12n
0160
(K12n
0160
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 9 3 5 12 6 10 8
Solving Sequence
6,10
11 12
3,5
2 1 4 9 7 8
c
10
c
11
c
5
c
2
c
1
c
4
c
9
c
6
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
34
+ 6u
33
+ ··· + b − 3, 3u
34
− 3u
33
+ ··· + a + 1, u
35
− 2u
34
+ ··· − 2u
2
− 1i
I
u
2
= h−u
7
− u
5
− 2u
3
+ u
2
+ b − u, −u
6
− u
4
− 2u
2
+ a + u − 1, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 44 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−3u
34
+6u
33
+· · ·+b−3, 3u
34
−3u
33
+· · ·+a+1, u
35
−2u
34
+· · ·−2u
2
−1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
12
=
u
2
+ 1
−u
2
a
3
=
−3u
34
+ 3u
33
+ ··· − 2u − 1
3u
34
− 6u
33
+ ··· + u + 3
a
5
=
−u
u
3
+ u
a
2
=
−2u
34
+ 2u
33
+ ··· − 2u − 1
2u
34
− 4u
33
+ ··· + 7u
2
+ 2
a
1
=
−u
20
− 3u
18
− 7u
16
− 10u
14
− 10u
12
− 7u
10
− u
8
+ 2u
6
+ 3u
4
+ u
2
− 1
u
22
+ 4u
20
+ ··· + 2u
4
+ u
2
a
4
=
−u
34
+ u
33
+ ··· + 3u
2
− 3u
u
34
− 2u
33
+ ··· + 4u
2
+ 1
a
9
=
u
4
+ u
2
+ 1
−u
4
a
7
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
−u
9
− u
7
− u
5
+ u
a
8
=
−u
8
− u
6
− u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
34
− 2u
33
+ 24u
32
− 8u
31
+ 92u
30
− 18u
29
+ 247u
28
− 13u
27
+
523u
26
+ 50u
25
+ 904u
24
+ 221u
23
+ 1321u
22
+ 524u
21
+ 1669u
20
+ 895u
19
+ 1845u
18
+
1222u
17
+ 1810u
16
+ 1360u
15
+ 1576u
14
+ 1256u
13
+ 1216u
12
+ 958u
11
+ 820u
10
+
594u
9
+ 460u
8
+ 299u
7
+ 205u
6
+ 110u
5
+ 63u
4
+ 27u
3
+ 5u
2
+ 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 52u
34
+ ··· + 32u + 1
c
2
, c
4
u
35
− 10u
34
+ ··· + 12u − 1
c
3
, c
7
u
35
− u
34
+ ··· − 1024u − 512
c
5
, c
10
u
35
− 2u
34
+ ··· − 2u
2
− 1
c
6
u
35
+ 10u
34
+ ··· − 206u − 31
c
8
u
35
− 2u
34
+ ··· − 412u − 241
c
9
, c
11
u
35
+ 12u
34
+ ··· − 4u − 1
c
12
u
35
+ 36u
33
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 128y
34
+ ··· + 420y −1
c
2
, c
4
y
35
− 52y
34
+ ··· + 32y −1
c
3
, c
7
y
35
+ 57y
34
+ ··· + 2621440y −262144
c
5
, c
10
y
35
+ 12y
34
+ ··· − 4y −1
c
6
y
35
+ 12y
34
+ ··· − 10140y −961
c
8
y
35
+ 12y
34
+ ··· − 1095024y −58081
c
9
, c
11
y
35
+ 24y
34
+ ··· − 16y −1
c
12
y
35
+ 72y
34
+ ··· − 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.737220 + 0.648144I
a = 1.74315 − 1.73886I
b = −2.41211 + 0.15211I
−0.58521 − 2.05799I 0.94554 + 1.75994I
u = 0.737220 − 0.648144I
a = 1.74315 + 1.73886I
b = −2.41211 − 0.15211I
−0.58521 + 2.05799I 0.94554 − 1.75994I
u = 0.101201 + 0.967150I
a = −0.223398 − 0.378771I
b = −0.343721 + 0.254391I
−2.08113 + 1.70930I 0.77222 − 3.96512I
u = 0.101201 − 0.967150I
a = −0.223398 + 0.378771I
b = −0.343721 − 0.254391I
−2.08113 − 1.70930I 0.77222 + 3.96512I
u = 0.678017 + 0.796351I
a = −1.63124 − 0.26748I
b = 0.89300 + 1.48039I
1.40101 + 2.20417I 3.92249 − 4.39905I
u = 0.678017 − 0.796351I
a = −1.63124 + 0.26748I
b = 0.89300 − 1.48039I
1.40101 − 2.20417I 3.92249 + 4.39905I
u = −0.030827 + 1.048300I
a = 0.987634 + 0.536168I
b = 0.592511 − 1.018810I
−6.06605 − 1.60204I −6.58193 + 1.49646I
u = −0.030827 − 1.048300I
a = 0.987634 − 0.536168I
b = 0.592511 + 1.018810I
−6.06605 + 1.60204I −6.58193 − 1.49646I
