −0.14705 + 1.53594I
3.83816 − 3.33221I 0
u = −0.382101 + 0.518429I
a = −1.066440 − 0.036820I
b = 0.434772 + 0.642582I
−0.164421 + 1.292600I −1.96598 − 5.14574I
u = −0.382101 − 0.518429I
a = −1.066440 + 0.036820I
b = 0.434772 − 0.642582I
−0.164421 − 1.292600I −1.96598 + 5.14574I
u = −1.52813 + 0.03469I
a = 0.749487 + 0.430849I
b = −0.082283 + 0.460779I
−3.85416 + 1.06668I 0
u = −1.52813 − 0.03469I
a = 0.749487 − 0.430849I
b = −0.082283 − 0.460779I
−3.85416 − 1.06668I 0
u = 1.49504 + 0.38475I
a = 0.007881 + 0.362733I
b = −0.372006 − 0.161707I
2.74848 + 0.89020I 0
u = 1.49504 − 0.38475I
a = 0.007881 − 0.362733I
b = −0.372006 + 0.161707I
2.74848 − 0.89020I 0
u = −1.52900 + 0.29105I
a = 0.706345 − 0.671808I
b = −1.06205 − 1.60612I
−2.00876 + 8.44086I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52900 − 0.29105I
a = 0.706345 + 0.671808I
b = −1.06205 + 1.60612I
−2.00876 − 8.44086I 0
u = 1.55775 + 0.15557I
a = 0.721994 + 0.568337I
b = −0.497955 + 1.196310I
−6.88003 − 3.75478I 0
u = 1.55775 − 0.15557I
a = 0.721994 − 0.568337I
b = −0.497955 − 1.196310I
−6.88003 + 3.75478I 0
u = −1.58783 + 0.13072I
a = −0.527458 + 0.690762I
b = 0.89707 + 1.86682I
−7.23928 + 3.38751I 0
u = −1.58783 − 0.13072I
a = −0.527458 − 0.690762I
b = 0.89707 − 1.86682I
−7.23928 − 3.38751I 0
u = −1.58112 + 0.20855I
a = −0.673201 − 0.601686I
b = −0.115011 − 0.480919I
−6.71802 + 6.70728I 0
u = −1.58112 − 0.20855I
a = −0.673201 + 0.601686I
b = −0.115011 + 0.480919I
−6.71802 − 6.70728I 0
u = 1.61634 + 0.04594I
a = −0.607271 + 0.648913I
b = 0.278472 + 1.264590I
−10.99530 − 1.69093I 0
u = 1.61634 − 0.04594I
a = −0.607271 − 0.648913I
b = 0.278472 − 1.264590I
−10.99530 + 1.69093I 0
u = −1.59092 + 0.39585I
a = −0.731570 + 0.550707I
b = 1.26602 + 1.60368I
−5.5392 + 14.3589I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59092 − 0.39585I
a = −0.731570 − 0.550707I
b = 1.26602 − 1.60368I
−5.5392 − 14.3589I 0
u = 1.68738 + 0.31170I
a = −0.685391 − 0.453228I
b = 0.64974 − 1.33823I
−11.1104 − 9.0785I 0
u = 1.68738 − 0.31170I
a = −0.685391 + 0.453228I
b = 0.64974 + 1.33823I
−11.1104 + 9.0785I 0
u = −1.74551 + 0.16291I
a = −0.577118 + 0.344131I
b = 0.165920 + 0.739123I
−8.76602 + 2.97970I 0
u = −1.74551 − 0.16291I
a = −0.577118 − 0.344131I
b = 0.165920 − 0.739123I
−8.76602 − 2.97970I 0
u = −0.088616 + 0.165371I
a = −5.53925 + 3.96896I
b = 0.242833 − 1.027870I
7.99255 − 2.76208I 5.58674 + 2.99226I
u = −0.088616 − 0.165371I
a = −5.53925 − 3.96896I
b = 0.242833 + 1.027870I
7.99255 + 2.76208I 5.58674 − 2.99226I
u = 0.0931699
a = 5.14127
b = −0.648531
−1.24876 −7.95330
9
II. I
u
2
= h−2a
2
b + b
2
− 2ba − 2a
2
− 4b − a − 3, a
3
+ a
2
+ 2a + 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
11
=
1
0
a
12
=
1
1
a
9
=
−1
0
a
1
=
0
1
a
4
=
a
b
a
3
=
a
b − a
a
2
=
−a
2
−ba + a
2
+ 1
a
7
=
a
2
