12a
0717
(K12a
0717
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 1 4 5 7 6
Solving Sequence
7,11
12 6 1 5 10 4 9 3 2 8
c
11
c
6
c
12
c
5
c
10
c
4
c
9
c
3
c
1
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
+ u
43
+ ··· + 3u
2
− 1i
* 1 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
= hu
44
+ u
43
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
6
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
−u
3
− 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
9
=
u
12
+ 5u
10
+ 9u
8
+ 4u
6
− 6u
4
− 5u
2
+ 1
−u
12
− 4u
10
− 6u
8
− 2u
6
+ 3u
4
+ 2u
2
a
3
=
−u
15
− 6u
13
− 14u
11
− 12u
9
+ 6u
7
+ 16u
5
+ 4u
3
− 4u
u
15
+ 5u
13
+ 10u
11
+ 7u
9
− 4u
7
− 8u
5
− 2u
3
+ u
a
2
=
u
34
+ 13u
32
+ ··· − 3u
2
+ 1
−u
34
− 12u
32
+ ··· − 12u
4
− u
2
a
8
=
−u
18
− 7u
16
− 20u
14
− 25u
12
− u
10
+ 31u
8
+ 24u
6
− 6u
4
− 9u
2
+ 1
u
20
+ 8u
18
+ 26u
16
+ 40u
14
+ 17u
12
− 32u
10
− 42u
8
− 6u
6
+ 11u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
42
+ 4u
41
+ ··· + 16u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 19u
43
+ ··· + 6u + 1
c
2
, c
7
u
44
+ u
43
+ ··· + 3u
2
− 1
c
3
, c
4
, c
5
c
9
, c
10
u
44
− u
43
+ ··· − 10u − 1
c
6
, c
11
, c
12
u
44
+ u
43
+ ··· + 3u
2
− 1
c
8
u
44
+ 3u
43
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 13y
43
+ ··· + 22y + 1
c
2
, c
7
y
44
− 19y
43
+ ··· − 6y + 1
c
3
, c
4
, c
5
c
9
, c
10
y
44
− 59y
43
+ ··· − 54y + 1
c
6
, c
11
, c
12
y
44
+ 33y
43
+ ··· − 6y + 1
c
8
y
44
− 7y
43
+ ··· − 82y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.082710 + 1.034130I
−1.54661 + 2.05611I 8.37488 − 3.95223I
u = 0.082710 − 1.034130I
−1.54661 − 2.05611I 8.37488 + 3.95223I
u = 0.936863 + 0.009278I
16.2934 + 1.8100I 14.1723 − 0.1493I
u = 0.936863 − 0.009278I
16.2934 − 1.8100I 14.1723 + 0.1493I
u = −0.935926 + 0.016671I
14.5097 − 7.3192I 11.79267 + 4.65141I
u = −0.935926 − 0.016671I
14.5097 + 7.3192I 11.79267 − 4.65141I
u = −0.922774
10.3646 8.49180
u = 0.334170 + 1.145250I
0.99109 − 2.19513I 8.38399 + 2.00652I
u = 0.334170 − 1.145250I
0.99109 + 2.19513I 8.38399 − 2.00652I
u = 0.111285 + 1.222780I
−3.02800 + 1.82177I 4.52707 − 4.00785I
u = 0.111285 − 1.222780I
−3.02800 − 1.82177I 4.52707 + 4.00785I
u = −0.332008 + 1.184600I
2.37614 − 2.74113I 10.71959 + 3.57074I
u = −0.332008 − 1.184600I
2.37614 + 2.74113I 10.71959 − 3.57074I
u = 0.735559 + 0.086101I
4.16453 + 6.09152I 11.57779 − 6.23652I
u = 0.735559 − 0.086101I
4.16453 − 6.09152I 11.57779 + 6.23652I
u = −0.737441 + 0.045521I
5.81912 − 1.13182I 14.6136 + 0.8297I
u = −0.737441 − 0.045521I
5.81912 + 1.13182I 14.6136 − 0.8297I
u = 0.254973 + 1.238130I
−2.72721 + 3.14387I 2.66290 − 3.97664I
u = 0.254973 − 1.238130I
−2.72721 − 3.14387I 2.66290 + 3.97664I
u = −0.052643 + 1.271300I
−6.04499 + 0.87730I −2.26593 + 0.I
u = −0.052643 − 1.271300I
−6.04499 − 0.87730I −2.26593 + 0.I
u = −0.125668 + 1.277410I
−5.21494 − 5.74437I 0. + 7.95874I
u = −0.125668 − 1.277410I
−5.21494 + 5.74437I 0. − 7.95874I
u = −0.317064 + 1.252810I
1.82759 − 4.91922I 6.00000 + 0.I
u = −0.317064 − 1.252810I
1.82759 + 4.91922I 6.00000 + 0.I
u = 0.310157 + 1.277730I
−0.05454 + 9.83837I 0. − 8.98455I
u = 0.310157 − 1.277730I
−0.05454 − 9.83837I 0. + 8.98455I
u = −0.463937 + 1.280720I
10.59120 + 2.33116I 0
u = −0.463937 − 1.280720I
10.59120 − 2.33116I 0
u = −0.447547 + 1.289390I
6.35891 − 4.89040I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447547 − 1.289390I
6.35891 + 4.89040I 0
u = 0.461829 + 1.286920I
12.32910 + 3.17505I 0
u = 0.461829 − 1.286920I
12.32910 − 3.17505I 0
u = 0.455030 + 1.300690I
12.21970 + 6.77393I 0
u = 0.455030 − 1.300690I
12.21970 − 6.77393I 0
u = −0.451869 + 1.305610I
10.3943 − 12.2700I 0
u = −0.451869 − 1.305610I
10.3943 + 12.2700I 0
u = 0.612221
1.07090 8.97140
u = −0.406842 + 0.274492I
−0.57374 − 3.95128I 7.80963 + 8.87694I
u = −0.406842 − 0.274492I
−0.57374 + 3.95128I 7.80963 − 8.87694I
u = −0.161520 + 0.396177I
−1.30168 + 1.57408I 3.52762 − 0.39378I
u = −0.161520 − 0.396177I
−1.30168 − 1.57408I 3.52762 + 0.39378I
u = 0.405167 + 0.094355I
0.790867 + 0.101940I 13.27829 − 1.93262I
u = 0.405167 − 0.094355I
0.790867 − 0.101940I 13.27829 + 1.93262I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
44
+ 19u
43
+ ··· + 6u + 1
c
2
, c
7
u
44
+ u
43
+ ··· + 3u
2
− 1
c
3
, c
4
, c
5
c
9
, c
10
u
44
− u
43
+ ··· − 10u − 1
c
6
, c
11
, c
12
u
44
+ u
43
+ ··· + 3u
2
− 1
c
8
u
44
+ 3u
43
+ ··· − 6u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 13y
43
+ ··· + 22y + 1
c
2
, c
7
y
44
− 19y
43
+ ··· − 6y + 1
c
3
, c
4
, c
5
c
9
, c
10
y
44
− 59y
43
+ ··· − 54y + 1
c
6
, c
11
, c
12
y
44
+ 33y
43
+ ··· − 6y + 1
c
8
y
44
− 7y
43
+ ··· − 82y + 1
8
