12a
1029
(K12a
1029
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 2 3 1 12 5 6 9
Solving Sequence
6,12
11 5 10 4 9 1 2 7 8 3
c
11
c
5
c
10
c
4
c
9
c
12
c
1
c
6
c
8
c
3
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
40
+ u
39
+ ··· − 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 40 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
40
+ u
39
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
u
3
− 2u
u
5
− 3u
3
+ u
a
9
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
2
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 71u
10
− 40u
8
+ 26u
6
− 12u
4
+ u
2
a
7
=
−u
33
+ 18u
31
+ ··· + 8u
3
− u
−u
35
+ 19u
33
+ ··· − u
3
+ u
a
8
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
−u
12
+ 6u
10
− 12u
8
+ 8u
6
− u
4
+ 2u
2
a
3
=
u
29
− 16u
27
+ ··· − 8u
3
− u
−u
29
+ 15u
27
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
37
+ 80u
35
− 4u
34
− 716u
33
+ 76u
32
+ 3776u
31
− 640u
30
− 13020u
29
+ 3140u
28
+
30896u
27
−9940u
26
−52168u
25
+21336u
24
+65184u
23
−32132u
22
−64416u
21
+35572u
20
+
54464u
19
−31380u
18
−39892u
17
+23748u
16
+24224u
15
−15004u
14
−12824u
13
+7500u
12
+
6132u
11
−3152u
10
−2204u
9
+1016u
8
+768u
7
−200u
6
−192u
5
−24u
4
+40u
3
+12u
2
−12u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
− 13u
39
+ ··· + 2144u − 367
c
2
, c
3
, c
6
c
7
u
40
− u
39
+ ··· − 2u
2
+ 1
c
4
, c
5
, c
10
c
11
u
40
− u
39
+ ··· − 2u
2
+ 1
c
8
, c
9
, c
12
u
40
+ 5u
39
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 23y
39
+ ··· + 70036y + 134689
c
2
, c
3
, c
6
c
7
y
40
− 47y
39
+ ··· − 4y + 1
c
4
, c
5
, c
10
c
11
y
40
− 43y
39
+ ··· − 4y + 1
c
8
, c
9
, c
12
y
40
+ 41y
39
+ ··· − 204y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542571 + 0.651532I
−15.0860 + 7.9109I −4.88905 − 5.84084I
u = 0.542571 − 0.651532I
−15.0860 − 7.9109I −4.88905 + 5.84084I
u = −0.527459 + 0.636297I
−6.73096 − 5.71035I −3.24171 + 7.29309I
u = −0.527459 − 0.636297I
−6.73096 + 5.71035I −3.24171 − 7.29309I
u = 0.464297 + 0.668009I
−15.3188 − 3.4663I −5.54451 − 0.11860I
u = 0.464297 − 0.668009I
−15.3188 + 3.4663I −5.54451 + 0.11860I
u = −0.473418 + 0.645260I
−6.89082 + 1.37781I −3.87753 − 1.00949I
u = −0.473418 − 0.645260I
−6.89082 − 1.37781I −3.87753 + 1.00949I
u = 0.499489 + 0.625257I
−4.40181 + 2.12074I 0.59127 − 3.19182I
u = 0.499489 − 0.625257I
−4.40181 − 2.12074I 0.59127 + 3.19182I
u = −0.618622 + 0.396214I
−7.28607 − 4.58384I −1.01784 + 7.01456I
u = −0.618622 − 0.396214I
−7.28607 + 4.58384I −1.01784 − 7.01456I
u = 0.718137
−5.12638 3.48520
u = 0.572228 + 0.316761I
0.05545 + 3.04563I 2.18963 − 10.11321I
u = 0.572228 − 0.316761I
0.05545 − 3.04563I 2.18963 + 10.11321I
u = 1.40155
−3.93842 0
u = −0.528521 + 0.160054I
0.971034 − 0.396253I 8.46848 + 1.43778I
u = −0.528521 − 0.160054I
0.971034 + 0.396253I 8.46848 − 1.43778I
u = −0.201519 + 0.501257I
−8.55103 + 1.48154I −5.89219 − 0.00172I
u = −0.201519 − 0.501257I
−8.55103 − 1.48154I −5.89219 + 0.00172I
u = −1.46893
4.21738 0
u = −1.48557 + 0.20651I
−8.98600 + 0.32573I 0
u = −1.48557 − 0.20651I
−8.98600 − 0.32573I 0
u = 1.49641 + 0.19308I
−0.46594 + 1.62239I 0
u = 1.49641 − 0.19308I
−0.46594 − 1.62239I 0
u = −1.51559 + 0.18786I
2.21863 − 5.03906I 0
u = −1.51559 − 0.18786I
2.21863 + 5.03906I 0
u = 1.53784 + 0.04515I
7.95920 + 1.14176I 0
u = 1.53784 − 0.04515I
7.95920 − 1.14176I 0
u = 1.52750 + 0.19715I
0.03564 + 8.72849I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52750 − 0.19715I
0.03564 − 8.72849I 0
u = −1.54376 + 0.07625I
7.16214 − 4.39597I 0
u = −1.54376 − 0.07625I
7.16214 + 4.39597I 0
u = −1.53396 + 0.20587I
−8.24623 − 11.03140I 0
u = −1.53396 − 0.20587I
−8.24623 + 11.03140I 0
u = 1.55491 + 0.10083I
0.00334 + 6.33230I 0
u = 1.55491 − 0.10083I
0.00334 − 6.33230I 0
u = −1.56390
2.49097 0
u = 0.189740 + 0.365299I
−1.060900 − 0.590018I −5.58523 + 1.45123I
u = 0.189740 − 0.365299I
−1.060900 + 0.590018I −5.58523 − 1.45123I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
40
− 13u
39
+ ··· + 2144u − 367
c
2
, c
3
, c
6
c
7
u
40
− u
39
+ ··· − 2u
2
+ 1
c
4
, c
5
, c
10
c
11
u
40
− u
39
+ ··· − 2u
2
+ 1
c
8
, c
9
, c
12
u
40
+ 5u
39
+ ··· − 8u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
40
− 23y
39
+ ··· + 70036y + 134689
c
2
, c
3
, c
6
c
7
y
40
− 47y
39
+ ··· − 4y + 1
c
4
, c
5
, c
10
c
11
y
40
− 43y
39
+ ··· − 4y + 1
c
8
, c
9
, c
12
y
40
+ 41y
39
+ ··· − 204y + 1
8
