11a
75
(K11a
75
)
A knot diagram
1
Linearized knot diagam
6 1 7 10 2 3 4 11 5 9 8
Solving Sequence
5,9
10 11 4 8 1 7 3 2 6
c
9
c
10
c
4
c
8
c
11
c
7
c
3
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
41
+ u
40
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 41 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
41
+ u
40
+ · · · + u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
11
=
u
2
+ 1
−u
2
a
4
=
−u
u
3
+ u
a
8
=
u
4
+ u
2
+ 1
−u
4
a
1
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
7
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
10
− 2u
8
− 3u
6
− 4u
4
− u
2
a
3
=
u
15
+ 2u
13
+ 6u
11
+ 8u
9
+ 10u
7
+ 8u
5
+ 4u
3
−u
17
− 3u
15
− 7u
13
− 12u
11
− 13u
9
− 12u
7
− 6u
5
+ u
a
2
=
−u
29
− 4u
27
+ ··· + 8u
3
+ u
u
29
+ 3u
27
+ ··· − u
3
+ u
a
6
=
−u
22
− 3u
20
+ ··· + 2u
2
+ 1
u
24
+ 4u
22
+ ··· − 6u
4
− 2u
2
a
6
=
−u
22
− 3u
20
+ ··· + 2u
2
+ 1
u
24
+ 4u
22
+ ··· − 6u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
39
−4u
38
−20u
37
−20u
36
−88u
35
−84u
34
−256u
33
−240u
32
−640u
31
−572u
30
−
1280u
29
− 1108u
28
− 2208u
27
− 1808u
26
− 3192u
25
− 2484u
24
− 3956u
23
− 2856u
22
−
4076u
21
−2692u
20
−3468u
19
−1996u
18
−2228u
17
−1004u
16
−924u
15
−144u
14
+ 56u
13
+
304u
12
+ 416u
11
+ 344u
10
+ 356u
9
+ 168u
8
+ 128u
7
+ 12u
6
−20u
4
−32u
3
−12u
2
−12u −6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− u
40
+ ··· + u + 1
c
2
u
41
+ 23u
40
+ ··· − 3u − 1
c
3
, c
6
, c
7
u
41
+ u
40
+ ··· − 7u + 1
c
4
, c
9
u
41
+ u
40
+ ··· + u + 1
c
8
, c
10
, c
11
u
41
+ 11u
40
+ ··· − 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 23y
40
+ ··· − 3y −1
c
2
y
41
− 9y
40
+ ··· − 19y −1
c
3
, c
6
, c
7
y
41
− 41y
40
+ ··· − 51y −1
c
4
, c
9
y
41
+ 11y
40
+ ··· − 3y −1
c
8
, c
10
, c
11
y
41
+ 39y
40
+ ··· − 11y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273309 + 1.007330I
−6.20529 − 3.05813I −7.49814 + 3.80729I
u = −0.273309 − 1.007330I
−6.20529 + 3.05813I −7.49814 − 3.80729I
u = 0.253711 + 1.021940I
−10.01040 − 1.50035I −11.08025 − 0.35088I
u = 0.253711 − 1.021940I
−10.01040 + 1.50035I −11.08025 + 0.35088I
u = 0.289765 + 1.022350I
−9.79545 + 7.79305I −10.43974 − 6.91622I
u = 0.289765 − 1.022350I
−9.79545 − 7.79305I −10.43974 + 6.91622I
u = −0.352546 + 0.864150I
−2.13456 − 4.94858I −7.01922 + 9.44337I
u = −0.352546 − 0.864150I
−2.13456 + 4.94858I −7.01922 − 9.44337I
u = −0.132698 + 0.868731I
−3.36085 + 0.49947I −12.33273 − 0.13229I
u = −0.132698 − 0.868731I
−3.36085 − 0.49947I −12.33273 + 0.13229I
