12a
0096
(K12a
0096
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 1 12 6 7 9
Solving Sequence
6,10
11 7 12
2,5
3 1 4 8 9
c
10
c
6
c
11
c
5
c
2
c
1
c
4
c
7
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
59
+ 31u
57
+ ··· − 4u
2
+ b, −u
62
− u
61
+ ··· + a − 1, u
63
+ 2u
62
+ ··· + 2u − 1i
I
u
2
= hu
4
− 2u
2
+ b + 2u, −u
5
+ 3u
3
+ a + 1, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 69 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−u
59
+31u
57
+· · ·−4u
2
+b, −u
62
−u
61
+· · ·+a −1, u
63
+2u
62
+· · ·+2u −1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
7
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
62
+ u
61
+ ··· + 2u + 1
u
59
− 31u
57
+ ··· − 3u
3
+ 4u
2
a
5
=
u
u
a
3
=
2u
62
+ u
61
+ ··· − 4u
2
+ 5u
u
62
− 33u
60
+ ··· + 3u − 1
a
1
=
−u
10
+ 5u
8
− 8u
6
+ 5u
4
− 3u
2
+ 1
−u
12
+ 6u
10
− 12u
8
+ 8u
6
− u
4
+ 2u
2
a
4
=
u
61
− 32u
59
+ ··· + u + 1
−u
62
+ 33u
60
+ ··· − 2u + 1
a
8
=
u
14
− 7u
12
+ 18u
10
− 21u
8
+ 14u
6
− 10u
4
+ 4u
2
− 1
u
16
− 8u
14
+ 24u
12
− 32u
10
+ 18u
8
− 8u
6
+ 8u
4
a
9
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
61
− u
60
+ ··· + 2u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 27u
62
+ ··· + 95u + 1
c
2
, c
4
u
63
− 7u
62
+ ··· + u + 1
c
3
, c
7
u
63
+ u
62
+ ··· + 192u + 64
c
5
, c
6
, c
10
c
11
u
63
− 2u
62
+ ··· + 2u + 1
c
8
, c
9
, c
12
u
63
− 8u
62
+ ··· + 6u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 25y
62
+ ··· + 5299y −1
c
2
, c
4
y
63
− 27y
62
+ ··· + 95y −1
c
3
, c
7
y
63
+ 39y
62
+ ··· − 40960y −4096
c
5
, c
6
, c
10
c
11
y
63
− 68y
62
+ ··· + 14y −1
c
8
, c
9
, c
12
y
63
+ 64y
62
+ ··· − 2246y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552072 + 0.648887I
a = 0.477044 + 0.191255I
b = 1.98574 − 0.28222I
8.36290 − 11.10910I −8.86571 + 8.37495I
u = 0.552072 − 0.648887I
a = 0.477044 − 0.191255I
b = 1.98574 + 0.28222I
8.36290 + 11.10910I −8.86571 − 8.37495I
u = 0.533877 + 0.656255I
a = −0.086296 + 0.604333I
b = −0.591871 − 0.592997I
10.28220 − 4.95595I −6.40227 + 3.95794I
u = 0.533877 − 0.656255I
a = −0.086296 − 0.604333I
b = −0.591871 + 0.592997I
10.28220 + 4.95595I −6.40227 − 3.95794I
u = −0.518166 + 0.638255I
a = 0.239548 + 0.425049I
b = 1.50926 + 0.75312I
4.80189 + 4.67051I −9.56411 − 5.84070I
u = −0.518166 − 0.638255I
a = 0.239548 − 0.425049I
b = 1.50926 − 0.75312I
4.80189 − 4.67051I −9.56411 + 5.84070I
u = 0.475260 + 0.668900I
a = −0.500436 − 0.356756I
b = 0.840809 − 0.212539I
10.45670 + 0.49427I −5.93156 + 2.06629I
u = 0.475260 − 0.668900I
a = −0.500436 + 0.356756I
b = 0.840809 + 0.212539I
10.45670 − 0.49427I −5.93156 − 2.06629I
u = 0.453215 + 0.669802I
a = −0.35281 + 1.85601I
b = −0.317027 + 0.198250I
8.65681 + 6.66761I −8.01120 − 2.46984I
