12n
0195
(K12n
0195
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 4 12 5 6 8 9
Solving Sequence
5,11 3,6
2 1 4 10 7 8 9 12
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.62072 × 10
18
u
23
+ 1.95726 × 10
19
u
22
+ ··· + 1.72477 × 10
21
b + 8.62668 × 10
20
,
− 2.65800 × 10
20
u
23
+ 1.49704 × 10
20
u
22
+ ··· + 1.03486 × 10
22
a − 3.34302 × 10
22
, u
24
− 2u
23
+ ··· − 8u − 8i
I
u
2
= hb + 1, 2u
5
− 4u
4
+ 7u
3
− 8u
2
+ 3a + 6u − 5, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= h4a
2
u − 6a
2
− 8au + 17b + 12a + 2u − 20, 4a
3
+ 6a
2
u − 8a
2
− 2au − u − 6, u
2
+ 2i
I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v −1i
* 4 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−1.62×10
18
u
23
+1.96×10
19
u
22
+· · ·+1.72×10
21
b+8.63×10
20
, −2.66×
10
20
u
23
+1.50×10
20
u
22
+· · ·+1.03×10
22
a−3.34×10
22
, u
24
−2u
23
+· · ·−8u−8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
0.0256846u
23
− 0.0144661u
22
+ ··· − 1.52339u + 3.23040
0.000939669u
23
− 0.0113479u
22
+ ··· + 0.985369u − 0.500163
a
6
=
1
−u
2
a
2
=
0.0266242u
23
− 0.0258140u
22
+ ··· − 0.538021u + 2.73023
0.000939669u
23
− 0.0113479u
22
+ ··· + 0.985369u − 0.500163
a
1
=
0.0583259u
23
− 0.126312u
22
+ ··· + 3.65005u + 0.821695
−0.0138991u
23
+ 0.0340693u
22
+ ··· + 0.0978404u − 0.00653011
a
4
=
0.00790799u
23
+ 0.00662412u
22
+ ··· − 2.90944u + 2.73115
−0.00229500u
23
− 0.00348046u
22
+ ··· + 1.12451u − 0.423114
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.0350146u
23
− 0.0584050u
22
+ ··· + 4.17403u + 0.781518
−0.000987363u
23
− 0.00177968u
22
+ ··· − 0.799250u − 0.0593477
a
9
=
−u
3
− 2u
u
3
+ u
a
12
=
0.0439159u
23
− 0.0866142u
22
+ ··· + 2.91071u + 0.725782
−0.00988867u
23
+ 0.0264295u
22
+ ··· + 0.464073u − 0.00361092
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2356346852274434342467
5174317777594090237716
u
23
−
1159968679518319967807
1293579444398522559429
u
22
+ ··· +
50179924203167367792392
1293579444398522559429
u +
1352352571446172898474
1293579444398522559429
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 2u
23
+ ··· + 1885u + 81
c
2
, c
4
u
24
− 10u
23
+ ··· + 25u + 9
c
3
, c
7
u
24
+ 2u
23
+ ··· + 960u − 576
c
5
, c
6
, c
10
u
24
− 2u
23
+ ··· − 8u − 8
c
8
, c
11
, c
12
u
24
− 5u
23
+ ··· − 357u + 49
c
9
u
24
+ 2u
23
+ ··· + 8216u − 1448
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 66y
23
+ ··· − 3758641y + 6561
c
2
, c
4
y
24
+ 2y
23
+ ··· − 1885y + 81
c
3
, c
7
y
24
+ 48y
23
+ ··· − 3022848y + 331776
c
5
, c
6
, c
10
y
24
+ 16y
23
+ ··· − 1472y + 64
c
8
, c
11
, c
12
y
24
− 41y
23
+ ··· − 196539y + 2401
c
9
y
24
− 80y
23
+ ··· + 25123008y + 2096704
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036962 + 1.068950I
