12n
0143
(K12n
0143
)
A knot diagram
1
Linearized knot diagam
3 4 10 2 9 3 12 4 6 8 7 11
Solving Sequence
8,12 3,7
6 11 1 10 4 2 5 9
c
7
c
6
c
11
c
12
c
10
c
3
c
2
c
4
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5018882u
19
− 3159071u
18
+ ··· + 35542844b − 8946208,
4030002u
19
+ 3341564u
18
+ ··· + 35542844a + 3081004, u
20
− u
19
+ ··· + 4u − 4i
I
u
2
= h−3u
3
a + 4u
2
a − 8u
3
+ 5au + 2u
2
+ 13b + 2a + 9u + 1, 3u
3
a − 2u
2
a + 2a
2
− u
2
+ 4a + 6u − 2,
u
4
− 2u
2
+ 2i
I
v
1
= ha, b + v, v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 30 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−5.02 × 10
6
u
19
− 3.16 × 10
6
u
18
+ · · · + 3.55 × 10
7
b − 8.95 × 10
6
, 4.03 ×
10
6
u
19
+ 3.34 × 10
6
u
18
+ · · · + 3.55 × 10
7
a + 3.08 × 10
6
, u
20
− u
19
+ · · · + 4u − 4i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
3
=
−0.113384u
19
− 0.0940151u
18
+ ··· + 0.649600u − 0.0866842
0.141207u
19
+ 0.0888806u
18
+ ··· + 0.434285u + 0.251702
a
7
=
1
−u
2
a
6
=
0.334897u
19
− 0.0768593u
18
+ ··· + 0.470869u + 2.67956
−0.0397535u
19
+ 0.166369u
18
+ ··· − 0.371958u − 0.816791
a
11
=
u
−u
3
+ u
a
1
=
−u
3
u
5
− u
3
+ u
a
10
=
u
3
−u
3
+ u
a
4
=
−0.254108u
19
− 0.153593u
18
+ ··· + 0.947053u − 0.825468
0.171597u
19
+ 0.0740954u
18
+ ··· + 0.128017u + 0.521714
a
2
=
−0.199337u
19
+ 0.0822480u
18
+ ··· + 0.449295u − 0.850726
0.0288459u
19
+ 0.0324049u
18
+ ··· + 1.28582u + 0.0973546
a
5
=
−0.0739774u
19
− 0.140245u
18
+ ··· + 0.662127u − 0.407213
0.137706u
19
− 0.0252866u
18
+ ··· + 0.141019u + 0.447024
a
9
=
−0.455718u
19
+ 0.276225u
18
+ ··· + 0.309258u − 2.11593
−0.200598u
19
− 0.0655987u
18
+ ··· + 0.985773u − 0.419904
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
16163108
8885711
u
19
+
7616138
8885711
u
18
+ ··· −
81238406
8885711
u −
119525194
8885711
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 48u
19
+ ··· − 52526u + 625
c
2
, c
4
u
20
+ 24u
18
+ ··· + 74u + 25
c
3
u
20
+ 2u
19
+ ··· + 12u + 5
c
5
, c
9
u
20
+ 3u
19
+ ··· + u − 1
c
6
u
20
+ 4u
19
+ ··· − 51528u − 13061
c
7
, c
11
u
20
+ u
19
+ ··· − 4u − 4
c
8
u
20
− 16u
19
+ ··· − 18622u − 15107
c
10
u
20
+ 3u
19
+ ··· + 116u + 76
c
12
u
20
+ 15u
19
+ ··· + 80u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 400y
19
+ ··· − 3308161926y + 390625
c
2
, c
4
y
20
+ 48y
19
+ ··· − 52526y + 625
c
3
y
20
+ 24y
18
+ ··· − 74y + 25
c
5
, c
9
y
20
− 45y
19
+ ··· + 77y + 1
c
6
y
20
+ 60y
19
+ ··· − 809328142y + 170589721
c
7
, c
11
y
20
− 15y
19
+ ··· − 80y + 16
c
8
y
20
− 120y
19
+ ··· − 367173334y + 228221449
c
10
y
20
+ 45y
19
+ ··· − 68176y + 5776
c
12
y
20
− 15y
19
+ ··· + 768y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027210 + 0.343771I
a = 0.25199 − 2.64585I
b = −0.766725 + 1.006540I
−2.86803 − 3.80264I −6.48723 + 4.67286I
u = 1.027210 − 0.343771I
a = 0.25199 + 2.64585I
b = −0.766725 − 1.006540I
−2.86803 + 3.80264I −6.48723 − 4.67286I
u = −1.095930 + 0.435073I
a = 1.163710 − 0.763492I
b = 0.458140 + 0.989102I
−2.45038 + 5.65982I −4.21302 − 7.24292I
u = −1.095930 − 0.435073I
a = 1.163710 + 0.763492I
