12a
1159
(K12a
1159
)
A knot diagram
1
Linearized knot diagam
4 9 8 10 11 12 1 3 2 7 6 5
Solving Sequence
5,11
6 12 7 1 8 10 4 2 3 9
c
5
c
11
c
6
c
12
c
7
c
10
c
4
c
1
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
56
+ u
55
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 56 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
= hu
56
+ u
55
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
3
− 2u
−u
3
+ u
a
8
=
u
10
− 5u
8
+ 8u
6
− 3u
4
− 3u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
10
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
−u
12
+ 5u
10
− 9u
8
+ 6u
6
− u
2
+ 1
−u
14
+ 6u
12
− 13u
10
+ 10u
8
+ 2u
6
− 4u
4
− u
2
a
2
=
u
29
− 12u
27
+ ··· + 6u
3
− 3u
u
31
− 13u
29
+ ··· − 24u
7
+ u
a
3
=
u
34
− 15u
32
+ ··· + 3u
2
+ 1
−u
34
+ 14u
32
+ ··· + 8u
4
− u
2
a
9
=
u
53
− 22u
51
+ ··· − 14u
3
+ u
u
55
− 23u
53
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
54
+ 92u
52
+ ··· + 24u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
− 17u
55
+ ··· − 14056u + 1697
c
2
, c
3
, c
8
c
9
u
56
+ u
55
+ ··· − 2u − 1
c
4
, c
7
u
56
+ u
55
+ ··· − 104u − 61
c
5
, c
6
, c
11
u
56
− u
55
+ ··· − 2u − 1
c
10
, c
12
u
56
+ 3u
55
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
− 23y
55
+ ··· − 40096324y + 2879809
c
2
, c
3
, c
8
c
9
y
56
+ 65y
55
+ ··· + 4y + 1
c
4
, c
7
y
56
− 43y
55
+ ··· − 18624y + 3721
c
5
, c
6
, c
11
y
56
− 47y
55
+ ··· + 4y + 1
c
10
, c
12
y
56
+ 29y
55
+ ··· + 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.007390 + 0.299100I
−11.32590 + 5.07175I −10.41136 − 2.14928I
u = 1.007390 − 0.299100I
−11.32590 − 5.07175I −10.41136 + 2.14928I
u = −1.037430 + 0.256406I
−3.34884 − 2.95517I −8.35409 + 4.14686I
u = −1.037430 − 0.256406I
−3.34884 + 2.95517I −8.35409 − 4.14686I
u = 1.121000 + 0.214806I
−1.62413 − 0.33326I 0
u = 1.121000 − 0.214806I
−1.62413 + 0.33326I 0
u = 0.755198 + 0.276814I
−11.72800 − 4.92772I −11.51035 + 4.25849I
u = 0.755198 − 0.276814I
−11.72800 + 4.92772I −11.51035 − 4.25849I
u = 0.174335 + 0.780042I
−8.76893 − 9.11894I −7.30154 + 6.10227I
u = 0.174335 − 0.780042I
−8.76893 + 9.11894I −7.30154 − 6.10227I
u = −0.163772 + 0.768213I
−0.71389 + 6.86037I −5.12714 − 7.81567I
u = −0.163772 − 0.768213I
−0.71389 − 6.86037I −5.12714 + 7.81567I
u = −0.056015 + 0.774634I
−2.40652 + 3.39994I −2.99197 − 3.55207I
u = −0.056015 − 0.774634I
−2.40652 − 3.39994I −2.99197 + 3.55207I
u = 0.150274 + 0.747044I
1.16768 − 3.31828I −1.06642 + 3.30903I
u = 0.150274 − 0.747044I
1.16768 + 3.31828I −1.06642 − 3.30903I
u = 0.019950 + 0.754347I
4.06747 − 1.63438I 1.40261 + 4.57782I