a = 0.84695 − 1.21226I
b = −0.194048 + 0.569807I
−2.00407 + 1.55521I 2.34191 − 4.04611I
u = −0.036962 − 1.068950I
a = 0.84695 + 1.21226I
b = −0.194048 − 0.569807I
−2.00407 − 1.55521I 2.34191 + 4.04611I
u = −0.323995 + 1.223880I
a = 0.417290 − 0.742338I
b = 0.894371 + 0.359693I
2.23459 − 5.45156I 5.30376 + 8.39066I
u = −0.323995 − 1.223880I
a = 0.417290 + 0.742338I
b = 0.894371 − 0.359693I
2.23459 + 5.45156I 5.30376 − 8.39066I
u = −0.538454 + 0.449191I
a = −1.08603 + 1.29257I
b = 1.060300 − 0.751864I
5.01148 + 2.07959I 5.62929 + 1.97986I
u = −0.538454 − 0.449191I
a = −1.08603 − 1.29257I
b = 1.060300 + 0.751864I
5.01148 − 2.07959I 5.62929 − 1.97986I
u = 0.024256 + 1.316950I
a = 0.95732 + 1.55302I
b = −1.005510 − 0.226269I
−4.97907 − 0.78003I −5.02882 + 0.00732I
u = 0.024256 − 1.316950I
a = 0.95732 − 1.55302I
b = −1.005510 + 0.226269I
−4.97907 + 0.78003I −5.02882 − 0.00732I
u = −0.846526 + 1.045030I
a = −0.40282 − 2.36685I
b = 0.92407 + 1.32486I
6.66087 − 5.31357I 3.74628 + 3.91274I
u = −0.846526 − 1.045030I
a = −0.40282 + 2.36685I
b = 0.92407 − 1.32486I
6.66087 + 5.31357I 3.74628 − 3.91274I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586420 + 0.250857I
a = 1.02868 − 2.84832I
b = −0.586430 + 0.543498I
0.984746 + 0.178881I 6.09874 − 3.14218I
u = 0.586420 − 0.250857I
a = 1.02868 + 2.84832I
b = −0.586430 − 0.543498I
0.984746 − 0.178881I 6.09874 + 3.14218I
u = 0.182077 + 1.361640I
a = 0.527856 + 0.849532I
b = 0.493008 − 0.547865I
−3.21229 + 2.94427I 1.02339 − 4.25834I
u = 0.182077 − 1.361640I
a = 0.527856 − 0.849532I
b = 0.493008 + 0.547865I
−3.21229 − 2.94427I 1.02339 + 4.25834I
u = −0.976649 + 0.994558I
a = −0.62257 + 2.02385I
b = 0.09341 − 1.47455I
6.90898 − 1.54857I 4.91054 + 1.41410I
u = −0.976649 − 0.994558I
a = −0.62257 − 2.02385I
b = 0.09341 + 1.47455I
6.90898 + 1.54857I 4.91054 − 1.41410I
u = 1.46226 + 0.22351I
a = −1.52657 + 2.40294I
b = 1.43989 − 1.34762I
−17.7659 + 5.2038I 4.94066 − 2.06441I
u = 1.46226 − 0.22351I
a = −1.52657 − 2.40294I
b = 1.43989 + 1.34762I
−17.7659 − 5.2038I 4.94066 + 2.06441I
u = 0.401729
a = 2.19393
b = −0.203908
0.910545 12.3570
u = 0.56079 + 1.60245I
a = −0.31621 + 1.95238I
b = 1.40238 − 1.01134I
15.8466 + 12.3266I 2.77536 − 4.87802I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.56079 − 1.60245I
a = −0.31621 − 1.95238I
b = 1.40238 + 1.01134I
15.8466 − 12.3266I 2.77536 + 4.87802I
u = −0.235957
a = 3.84635
b = −0.892923
−1.27848 −10.9250
u = 0.82389 + 1.57851I
a = −1.34403 − 1.58945I
b = 1.02698 + 1.58176I
17.6395 + 2.9890I 3.87648 − 0.98637I
u = 0.82389 − 1.57851I
a = −1.34403 + 1.58945I
b = 1.02698 − 1.58176I
17.6395 − 2.9890I 3.87648 + 0.98637I
7
II.