u = 0.453215 − 0.669802I
a = −0.35281 − 1.85601I
b = −0.317027 − 0.198250I
8.65681 − 6.66761I −8.01120 + 2.46984I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500444 + 0.632445I
a = −0.016435 − 1.256630I
b = −1.040210 + 0.063749I
3.24652 − 2.14201I −8.59063 + 3.32182I
u = 0.500444 − 0.632445I
a = −0.016435 + 1.256630I
b = −1.040210 − 0.063749I
3.24652 + 2.14201I −8.59063 − 3.32182I
u = −0.484205 + 0.643677I
a = −0.75821 − 1.21698I
b = −0.773190 + 0.091630I
4.90236 − 0.33637I −9.15743 − 0.38817I
u = −0.484205 − 0.643677I
a = −0.75821 + 1.21698I
b = −0.773190 − 0.091630I
4.90236 + 0.33637I −9.15743 + 0.38817I
u = −0.657206 + 0.383548I
a = −0.498372 + 0.026703I
b = −2.07884 + 0.04909I
0.73856 + 7.23469I −12.7532 − 9.6424I
u = −0.657206 − 0.383548I
a = −0.498372 − 0.026703I
b = −2.07884 − 0.04909I
0.73856 − 7.23469I −12.7532 + 9.6424I
u = 0.750394 + 0.085615I
a = 0.447881 + 0.312629I
b = 1.52225 − 0.54267I
−0.91500 + 2.18703I −15.1580 − 2.5589I
u = 0.750394 − 0.085615I
a = 0.447881 − 0.312629I
b = 1.52225 + 0.54267I
−0.91500 − 2.18703I −15.1580 + 2.5589I
u = −0.495914 + 0.538413I
a = −0.181479 + 0.681833I
b = −0.586391 + 0.071931I
2.22957 + 1.86380I −4.96531 − 3.49525I
u = −0.495914 − 0.538413I
a = −0.181479 − 0.681833I
b = −0.586391 − 0.071931I
2.22957 − 1.86380I −4.96531 + 3.49525I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572206 + 0.430292I
a = −0.149585 + 0.569347I
b = −0.199905 − 0.583366I
2.16114 + 2.24871I −8.78086 − 4.77265I
u = −0.572206 − 0.430292I
a = −0.149585 − 0.569347I
b = −0.199905 + 0.583366I
2.16114 − 2.24871I −8.78086 + 4.77265I
u = 0.539929 + 0.300101I
a = −0.044166 + 0.631034I
b = −1.65764 + 0.85420I
−1.85220 − 2.46880I −16.2123 + 7.6233I
u = 0.539929 − 0.300101I
a = −0.044166 − 0.631034I
b = −1.65764 − 0.85420I
−1.85220 + 2.46880I −16.2123 − 7.6233I
u = 1.398670 + 0.035211I
a = 0.815049 − 0.521609I
b = 1.42294 − 0.01679I
−1.87097 − 2.75507I 0
u = 1.398670 − 0.035211I
a = 0.815049 + 0.521609I
b = 1.42294 + 0.01679I
−1.87097 + 2.75507I 0
u = −0.259599 + 0.510135I
a = 1.097040 + 0.502994I
b = −0.487176 − 0.027827I
3.10941 + 0.98990I −5.62147 − 3.24587I
u = −0.259599 − 0.510135I
a = 1.097040 − 0.502994I
b = −0.487176 + 0.027827I
3.10941 − 0.98990I −5.62147 + 3.24587I
u = −0.155783 + 0.518364I
a = −0.34678 + 2.21283I
b = 0.279971 + 0.161759I
2.26897 − 4.12732I −7.16888 + 3.41220I
u = −0.155783 − 0.518364I
a = −0.34678 − 2.21283I
b = 0.279971 − 0.161759I
2.26897 + 4.12732I −7.16888 − 3.41220I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500479 + 0.194028I
a = −0.284102 − 1.118860I
b = 1.55555 − 0.14096I
−2.49270 + 0.60644I −15.4557 − 10.2077I
u = −0.500479 − 0.194028I
a = −0.284102 + 1.118860I
b = 1.55555 + 0.14096I