u = −0.830272 + 0.762818I
−2.92978 − 2.50596I −5.15377 + 2.93090I
u = −0.830272 − 0.762818I
−2.92978 + 2.50596I −5.15377 − 2.93090I
u = 0.842291 + 0.783314I
1.03604 − 1.75419I −1.142381 + 0.318926I
u = 0.842291 − 0.783314I
1.03604 + 1.75419I −1.142381 − 0.318926I
u = −0.858015 + 0.778364I
−2.29038 + 6.57620I −4.18692 − 3.44855I
u = −0.858015 − 0.778364I
−2.29038 − 6.57620I −4.18692 + 3.44855I
u = 0.756645 + 0.885386I
1.40338 + 2.86651I −6.38250 − 2.83312I
u = 0.756645 − 0.885386I
1.40338 − 2.86651I −6.38250 + 2.83312I
u = 0.836690 + 0.850906I
5.01543 − 2.00642I −0.12467 + 3.31909I
u = 0.836690 − 0.850906I
5.01543 + 2.00642I −0.12467 − 3.31909I
u = −0.823694 + 0.876027I
6.13950 − 2.34478I 2.43085 + 2.90580I
u = −0.823694 − 0.876027I
6.13950 + 2.34478I 2.43085 − 2.90580I
u = 0.300266 + 0.727840I
−0.31190 + 1.38897I −2.22878 − 5.19649I
u = 0.300266 − 0.727840I
−0.31190 − 1.38897I −2.22878 + 5.19649I
u = −0.810647 + 0.914894I
6.01823 − 3.75969I 2.08469 + 2.66327I
u = −0.810647 − 0.914894I
6.01823 + 3.75969I 2.08469 − 2.66327I
u = 0.807712 + 0.939287I
4.74123 + 8.14027I −0.92451 − 8.45750I
u = 0.807712 − 0.939287I
4.74123 − 8.14027I −0.92451 + 8.45750I
u = −0.766003 + 0.985130I
−3.60687 − 3.46651I −6.32048 + 2.17214I
u = −0.766003 − 0.985130I
−3.60687 + 3.46651I −6.32048 − 2.17214I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.779460 + 0.981810I
0.42502 + 7.80969I −2.24693 − 5.23664I
u = 0.779460 − 0.981810I
0.42502 − 7.80969I −2.24693 + 5.23664I
u = −0.784350 + 0.990912I
−2.94834 − 12.69200I −5.29244 + 8.24315I
u = −0.784350 − 0.990912I
−2.94834 + 12.69200I −5.29244 − 8.24315I
u = 0.675007 + 0.033462I
−6.66197 − 4.52417I −4.64346 + 3.30102I
u = 0.675007 − 0.033462I
−6.66197 + 4.52417I −4.64346 − 3.30102I
u = −0.642653
−3.07852 −1.30900
u = 0.368440 + 0.507445I
0.258138 + 1.315180I 0.82726 − 5.55607I
u = 0.368440 − 0.507445I
0.258138 − 1.315180I 0.82726 + 5.55607I
u = −0.457128 + 0.246194I
−0.38333 + 1.88364I −0.67137 − 3.86434I
u = −0.457128 − 0.246194I
−0.38333 − 1.88364I −0.67137 + 3.86434I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− u
40
+ ··· + u + 1
c
2
u
41
+ 23u
40
+ ··· − 3u − 1
c
3
, c
6
, c
7
u
41
+ u
40
+ ··· − 7u + 1
c
4
, c
9
u
41
+ u
40
+ ··· + u + 1
c
8
, c
10
, c
11
u
41
+ 11u
40
+ ··· − 3u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 23y
40
+ ··· − 3y −1
c
2
y
41
− 9y
40
+ ··· − 19y −1
c
3
, c
6
, c
7
y
41
− 41y
40
+ ··· − 51y −1
c
4
, c
9
y
41
+ 11y
40
+ ··· − 3y −1
c
8
, c
10
, c
11
y
41
+ 39y
40
+ ··· − 11y −1
8