u = 0.838636 + 0.644982I
a = −0.76138 + 2.67985I
b = 2.36698 − 1.75635I
−10.48130 − 6.27093I 0.94475 + 1.94965I
u = 0.838636 − 0.644982I
a = −0.76138 − 2.67985I
b = 2.36698 + 1.75635I
−10.48130 + 6.27093I 0.94475 − 1.94965I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781183 + 0.727089I
a = −0.051887 + 0.135238I
b = 0.057797 + 0.143372I
3.78767 + 1.08265I 9.73080 − 0.41634I
u = −0.781183 − 0.727089I
a = −0.051887 − 0.135238I
b = 0.057797 − 0.143372I
3.78767 − 1.08265I 9.73080 + 0.41634I
u = −0.632282 + 0.665654I
a = 0.152240 − 0.624708I
b = −0.319580 − 0.496331I
−1.37778 − 0.83460I 0.396623 + 0.019030I
u = −0.632282 − 0.665654I
a = 0.152240 + 0.624708I
b = −0.319580 + 0.496331I
−1.37778 + 0.83460I 0.396623 − 0.019030I
u = −0.121893 + 1.112050I
a = −1.224660 − 0.088950I
b = −0.248194 + 1.351040I
−17.1086 − 5.6948I −5.50780 + 3.28741I
u = −0.121893 − 1.112050I
a = −1.224660 + 0.088950I
b = −0.248194 − 1.351040I
−17.1086 + 5.6948I −5.50780 − 3.28741I
u = 0.660177 + 0.922712I
a = 0.183127 − 1.365060I
b = −1.38045 + 0.73221I
1.00684 + 2.97409I 3.31167 − 1.92596I
u = 0.660177 − 0.922712I
a = 0.183127 + 1.365060I
b = −1.38045 − 0.73221I
1.00684 − 2.97409I 3.31167 + 1.92596I
u = −0.518083 + 1.034140I
a = −0.493003 + 0.558538I
b = 0.322191 + 0.799204I
−14.7020 − 1.1608I −3.27320 + 2.65041I
u = −0.518083 − 1.034140I
a = −0.493003 − 0.558538I
b = 0.322191 − 0.799204I
−14.7020 + 1.1608I −3.27320 − 2.65041I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645286 + 0.989574I
a = 0.110285 − 0.455498I
b = −0.379583 − 0.403061I
−2.35824 − 4.23049I −1.64611 + 4.83730I
u = −0.645286 − 0.989574I
a = 0.110285 + 0.455498I
b = −0.379583 + 0.403061I
−2.35824 + 4.23049I −1.64611 − 4.83730I
u = 0.801511 + 0.879701I
a = 1.77931 + 2.04057I
b = 0.36896 − 3.20080I
−6.25391 + 2.99402I 1.83860 − 2.69092I
u = 0.801511 − 0.879701I
a = 1.77931 − 2.04057I
b = 0.36896 + 3.20080I
−6.25391 − 2.99402I 1.83860 + 2.69092I
u = 0.677300 + 1.008060I
a = −2.02100 + 1.40176I
b = 2.78188 + 1.08787I
−1.65574 + 7.47330I −0.96819 − 6.53783I
u = 0.677300 − 1.008060I
a = −2.02100 − 1.40176I
b = 2.78188 − 1.08787I
−1.65574 − 7.47330I −0.96819 + 6.53783I
u = −0.718651 + 0.985154I
a = 0.0048122 + 0.1319630I
b = 0.133462 + 0.090095I
3.00104 − 6.75637I 7.73187 + 5.52332I
u = −0.718651 − 0.985154I
a = 0.0048122 − 0.1319630I
b = 0.133462 − 0.090095I
3.00104 + 6.75637I 7.73187 − 5.52332I
u = −0.715979 + 0.271293I
a = 0.797619 + 0.724413I
b = 0.767607 + 0.302276I
−12.50660 − 3.28011I 0.69781 + 2.19401I
u = −0.715979 − 0.271293I
a = 0.797619 − 0.724413I
b = 0.767607 − 0.302276I
−12.50660 + 3.28011I 0.69781 − 2.19401I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715761 + 1.041330I
a = 2.74535 − 0.31064I
b = −2.28849 − 2.63647I
−11.6867 + 12.0828I −0.83819 − 6.56234I
u = 0.715761 − 1.041330I
a = 2.74535 + 0.31064I
b = −2.28849 + 2.63647I
−11.6867 − 12.0828I −0.83819 + 6.56234I
u = −0.268541 + 0.381611I
a = 0.20602 − 1.57922I
b = −0.547327 − 0.502704I
−1.72551 − 0.80413I −2.43242 + 1.76310I
u = −0.268541 − 0.381611I
a = 0.20602 + 1.57922I
b = −0.547327 + 0.502704I
−1.72551 + 0.80413I −2.43242 − 1.76310I