−2.49270 − 0.60644I −15.4557 + 10.2077I
u = −1.47733 + 0.20560I
a = −0.725820 + 0.543718I
b = −1.393370 − 0.049721I
2.40189 − 3.52842I 0
u = −1.47733 − 0.20560I
a = −0.725820 − 0.543718I
b = −1.393370 + 0.049721I
2.40189 + 3.52842I 0
u = −1.50553 + 0.02610I
a = −0.820872 − 0.167823I
b = −0.584397 + 0.092393I
−6.94722 + 0.20354I 0
u = −1.50553 − 0.02610I
a = −0.820872 + 0.167823I
b = −0.584397 − 0.092393I
−6.94722 − 0.20354I 0
u = −1.49289 + 0.20909I
a = −0.845794 − 0.652481I
b = −1.309020 − 0.075246I
4.05173 + 2.66575I 0
u = −1.49289 − 0.20909I
a = −0.845794 + 0.652481I
b = −1.309020 + 0.075246I
4.05173 − 2.66575I 0
u = 1.50358 + 0.19450I
a = 0.475568 − 0.695908I
b = 0.009106 − 0.203705I
−1.59595 − 2.66985I 0
u = 1.50358 − 0.19450I
a = 0.475568 + 0.695908I
b = 0.009106 + 0.203705I
−1.59595 + 2.66985I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51480 + 0.19165I
a = 2.26122 + 0.97687I
b = 3.13502 + 1.11443I
−3.36903 + 5.10417I 0
u = −1.51480 − 0.19165I
a = 2.26122 − 0.97687I
b = 3.13502 − 1.11443I
−3.36903 − 5.10417I 0
u = 1.53183 + 0.05064I
a = −3.83982 + 0.14262I
b = −4.60648 + 0.30137I
−9.36673 − 1.46427I 0
u = 1.53183 − 0.05064I
a = −3.83982 − 0.14262I
b = −4.60648 − 0.30137I
−9.36673 + 1.46427I 0
u = 1.52279 + 0.19719I
a = −1.54244 + 2.21672I
b = −2.17598 + 1.87956I
−1.90943 − 7.69003I 0
u = 1.52279 − 0.19719I
a = −1.54244 − 2.21672I
b = −2.17598 − 1.87956I
−1.90943 + 7.69003I 0
u = 1.53422 + 0.10683I
a = 0.273455 − 0.876541I
b = 0.465154 − 1.309920I
−4.84076 − 4.12450I 0
u = 1.53422 − 0.10683I
a = 0.273455 + 0.876541I
b = 0.465154 + 1.309920I
−4.84076 + 4.12450I 0
u = −1.53626 + 0.07185I
a = 3.07876 + 2.19965I
b = 3.75488 + 1.96290I
−8.82652 + 3.73842I 0
u = −1.53626 − 0.07185I
a = 3.07876 − 2.19965I
b = 3.75488 − 1.96290I
−8.82652 − 3.73842I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53186 + 0.15244I
a = 1.54941 − 0.72159I
b = 1.94893 − 0.88041I
−4.52737 − 4.30571I 0
u = 1.53186 − 0.15244I
a = 1.54941 + 0.72159I
b = 1.94893 + 0.88041I
−4.52737 + 4.30571I 0
u = −1.52911 + 0.20775I
a = 0.822400 − 0.471262I
b = 0.592425 − 1.140080I
3.49790 + 8.09634I 0
u = −1.52911 − 0.20775I
a = 0.822400 + 0.471262I
b = 0.592425 + 1.140080I
3.49790 − 8.09634I 0
u = −1.53893 + 0.20501I
a = −2.79319 − 1.84720I
b = −3.58877 − 1.49346I
1.4654 + 14.2222I 0
u = −1.53893 − 0.20501I
a = −2.79319 + 1.84720I
b = −3.58877 + 1.49346I
1.4654 − 14.2222I 0
u = 1.56803 + 0.09676I
a = 3.77845 − 0.81683I
b = 4.48012 − 0.48475I
−6.75258 − 8.93003I 0
u = 1.56803 − 0.09676I
a = 3.77845 + 0.81683I
b = 4.48012 + 0.48475I
−6.75258 + 8.93003I 0
u = −1.57741 + 0.02042I
a = −3.19867 − 1.01092I
b = −3.77337 − 1.31247I
−8.71900 − 1.82197I 0
u = −1.57741 − 0.02042I