b = 0.458140 − 0.989102I
−2.45038 − 5.65982I −4.21302 + 7.24292I
u = −0.722942 + 0.357669I
a = −0.128326 − 1.009150I
b = −0.238239 − 0.123051I
0.99363 + 1.64776I 1.20276 − 5.62384I
u = −0.722942 − 0.357669I
a = −0.128326 + 1.009150I
b = −0.238239 + 0.123051I
0.99363 − 1.64776I 1.20276 + 5.62384I
u = 0.106031 + 1.190120I
a = −0.299156 + 0.869186I
b = 0.09465 − 2.29475I
19.2969 + 4.5215I −5.96688 − 1.69232I
u = 0.106031 − 1.190120I
a = −0.299156 − 0.869186I
b = 0.09465 + 2.29475I
19.2969 − 4.5215I −5.96688 + 1.69232I
u = 0.634751 + 0.432509I
a = 0.196432 − 0.368569I
b = 0.643286 + 0.493353I
−1.74557 + 0.63892I −5.74453 + 1.51352I
u = 0.634751 − 0.432509I
a = 0.196432 + 0.368569I
b = 0.643286 − 0.493353I
−1.74557 − 0.63892I −5.74453 − 1.51352I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.739383
a = −0.350220
b = 0.508808
−0.989681 −10.9360
u = 1.350830 + 0.261047I
a = −1.05824 − 1.16450I
b = 0.045773 + 1.216250I
−4.75007 − 0.87462I −9.06700 + 0.37407I
u = 1.350830 − 0.261047I
a = −1.05824 + 1.16450I
b = 0.045773 − 1.216250I
−4.75007 + 0.87462I −9.06700 − 0.37407I
u = −0.255829 + 0.544433I
a = −0.156916 + 1.044260I
b = −0.341861 + 0.731952I
−0.11659 − 1.77179I −0.89537 + 3.37821I
u = −0.255829 − 0.544433I
a = −0.156916 − 1.044260I
b = −0.341861 − 0.731952I
−0.11659 + 1.77179I −0.89537 − 3.37821I
u = 1.35494 + 0.64126I
a = 1.91114 + 2.01731I
b = −0.21695 − 2.30777I
15.4383 − 10.9552I −7.83113 + 4.63988I
u = 1.35494 − 0.64126I
a = 1.91114 − 2.01731I
b = −0.21695 + 2.30777I
15.4383 + 10.9552I −7.83113 − 4.63988I
u = −1.52619
a = −1.06989
b = 0.168676
−9.28250 −9.91420
u = −1.50565 + 0.55625I
a = −0.67058 + 2.22111I
b = −0.01682 − 2.17499I
14.2365 + 1.7524I −8.57238 − 0.70411I
u = −1.50565 − 0.55625I
a = −0.67058 − 2.22111I
b = −0.01682 + 2.17499I
14.2365 − 1.7524I −8.57238 + 0.70411I
6
II. I
u
2
=
h−3u
3
a −8u
3
+· · ·+ 2a +1, 3u
3
a −2u
2
a +2a
2
−u
2
+4a + 6u −2, u
4
−2u
2
+2i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
3
=
a
0.230769au
3
+ 0.615385u
3
+ ··· − 0.153846a − 0.0769231
a
7
=
1
−u
2
a
6
=
−1.61538au
3
− 1.80769u
3
+ ··· − 0.923077a + 1.53846
0.769231au
3
+ 1.38462u
3
+ ··· + 0.153846a + 1.07692
a
11
=
u
−u
3
+ u
a
1
=
−u
3
u
3
− u
a
10
=
u
3
−u
3
+ u
a
4
=
0.769231au
3
+ 1.38462u
3
+ ··· + 1.15385a − 0.923077
−0.230769au
3
− 0.615385u
3
+ ··· + 0.153846a + 0.0769231
a
2
=
−0.384615au
3
− 2.19231u
3
+ ··· − 0.0769231a − 1.53846
0.461538au
3
+ 2.23077u
3
+ ··· − 0.307692a + 0.846154
a
5
=
u
3
−u
3
+ u
a
9
=
1.61538au
3
+ 2.80769u
3
+ ··· + 0.923077a − 1.53846
−0.769231au
3
− 2.38462u
3
+ ··· − 0.153846a − 1.07692
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
12
13
u
3
a +
16
13
u
2
a +
20
13
u
3
+
20
13
au +
60
13
u
2
+
8
13
a −
16
13
u −
152
13
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
5
(u + 1)
8
c
6
u
8
+ 4u
7
+ 8u
6
+ 16u
5
+ 27u
4
+ 24u
3
+ 24u
2
+ 40u + 25
c
7
, c
11
(u
4
− 2u
2
+ 2)
2
c
8
u
8
− 4u
7
+ 8u
6
− 16u
5
+ 27u
4
− 24u
3
+ 24u
2
− 40u + 25
c
9
(u − 1)
8
c
10
(u
4
+ 2u
2
+ 2)
2
c
12
(u
2
+ 2u + 2)
