11a
184
(K11a
184
)
A knot diagram
1
Linearized knot diagam
7 1 11 9 10 2 3 4 5 8 6
Solving Sequence
1,7
2 3 8 6 11 4 9 10 5
c
1
c
2
c
7
c
6
c
11
c
3
c
8
c
10
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
43
− u
42
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 43 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
43
− u
42
+ · · · − u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
8
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
6
=
−u
u
3
+ u
a
11
=
u
4
+ u
2
+ 1
−u
6
− 2u
4
− u
2
a
4
=
−u
12
− 3u
10
− 5u
8
− 4u
6
− 2u
4
+ u
2
+ 1
u
14
+ 4u
12
+ 7u
10
+ 6u
8
+ 2u
6
− u
2
a
9
=
−u
31
− 8u
29
+ ··· − 12u
7
− 4u
5
u
33
+ 9u
31
+ ··· + 4u
7
+ u
a
10
=
u
16
+ 5u
14
+ 11u
12
+ 12u
10
+ 5u
8
− 2u
6
− 2u
4
+ 1
−u
16
− 4u
14
− 8u
12
− 8u
10
− 4u
8
a
5
=
−u
35
− 10u
33
+ ··· − u
3
− 2u
u
35
+ 9u
33
+ ··· + u
3
+ u
a
5
=
−u
35
− 10u
33
+ ··· − u
3
− 2u
u
35
+ 9u
33
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
41
+4u
40
−44u
39
+44u
38
−236u
37
+240u
36
−796u
35
+832u
34
−1848u
33
+2004u
32
−
3040u
31
+3444u
30
−3480u
29
+4132u
28
−2468u
27
+3044u
26
−428u
25
+452u
24
+1264u
23
−
1860u
22
+ 1600u
21
− 2240u
20
+ 824u
19
− 920u
18
− 84u
17
+ 456u
16
− 464u
15
+ 772u
14
−
336u
13
+332u
12
−72u
11
−72u
10
+76u
9
−136u
8
+68u
7
−44u
6
+16u
5
+8u
4
−8u
3
+8u
2
−4u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
43
+ u
42
+ ··· + u
2
− 1
c
2
u
43
+ 23u
42
+ ··· + 2u − 1
c
3
u
43
− 5u
42
+ ··· − 2u + 5
c
4
, c
5
, c
8
c
9
u
43
+ u
42
+ ··· + u
2
− 1
c
7
, c
11
u
43
− u
42
+ ··· − 5u − 2
c
10
u
43
+ 11u
42
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
43
+ 23y
42
+ ··· + 2y −1
c
2
y
43
− 5y
42
+ ··· + 14y −1
c
3
y
43
+ 7y
42
+ ··· − 926y −25
c
4
, c
5
, c
8
c
9
y
43
− 49y
42
+ ··· + 2y −1
c
7
, c
11
y
43
− 33y
42
+ ··· + 125y −4
c
10
y
43
− y
42
+ ··· − 18y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.521315 + 0.837611I
1.91297 + 4.88049I 7.17506 − 8.80545I
u = 0.521315 − 0.837611I
1.91297 − 4.88049I 7.17506 + 8.80545I
u = −0.564675 + 0.846085I
9.73939 − 6.81501I 9.15243 + 6.58080I
u = −0.564675 − 0.846085I
9.73939 + 6.81501I 9.15243 − 6.58080I
u = −0.070971 + 0.949282I
−1.88710 − 1.49301I −2.49179 + 5.12316I
u = −0.070971 − 0.949282I
−1.88710 + 1.49301I −2.49179 − 5.12316I
u = 0.157033 + 1.039100I
4.88985 + 3.07247I 2.04876 − 3.22790I
u = 0.157033 − 1.039100I
4.88985 − 3.07247I 2.04876 + 3.22790I
u = −0.443218 + 0.795583I