I
u
2
= hb+1, 2u
5
−4u
4
+7u
3
−8u
2
+3a+6u−5, u
6
−u
5
+3u
4
−2u
3
+2u
2
−u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
5
3
−1
a
6
=
1
−u
2
a
2
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
2
3
−1
a
1
=
−1
0
a
4
=
−
2
3
u
5
+
4
3
u
4
+ ··· − 2u +
5
3
−1
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
3
− 2u
u
3
+ u
a
12
=
u
5
+ 2u
3
+ u
−u
5
+ u
4
− 2u
3
+ u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7
9
u
5
+
41
9
u
4
−
62
9
u
3
+
103
9
u
2
− 6u +
70
9
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
8
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
9
, c
11
, c
12
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
6
, c
10
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
c
8
, c
9
, c
11
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = 0.836730
b = −1.00000
6.01515 8.93190
u = −0.138835 + 1.234450I
a = 0.366605 + 0.544193I
b = −1.00000
−4.60518 − 1.97241I −1.96265 + 3.88708I
u = −0.138835 − 1.234450I
a = 0.366605 − 0.544193I
b = −1.00000
−4.60518 + 1.97241I −1.96265 − 3.88708I
u = 0.408802 + 1.276380I
a = −0.031424 − 0.540243I
b = −1.00000
2.05064 + 4.59213I 3.29989 + 0.22957I
u = 0.408802 − 1.276380I
a = −0.031424 + 0.540243I
b = −1.00000
2.05064 − 4.59213I 3.29989 − 0.22957I
u = −0.413150
a = 3.15957
b = −1.00000
−0.906083 12.8380
11
III. I
u
3
=
h4a
2
u−6a
2
−8au+17b +12a +2u − 20, 4a
3
+6a
2
u−8a
2
−2au−u −6, u
2
+2i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
a
−0.235294a
2
u + 0.470588au + ··· − 0.705882a + 1.17647
a
6
=
1
2
a
2
=
−0.235294a
2
u + 0.470588au + ··· + 0.294118a + 1.17647
−0.235294a
2
u + 0.470588au + ··· − 0.705882a + 1.17647
a
1
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
a
4
=
0.411765a
2
u − 0.823529au + ··· + 0.235294a − 0.0588235
−0.117647a
2
u − 0.764706au + ··· + 1.64706a − 0.411765
a
10
=
−u
−u
a
7
=
−1
0
a
8
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
a
9
=
0
−u
a
12
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
16
17
a
2
u +
24
17
a
2
+
32
17
au −
48
17
a −
8
17
u +
80
17
12
(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
(u − 1)
6
c
11
, c
12
(u + 1)
6
13
(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
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.520153 − 0.983610I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 1.414210I
a = −0.275030 + 0.506114I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 1.414210I
a = 1.75488 − 1.64382I
b = −0.754878
−4.40332 −3.01951 + 0.I
u = − 1.414210I
a = 0.520153 + 0.983610I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = − 1.414210I
a = −0.275030 − 0.506114I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = − 1.414210I
a = 1.75488 + 1.64382I
b = −0.754878
−4.40332 −3.01951 + 0.I
15
IV. I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
3
=
0
v
2
− 3v − 1
a
6
=
1
0
a
2
=
v
2
− 3v − 1
v
2
− 3v − 1
a
1
=
v
2
− 3v − 1
−v
2
+ 2v + 3
a
4
=
−2v
2
+ 5v + 4
−2v
2
+ 5v + 3
a
10
=
v
0
a
7
=
1
0
a
8
=
−v
2
+ 3v + 1
v
2
− 2v − 3
a
9
=
v
0
a
12
=
v
2
− 2v − 1
−v
2
+ 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v
2
− 26v − 14
16
(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
17
(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
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.539798 + 0.182582I
a = 0
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 2.09911 − 6.32406I
v = −0.539798 − 0.182582I
a = 0
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 2.09911 + 6.32406I
v = 3.07960
a = 0
b = −0.754878
0.531480 −18.1980
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− u
2
+ 2u − 1)
3
(u
24
− 2u
23
+ ··· + 1885u + 81)
c
2
((u − 1)
6
)(u
3
+ u
2
− 1)
3
(u
24
− 10u
23
+ ··· + 25u + 9)
c
3
u
6
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
24
+ 2u
23
+ ··· + 960u − 576)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)
3
(u
24
− 10u
23
+ ··· + 25u + 9)
c
5
, c
6
u
3
(u
2
+ 2)
3
(u
6
− u
5
+ ··· − u − 1)(u
24
− 2u
23
+ ··· − 8u − 8)
c
7
u
6
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
24
+ 2u
23
+ ··· + 960u − 576)
c
8
(u − 1)
6
(u + 1)
3
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
24
− 5u
23
+ ··· − 357u + 49)
c
9
u
3
(u
2
+ 2)
3
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
24
+ 2u
23
+ ··· + 8216u − 1448)
c
10
u
3
(u
2
+ 2)
3
(u
6
+ u
5
+ ··· + u − 1)(u
24
− 2u
23
+ ··· − 8u − 8)
c
11
, c
12
(u − 1)
3
(u + 1)
6
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
24
− 5u
23
+ ··· − 357u + 49)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
24
+ 66y
23
+ ··· − 3758641y + 6561)
c
2
, c
4
((y − 1)
6
)(y
3
− y
2
+ 2y − 1)
3
(y
24
+ 2y
23
+ ··· − 1885y + 81)
c
3
, c
7
y
6
(y
3
+ 3y
2
+ 2y − 1)
3
(y
24
+ 48y
23
+ ··· − 3022848y + 331776)
c
5
, c
6
, c
10
y
3
(y + 2)
6
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
24
+ 16y
23
+ ··· − 1472y + 64)
c
8
, c
11
, c
12
(y − 1)
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
24
− 41y
23
+ ··· − 196539y + 2401)
c
9
y
3
(y + 2)
6
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
24
− 80y
23
+ ··· + 25123008y + 2096704)
21