u = 0.019950 − 0.754347I
4.06747 + 1.63438I 1.40261 − 4.57782I
u = −0.728627 + 0.195550I
−3.63602 + 3.02560I −10.17603 − 5.79656I
u = −0.728627 − 0.195550I
−3.63602 − 3.02560I −10.17603 + 5.79656I
u = −1.205440 + 0.317841I
−5.92121 + 0.55972I 0
u = −1.205440 − 0.317841I
−5.92121 − 0.55972I 0
u = 0.210116 + 0.707797I
−9.83896 + 1.27867I −8.53672 + 1.04653I
u = 0.210116 − 0.707797I
−9.83896 − 1.27867I −8.53672 − 1.04653I
u = −1.254520 + 0.166796I
−4.29080 + 2.46551I 0
u = −1.254520 − 0.166796I
−4.29080 − 2.46551I 0
u = −0.174059 + 0.708931I
−1.55154 + 0.37866I −6.90408 + 0.22967I
u = −0.174059 − 0.708931I
−1.55154 − 0.37866I −6.90408 − 0.22967I
u = 1.247700 + 0.308289I
0.28331 − 2.20403I 0
u = 1.247700 − 0.308289I
0.28331 + 2.20403I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276230 + 0.317717I
0.03967 + 5.50640I 0
u = −1.276230 − 0.317717I
0.03967 − 5.50640I 0
u = 1.323630 + 0.151327I
−12.15060 − 3.21011I 0
u = 1.323630 − 0.151327I
−12.15060 + 3.21011I 0
u = 0.662825
−1.52718 −5.96610
u = 1.297740 + 0.332753I
−6.63103 − 7.39587I 0
u = 1.297740 − 0.332753I
−6.63103 + 7.39587I 0
u = −1.354420 + 0.316273I
−3.57922 + 7.17640I 0
u = −1.354420 − 0.316273I
−3.57922 − 7.17640I 0
u = 1.359410 + 0.299615I
−6.38721 − 4.05791I 0
u = 1.359410 − 0.299615I
−6.38721 + 4.05791I 0
u = 1.362120 + 0.324699I
−5.53028 − 10.81760I 0
u = 1.362120 − 0.324699I
−5.53028 + 10.81760I 0
u = −1.40068
−7.76419 0
u = −1.372010 + 0.293076I
−14.8334 + 2.3638I 0
u = −1.372010 − 0.293076I
−14.8334 − 2.3638I 0
u = −1.368570 + 0.329070I
−13.6427 + 13.1311I 0
u = −1.368570 − 0.329070I
−13.6427 − 13.1311I 0
u = 1.411120 + 0.016554I
−10.10810 − 3.41472I 0
u = 1.411120 − 0.016554I
−10.10810 + 3.41472I 0
u = −1.42291 + 0.02306I
−18.4140 + 5.4847I 0
u = −1.42291 − 0.02306I
−18.4140 − 5.4847I 0
u = −0.343458 + 0.381016I
−7.13429 + 1.35752I −8.42167 − 4.66731I
u = −0.343458 − 0.381016I
−7.13429 − 1.35752I −8.42167 + 4.66731I
u = 0.186399 + 0.279972I
−0.195308 − 0.800076I −5.29681 + 8.55548I
u = 0.186399 − 0.279972I
−0.195308 + 0.800076I −5.29681 − 8.55548I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
56
− 17u
55
+ ··· − 14056u + 1697
c
2
, c
3
, c
8
c
9
u
56
+ u
55
+ ··· − 2u − 1
c
4
, c
7
u
56
+ u
55
+ ··· − 104u − 61
c
5
, c
6
, c
11
u
56
− u
55
+ ··· − 2u − 1
c
10
, c
12
u
56
+ 3u
55
+ ··· + 4u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
56
− 23y
55
+ ··· − 40096324y + 2879809
c
2
, c
3
, c
8
c
9
y
56
+ 65y
55
+ ··· + 4y + 1
c
4
, c
7
y
56
− 43y
55
+ ··· − 18624y + 3721
c
5
, c
6
, c
11
y
56
− 47y
55
+ ··· + 4y + 1
c
10
, c
12
y
56
+ 29y
55
+ ··· + 4y + 1
8
