11a
174
(K11a
174
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 11 2 3 4 5 9 7
Solving Sequence
4,10
5 9 11 6 8 3 7 1 2
c
4
c
9
c
10
c
5
c
8
c
3
c
7
c
11
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
39
− u
38
+ ··· + 2u
3
− 1i
* 1 irreducible components of dim
C
= 0, with total 39 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
39
− u
38
+ · · · + 2u
3
− 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
9
=
u
u
3
+ u
a
11
=
u
3
u
5
+ u
3
+ u
a
6
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
7
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
23
+ 6u
21
+ ··· + 6u
5
+ 2u
3
−u
23
− 7u
21
+ ··· − 3u
5
+ u
a
2
=
u
37
+ 10u
35
+ ··· + 2u
3
− u
u
38
− u
37
+ ··· + u + 1
a
2
=
u
37
+ 10u
35
+ ··· + 2u
3
− u
u
38
− u
37
+ ··· + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
37
+ 4u
36
− 44u
35
+ 40u
34
− 228u
33
+ 192u
32
− 708u
31
+ 556u
30
− 1396u
29
+
1024u
28
− 1636u
27
+ 1100u
26
− 628u
25
+ 284u
24
+ 1308u
23
− 1084u
22
+ 2424u
21
−
1760u
20
+ 1512u
19
− 1012u
18
− 320u
17
+ 300u
16
− 1080u
15
+ 804u
14
− 528u
13
+
396u
12
+ 92u
11
−44u
10
+ 132u
9
−92u
8
−16u
7
−12u
6
−36u
5
+ 8u
4
+ 4u
3
+ 4u
2
+ 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
39
− u
38
+ ··· + 2u − 1
c
2
u
39
+ 17u
38
+ ··· + 2u
2
+ 1
c
3
, c
5
, c
7
c
8
u
39
+ u
38
+ ··· + 14u − 1
c
4
, c
9
u
39
− u
38
+ ··· + 2u
3
− 1
c
10
u
39
− 23u
38
+ ··· − 2u
2
+ 1
c
11
u
39
− 3u
38
+ ··· − 14u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
39
− 17y
38
+ ··· − 2y
2
− 1
c
2
y
39
+ 11y
38
+ ··· − 4y −1
c
3
, c
5
, c
7
c
8
y
39
− 49y
38
+ ··· + 96y −1
c
4
, c
9
y
39
+ 23y
38
+ ··· + 2y
2
− 1
c
10
y
39
− 13y
38
+ ··· + 4y −1
c
11
y
39
− 5y
38
+ ··· + 64y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071922 + 0.993246I
1.71946 + 2.04419I 8.16431 − 3.89320I
u = −0.071922 − 0.993246I
1.71946 − 2.04419I 8.16431 + 3.89320I
u = 0.435411 + 0.809083I
−1.87228 − 5.10221I −1.97486 + 8.58209I
u = 0.435411 − 0.809083I
−1.87228 + 5.10221I −1.97486 − 8.58209I
u = −0.909371 + 0.016687I
10.31070 − 1.71289I 5.85984 + 0.15979I
u = −0.909371 − 0.016687I
10.31070 + 1.71289I 5.85984 − 0.15979I
u = 0.908911 + 0.030266I
8.53389 + 7.14392I 3.38402 − 4.70933I
u = 0.908911 − 0.030266I
8.53389 − 7.14392I 3.38402 + 4.70933I
u = −0.411819 + 1.010030I
0.09606 + 2.71206I 0.59234 − 4.52974I
u = −0.411819 − 1.010030I
0.09606 − 2.71206I 0.59234 + 4.52974I
u = 0.880484
4.53816 −0.00697750
u = −0.305665 + 0.802271I
0.32922 + 1.44532I 2.59215 − 4.77277I
u = −0.305665 − 0.802271I
0.32922 − 1.44532I 2.59215 + 4.77277I
u = −0.293342 + 1.133220I
3.74981 − 2.16888I 7.25820 + 2.13079I
u = −0.293342 − 1.133220I
3.74981 + 2.16888I 7.25820 − 2.13079I
u = 0.342277 + 1.124620I
5.04615 − 2.65347I 9.41633 + 3.85440I
u = 0.342277 − 1.124620I
5.04615 + 2.65347I 9.41633 − 3.85440I
u = 0.429374 + 1.097570I
4.38863 − 4.56519I 7.75323 + 4.92219I
u = 0.429374 − 1.097570I
4.38863 + 4.56519I 7.75323 − 4.92219I
u = −0.464708 + 1.087840I
2.47286 + 9.36763I 4.01171 − 9.56282I
u = −0.464708 − 1.087840I
2.47286 − 9.36763I 4.01171 + 9.56282I
u = 0.415674 + 0.642054I
−2.32655 + 1.37512I −4.12538 − 0.53412I
u = 0.415674 − 0.642054I
−2.32655 − 1.37512I −4.12538 + 0.53412I
u = −0.632416 + 0.199765I
−0.01291 − 5.16822I 0.66391 + 6.04707I
u = −0.632416 − 0.199765I
−0.01291 + 5.16822I 0.66391 − 6.04707I
u = 0.467898 + 1.254570I
8.33752 − 4.79855I 3.23494 + 3.06059I
u = 0.467898 − 1.254570I
8.33752 + 4.79855I 3.23494 − 3.06059I
u = 0.454344 + 1.275250I
12.54280 + 2.32319I 6.85027 − 1.71176I
u = 0.454344 − 1.275250I
12.54280 − 2.32319I 6.85027 + 1.71176I
u = 0.488216 + 1.263380I
12.2898 − 12.1343I 6.37996 + 7.62883I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.488216 − 1.263380I
12.2898 + 12.1343I 6.37996 − 7.62883I
u = −0.462613 + 1.273220I
14.2633 + 3.1512I 9.14562 − 2.87617I
u = −0.462613 − 1.273220I
14.2633 − 3.1512I 9.14562 + 2.87617I
u = −0.481297 + 1.266520I
14.1233 + 6.6701I 8.91783 − 3.16828I
u = −0.481297 − 1.266520I
14.1233 − 6.6701I 8.91783 + 3.16828I
u = 0.599274 + 0.105705I
1.67499 + 0.65150I 4.60786 − 0.90927I
u = 0.599274 − 0.105705I
1.67499 − 0.65150I 4.60786 + 0.90927I
u = −0.448469 + 0.341157I
−1.70724 + 0.92516I −3.72881 − 0.98147I
u = −0.448469 − 0.341157I
−1.70724 − 0.92516I −3.72881 + 0.98147I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
39
− u
38
+ ··· + 2u − 1
c
2
u
39
+ 17u
38
+ ··· + 2u
2
+ 1
c
3
, c
5
, c
7
c
8
u
39
+ u
38
+ ··· + 14u − 1
c
4
, c
9
u
39
− u
38
+ ··· + 2u
3
− 1
c
10
u
39
− 23u
38
+ ··· − 2u
2
+ 1
c
11
u
39
− 3u
38
+ ··· − 14u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
39
− 17y
38
+ ··· − 2y
2
− 1
c
2
y
39
+ 11y
38
+ ··· − 4y −1
c
3
, c
5
, c
7
c
8
y
39
− 49y
38
+ ··· + 96y −1
c
4
, c
9
y
39
+ 23y
38
+ ··· + 2y
2
− 1
c
10
y
39
− 13y
38
+ ··· + 4y −1
c
11
y
39
− 5y
38
+ ··· + 64y −9
8
