12a
0796
(K12a
0796
)
A knot diagram
1
Linearized knot diagam
3 8 11 12 1 10 9 2 7 6 4 5
Solving Sequence
2,9
8 3 1 7 10 6 11 4 5 12
c
8
c
2
c
1
c
7
c
9
c
6
c
10
c
3
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
28
+ u
27
+ ··· − u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 28 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
28
+ u
27
+ · · · − u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
u
2
+ 1
u
2
a
10
=
u
4
+ u
2
+ 1
u
4
a
6
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
11
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
4
a
4
=
−u
19
− 2u
17
− 8u
15
− 12u
13
− 21u
11
− 22u
9
− 20u
7
− 12u
5
− 5u
3
−u
19
− u
17
− 6u
15
− 5u
13
− 11u
11
− 7u
9
− 6u
7
− 2u
5
+ u
3
+ u
a
5
=
−u
14
− u
12
− 4u
10
− 3u
8
− 2u
6
+ 2u
2
+ 1
−u
16
− 2u
14
− 6u
12
− 8u
10
− 10u
8
− 6u
6
− 4u
4
a
12
=
−u
25
− 2u
23
+ ··· + 6u
3
+ u
−u
27
− 3u
25
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
27
− 8u
25
+ 4u
24
− 44u
23
+ 8u
22
− 72u
21
+ 40u
20
− 184u
19
+
60u
18
− 240u
17
+ 140u
16
− 364u
15
+ 148u
14
− 360u
13
+ 200u
12
− 336u
11
+ 128u
10
−
228u
9
+ 96u
8
− 108u
7
+ 20u
6
− 32u
5
+ 4u
3
− 12u
2
+ 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
u
28
+ 5u
27
+ ··· + 2u + 1
c
2
, c
8
u
28
− u
27
+ ··· − u
2
− 1
c
3
, c
4
, c
5
c
11
, c
12
u
28
+ u
27
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
y
28
+ 37y
27
+ ··· − 34y + 1
c
2
, c
8
y
28
+ 5y
27
+ ··· + 2y + 1
c
3
, c
4
, c
5
c
11
, c
12
y
28
− 35y
27
+ ··· + 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.653471 + 0.778202I
3.53035 + 2.44157I −1.95206 − 4.13656I
u = 0.653471 − 0.778202I
3.53035 − 2.44157I −1.95206 + 4.13656I
u = −0.675349 + 0.676658I
1.40633 + 0.49885I −6.53440 − 1.41082I
u = −0.675349 − 0.676658I
1.40633 − 0.49885I −6.53440 + 1.41082I
u = 0.733930 + 0.599761I
−6.94317 − 1.86401I −7.90882 + 0.19524I
u = 0.733930 − 0.599761I
−6.94317 + 1.86401I −7.90882 − 0.19524I
u = −0.619172 + 0.858733I
0.82022 − 5.33799I −8.56972 + 7.97469I
u = −0.619172 − 0.858733I
0.82022 + 5.33799I −8.56972 − 7.97469I
u = −0.204914 + 0.910458I
−12.53370 − 2.51044I −16.1255 + 4.0009I
u = −0.204914 − 0.910458I
−12.53370 + 2.51044I −16.1255 − 4.0009I
u = 0.603718 + 0.919286I
−7.98654 + 6.81286I −10.46299 − 6.27742I
u = 0.603718 − 0.919286I
−7.98654 − 6.81286I −10.46299 + 6.27742I
u = 0.205807 + 0.816083I
−3.50231 + 2.01539I −16.4015 − 5.8251I
u = 0.205807 − 0.816083I
−3.50231 − 2.01539I −16.4015 + 5.8251I
u = −0.930865 + 0.909652I
2.22097 + 2.66758I −7.83362 − 0.34269I
u = −0.930865 − 0.909652I
2.22097 − 2.66758I −7.83362 + 0.34269I
u = 0.922794 + 0.925907I
10.83490 − 0.43343I −6.08489 + 1.46658I
u = 0.922794 − 0.925907I
10.83490 + 0.43343I −6.08489 − 1.46658I
u = −0.916621 + 0.942227I
13.36070 − 3.37331I −2.23945 + 2.35871I
u = −0.916621 − 0.942227I
13.36070 + 3.37331I −2.23945 − 2.35871I
u = 0.906845 + 0.956007I
10.73640 + 7.16764I −6.31746 − 6.03607I
u = 0.906845 − 0.956007I
10.73640 − 7.16764I −6.31746 + 6.03607I
u = −0.898590 + 0.970044I
2.02326 − 9.39889I −8.16467 + 4.89860I
u = −0.898590 − 0.970044I
2.02326 + 9.39889I −8.16467 − 4.89860I
u = −0.605156
−9.60647 −7.91280
u = −0.191210 + 0.569318I
−0.320623 − 0.807047I −7.76798 + 8.33007I
u = −0.191210 − 0.569318I
−0.320623 + 0.807047I −7.76798 − 8.33007I
u = 0.425468
−1.23780 −7.36100
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
u
28
+ 5u
27
+ ··· + 2u + 1
c
2
, c
8
u
28
− u
27
+ ··· − u
2
− 1
c
3
, c
4
, c
5
c
11
, c
12
u
28
+ u
27
+ ··· − 4u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
y
28
+ 37y
27
+ ··· − 34y + 1
c
2
, c
8
y
28
+ 5y
27
+ ··· + 2y + 1
c
3
, c
4
, c
5
c
11
, c
12
y
28
− 35y
27
+ ··· + 2y + 1
7