4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
(y
2
+ y + 1)
4
c
5
, c
9
(y −1)
8
c
6
, c
8
y
8
− 10y
6
+ 32y
5
+ 75y
4
− 160y
3
+ 6y
2
− 400y + 625
c
7
, c
11
(y
2
− 2y + 2)
4
c
10
(y
2
+ 2y + 2)
4
c
12
(y
2
+ 4)
4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −0.789474 + 0.479379I
b = 0.044910 + 0.232659I
−4.11234 − 5.69375I −10.00000 + 7.46410I
u = 1.098680 + 0.455090I
a = −1.17592 − 1.81004I
b = 0.04491 + 1.96471I
−4.11234 − 1.63398I −10.00000 + 0.53590I
u = 1.098680 − 0.455090I
a = −0.789474 − 0.479379I
b = 0.044910 − 0.232659I
−4.11234 + 5.69375I −10.00000 − 7.46410I
u = 1.098680 − 0.455090I
a = −1.17592 + 1.81004I
b = 0.04491 − 1.96471I
−4.11234 + 1.63398I −10.00000 − 0.53590I
u = −1.098680 + 0.455090I
a = −1.55613 − 1.07799I
b = 0.955090 + 0.232659I
−4.11234 + 1.63398I −10.00000 − 0.53590I
u = −1.098680 + 0.455090I
a = 1.52152 − 2.25267I
b = 0.95509 + 1.96471I
−4.11234 + 5.69375I −10.00000 − 7.46410I
u = −1.098680 − 0.455090I
a = −1.55613 + 1.07799I
b = 0.955090 − 0.232659I
−4.11234 − 1.63398I −10.00000 + 0.53590I
u = −1.098680 − 0.455090I
a = 1.52152 + 2.25267I
b = 0.95509 − 1.96471I
−4.11234 − 5.69375I −10.00000 + 7.46410I
10
III. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
v
0
a
3
=
0
−v
a
7
=
1
0
a
6
=
1
v − 1
a
11
=
v
0
a
1
=
v
0
a
10
=
v
0
a
4
=
−1
−v
a
2
=
v
−1
a
5
=
−v
0
a
9
=
v + 1
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
2
− u + 1
c
2
, c
3
, c
6
c
8
u
2
+ u + 1
c
5
(u − 1)
2
c
7
, c
10
, c
11
c
12
u
2
c
9
(u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
8
y
2
+ y + 1
c
5
, c
9
(y − 1)
2
c
7
, c
10
, c
11
c
12
y
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
14
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
20
+ 48u
19
+ ··· − 52526u + 625)
c
2
((u
2
+ u + 1)
5
)(u
20
+ 24u
18
+ ··· + 74u + 25)
c
3
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
20
+ 2u
19
+ ··· + 12u + 5)
c
4
((u
2
− u + 1)
5
)(u
20
+ 24u
18
+ ··· + 74u + 25)
c
5
((u − 1)
2
)(u + 1)
8
(u
20
+ 3u
19
+ ··· + u − 1)
c
6
(u
2
+ u + 1)(u
8
+ 4u
7
+ ··· + 40u + 25)
· (u
20
+ 4u
19
+ ··· − 51528u − 13061)
c
7
, c
11
u
2
(u
4
− 2u
2
+ 2)
2
(u
20
+ u
19
+ ··· − 4u − 4)
c
8
(u
2
+ u + 1)(u
8
− 4u
7
+ ··· − 40u + 25)
· (u
20
− 16u
19
+ ··· − 18622u − 15107)
c
9
((u − 1)
8
)(u + 1)
2
(u
20
+ 3u
19
+ ··· + u − 1)
c
10
u
2
(u
4
+ 2u
2
+ 2)
2
(u
20
+ 3u
19
+ ··· + 116u + 76)
c
12
u
2
(u
2
+ 2u + 2)
4
(u
20
+ 15u
19
+ ··· + 80u + 16)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
20
− 400y
19
+ ··· − 3.30816 × 10
9
y + 390625)
c
2
, c
4
((y
2
+ y + 1)
5
)(y
20
+ 48y
19
+ ··· − 52526y + 625)
c
3
((y
2
+ y + 1)
5
)(y
20
+ 24y
18
+ ··· − 74y + 25)
c
5
, c
9
((y − 1)
10
)(y
20
− 45y
19
+ ··· + 77y + 1)
c
6
(y
2
+ y + 1)(y
8
− 10y
6
+ ··· − 400y + 625)
· (y
20
+ 60y
19
+ ··· − 809328142y + 170589721)
c
7
, c
11
y
2
(y
2
− 2y + 2)
4
(y
20
− 15y
19
+ ··· − 80y + 16)
c
8
(y
2
+ y + 1)(y
8
− 10y
6
+ ··· − 400y + 625)
· (y
20
− 120y
19
+ ··· − 367173334y + 228221449)
c
10
y
2
(y
2
+ 2y + 2)
4
(y
20
+ 45y
19
+ ··· − 68176y + 5776)
c
12
y
2
(y
2
+ 4)
4
(y
20
− 15y
19
+ ··· + 768y + 256)
16