a = −3.19867 + 1.01092I
b = −3.77337 + 1.31247I
−8.71900 + 1.82197I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.403832
a = 0.621632
b = 0.331645
−0.597749 −16.5810
u = 0.217719 + 0.282787I
a = 1.35864 − 1.85170I
b = 0.495682 + 0.230950I
−0.947414 + 0.254780I −11.01418 + 1.68068I
u = 0.217719 − 0.282787I
a = 1.35864 + 1.85170I
b = 0.495682 − 0.230950I
−0.947414 − 0.254780I −11.01418 − 1.68068I
11
II.
I
u
2
= hu
4
− 2u
2
+ b + 2u, −u
5
+ 3u
3
+ a + 1, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
7
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
5
− 3u
3
− 1
−u
4
+ 2u
2
− 2u
a
5
=
u
u
a
3
=
u
5
− 3u
3
+ u − 1
−u
4
+ 2u
2
− u
a
1
=
−u
−u
a
4
=
u
5
− 3u
3
+ u − 1
−u
4
+ 2u
2
− u
a
8
=
−u
−u
3
+ u
a
9
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
− u
4
+ 6u
3
+ u
2
+ 2u − 14
12
(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
, c
9
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
, c
11
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
12
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
13
(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
c
11
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
8
, c
9
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = 0.011399 − 0.918055I
b = −0.847526 + 0.083869I
1.31531 − 1.97241I −14.7121 + 3.8836I
u = 0.493180 − 0.575288I
a = 0.011399 + 0.918055I
b = −0.847526 − 0.083869I
1.31531 + 1.97241I −14.7121 − 3.8836I
u = −0.483672
a = −0.687021
b = 1.38049
−2.38379 −15.3880
u = −1.52087 + 0.16310I
a = 1.98288 + 0.88048I
b = 2.63293 + 0.95019I
−5.34051 + 4.59213I −18.4963 − 3.9250I
u = −1.52087 − 0.16310I
a = 1.98288 − 0.88048I
b = 2.63293 − 0.95019I
−5.34051 − 4.59213I −18.4963 + 3.9250I
u = 1.53904
a = −3.30155
b = −3.95130
−9.30502 −18.1960
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
63
+ 27u
62
+ ··· + 95u + 1)
c
2
((u − 1)
6
)(u
63
− 7u
62
+ ··· + u + 1)
c
3
, c
7
u
6
(u
63
+ u
62
+ ··· + 192u + 64)
c
4
((u + 1)
6
)(u
63
− 7u
62
+ ··· + u + 1)
c
5
, c
6
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
63
− 2u
62
+ ··· + 2u + 1)
c
8
, c
9
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
63
− 8u
62
+ ··· + 6u + 7)
c
10
, c
11
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
63
− 2u
62
+ ··· + 2u + 1)
c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
63
− 8u
62
+ ··· + 6u + 7)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
63
+ 25y
62
+ ··· + 5299y −1)
c
2
, c
4
((y −1)
6
)(y
63
− 27y
62
+ ··· + 95y −1)
c
3
, c
7
y
6
(y
63
+ 39y
62
+ ··· − 40960y −4096)
c
5
, c
6
, c
10
c
11
(y
6
− 7y
5
+ ··· − 5y + 1)(y
63
− 68y
62
+ ··· + 14y −1)
c
8
, c
9
, c
12
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
63
+ 64y
62
+ ··· − 2246y −49)
17