u = 0.445806
a = −0.605941
b = 0.270132
0.870658 11.9110
8
II. I
u
2
= h−u
7
− u
5
− 2u
3
+ u
2
+ b − u, −u
6
− u
4
− 2u
2
+ a + u − 1, u
9
+
u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
12
=
u
2
+ 1
−u
2
a
3
=
u
6
+ u
4
+ 2u
2
− u + 1
u
7
+ u
5
+ 2u
3
− u
2
+ u
a
5
=
−u
u
3
+ u
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
7
+ u
5
+ u
3
− u
2
a
1
=
u
−u
3
− u
a
4
=
u
6
+ u
4
+ 2u
2
− u + 1
u
7
+ u
5
+ 2u
3
− u
2
+ u
a
9
=
u
4
+ u
2
+ 1
−u
4
a
7
=
−u
8
− u
6
− u
4
+ 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
a
8
=
−u
8
− u
6
− u
4
+ 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 6u
3
+ 3u
2
− u + 1
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
8
, c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = −0.770941 − 0.258974I
b = 0.142194 − 0.781734I
−3.42837 + 2.09337I −5.30979 − 3.87975I
u = 0.140343 − 0.966856I
a = −0.770941 + 0.258974I
b = 0.142194 + 0.781734I
−3.42837 − 2.09337I −5.30979 + 3.87975I
u = 0.628449 + 0.875112I
a = −0.147409 − 0.367985I
b = 0.229389 − 0.360259I
−1.02799 + 2.45442I 0.49381 − 3.35442I
u = 0.628449 − 0.875112I
a = −0.147409 + 0.367985I
b = 0.229389 + 0.360259I
−1.02799 − 2.45442I 0.49381 + 3.35442I
u = −0.796005 + 0.733148I
a = 0.24323 − 1.73417I
b = 1.07779 + 1.55873I
2.72642 + 1.33617I 1.53709 − 1.22905I
u = −0.796005 − 0.733148I
a = 0.24323 + 1.73417I
b = 1.07779 − 1.55873I
2.72642 − 1.33617I 1.53709 + 1.22905I
u = −0.728966 + 0.986295I
a = 1.62529 − 0.46000I
b = −0.73109 + 1.93833I
1.95319 − 7.08493I 0.02676 + 6.64241I
u = −0.728966 − 0.986295I
a = 1.62529 + 0.46000I
b = −0.73109 − 1.93833I
1.95319 + 7.08493I 0.02676 − 6.64241I
u = 0.512358
a = 1.09967
b = 0.563422
−0.446489 2.50430
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
35
+ 52u
34
+ ··· + 32u + 1)
c
2
((u − 1)
9
)(u
35
− 10u
34
+ ··· + 12u − 1)
c
3
, c
7
u
9
(u
35
− u
34
+ ··· − 1024u − 512)
c
4
((u + 1)
9
)(u
35
− 10u
34
+ ··· + 12u − 1)
c
5
(u
9
− u
8
+ ··· + u + 1)(u
35
− 2u
34
+ ··· − 2u
2
− 1)
c
6
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
35
+ 10u
34
+ ··· − 206u − 31)
c
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
35
− 2u
34
+ ··· − 412u − 241)
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
35
+ 12u
34
+ ··· − 4u − 1)
c
10
(u
9
+ u
8
+ ··· + u − 1)(u
35
− 2u
34
+ ··· − 2u
2
− 1)
c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
35
+ 12u
34
+ ··· − 4u − 1)
c
12
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
35
+ 36u
33
+ ··· − 2u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
35
− 128y
34
+ ··· + 420y −1)
c
2
, c
4
((y −1)
9
)(y
35
− 52y
34
+ ··· + 32y −1)
c
3
, c
7
y
9
(y
35
+ 57y
34
+ ··· + 2621440y −262144)
c
5
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
35
+ 12y
34
+ ··· − 4y −1)
c
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
35
+ 12y
34
+ ··· − 10140y −961)
c
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
35
+ 12y
34
+ ··· − 1095024y −58081)
c
9
, c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
35
+ 24y
34
+ ··· − 16y −1)
c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
35
+ 72y
34
+ ··· − 4y −1)
14