ba + 1
a
6
=
−ba + a
2
− 1
ba + 1
a
10
=
−a
2
b − 2ba + a
2
− b − 1
2
a
5
=
−a
2
−ba − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
− 4a − 8
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
− 2)
3
c
8
, c
12
(u + 1)
6
c
11
(u − 1)
6
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
9
c
10
(y −2)
6
c
8
, c
11
, c
12
(y −1)
6
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.215080 + 1.307140I
b = −0.050766 − 0.308532I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 1.00000
a = −0.215080 + 1.307140I
b = 0.29589 + 1.79826I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 1.00000
a = −0.215080 − 1.307140I
b = −0.050766 + 0.308532I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 1.00000
a = −0.215080 − 1.307140I
b = 0.29589 − 1.79826I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 1.00000
a = −0.569840
b = −0.726894
2.17641 −7.01950
u = 1.00000
a = −0.569840
b = 4.23665
2.17641 −7.01950
13
III. I
u
3
= h−a
2
+ b − a − 2, a
3
+ a
2
+ 2a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
9
=
1
0
a
1
=
0
1
a
4
=
a
a
2
+ a + 2
a
3
=
a
a
2
+ 2
a
2
=
−a
2
a
2
+ 2
a
7
=
−a
2
0
a
6
=
−a
2
0
a
10
=
1
0
a
5
=
−a
2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12a
2
− 10a − 32
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
(u − 1)
3
c
11
, c
12
(u + 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y −1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.215080 + 1.307140I
b = 0.122561 + 0.744862I
1.37919 + 2.82812I −9.90089 − 6.32406I
u = −1.00000
a = −0.215080 − 1.307140I
b = 0.122561 − 0.744862I
1.37919 − 2.82812I −9.90089 + 6.32406I
u = −1.00000
a = −0.569840
b = 1.75488
−2.75839 −30.1980
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
3
)(u
48
+ 28u
47
+ ··· + 2u + 1)
c
2
((u
3
+ u
2
− 1)
3
)(u
48
− 4u
47
+ ··· + 2u + 1)
c
3
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
48
+ 2u
47
+ ··· + 8u − 1)
c
4
((u
3
− u
2
+ 1)
3
)(u
48
− 4u
47
+ ··· + 2u + 1)
c
5
, c
6
, c
10
u
3
(u
2
− 2)
3
(u
48
− 3u
47
+ ··· − 8u − 8)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
48
+ 2u
47
+ ··· + 8u − 1)
c
8
((u − 1)
3
)(u + 1)
6
(u
48
+ 4u
47
+ ··· + 59u − 7)
c
9
u
3
(u
2
− 2)
3
(u
48
+ 9u
47
+ ··· − 6632u − 1192)
c
11
((u − 1)
6
)(u + 1)
3
(u
48
+ 4u
47
+ ··· + 59u − 7)
c
12
((u + 1)
9
)(u
48
+ 54u
47
+ ··· + 4853u + 49)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
3
)(y
48
− 12y
47
+ ··· − 250y + 1)
c
2
, c
4
((y
3
− y
2
+ 2y −1)
3
)(y
48
− 28y
47
+ ··· − 2y + 1)
c
3
, c
7
((y
3
+ 3y
2
+ 2y −1)
3
)(y
48
+ 12y
47
+ ··· − 42y + 1)
c
5
, c
6
, c
10
y
3
(y −2)
6
(y
48
− 41y
47
+ ··· − 1984y + 64)
c
8
, c
11
((y −1)
9
)(y
48
− 54y
47
+ ··· − 4853y + 49)
c
9
y
3
(y −2)
6
(y
48
+ 43y
47
+ ··· − 5.81730 × 10
7
y + 1420864)
c
12
((y −1)
9
)(y
48
− 110y
47
+ ··· − 3.03518 × 10
7
y + 2401)
19