0.18390 − 1.87415I 2.36398 + 3.86442I
u = −0.443218 − 0.795583I
0.18390 + 1.87415I 2.36398 − 3.86442I
u = −0.578652 + 0.674431I
10.22700 + 2.27386I 10.59990 + 0.05953I
u = −0.578652 − 0.674431I
10.22700 − 2.27386I 10.59990 − 0.05953I
u = 0.509969 + 0.679497I
2.36364 − 0.64965I 9.29098 + 1.48220I
u = 0.509969 − 0.679497I
2.36364 + 0.64965I 9.29098 − 1.48220I
u = 0.802703 + 0.162351I
6.46390 − 7.57490I 7.29481 + 4.51486I
u = 0.802703 − 0.162351I
6.46390 + 7.57490I 7.29481 − 4.51486I
u = −0.783539 + 0.138077I
−1.13687 + 5.20298I 4.40416 − 6.22689I
u = −0.783539 − 0.138077I
−1.13687 − 5.20298I 4.40416 + 6.22689I
u = 0.495820 + 1.104130I
6.52652 + 3.46599I 6.43711 − 3.77434I
u = 0.495820 − 1.104130I
6.52652 − 3.46599I 6.43711 + 3.77434I
u = −0.781151
2.55363 4.52390
u = 0.758021 + 0.099035I
−2.34232 − 1.57976I 0.847135 + 0.282398I
u = 0.758021 − 0.099035I
−2.34232 + 1.57976I 0.847135 − 0.282398I
u = −0.463782 + 1.145440I
−1.69075 − 3.98657I 4.72929 + 3.11894I
u = −0.463782 − 1.145440I
−1.69075 + 3.98657I 4.72929 − 3.11894I
u = −0.382526 + 1.197980I
−5.08887 + 1.28085I 0. − 2.90376I
u = −0.382526 − 1.197980I
−5.08887 − 1.28085I 0. + 2.90376I
u = 0.362492 + 1.206110I
2.33692 − 3.70518I 2.48681 + 1.54084I
u = 0.362492 − 1.206110I
2.33692 + 3.70518I 2.48681 − 1.54084I
u = 0.407336 + 1.191840I
−6.07657 + 2.44102I −3.16979 − 3.57779I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407336 − 1.191840I
−6.07657 − 2.44102I −3.16979 + 3.57779I
u = −0.448865 + 1.200600I
−0.96199 − 4.39851I 0. + 3.54146I
u = −0.448865 − 1.200600I
−0.96199 + 4.39851I 0. − 3.54146I
u = 0.490454 + 1.184460I
−5.48574 + 6.18515I −2.04828 − 3.59368I
u = 0.490454 − 1.184460I
−5.48574 − 6.18515I −2.04828 + 3.59368I
u = 0.645564 + 0.300310I
8.84662 + 0.96374I 10.02944 − 0.37589I
u = 0.645564 − 0.300310I
8.84662 − 0.96374I 10.02944 + 0.37589I
u = −0.507296 + 1.186730I
−4.20932 − 9.96665I 0. + 9.16746I
u = −0.507296 − 1.186730I
−4.20932 + 9.96665I 0. − 9.16746I
u = 0.519799 + 1.187960I
3.43954 + 12.44990I 4.17518 − 7.63100I
u = 0.519799 − 1.187960I
3.43954 − 12.44990I 4.17518 + 7.63100I
u = −0.536405 + 0.171930I
1.103730 − 0.098765I 9.44099 + 0.91027I
u = −0.536405 − 0.171930I
1.103730 + 0.098765I 9.44099 − 0.91027I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
43
+ u
42
+ ··· + u
2
− 1
c
2
u
43
+ 23u
42
+ ··· + 2u − 1
c
3
u
43
− 5u
42
+ ··· − 2u + 5
c
4
, c
5
, c
8
c
9
u
43
+ u
42
+ ··· + u
2
− 1
c
7
, c
11
u
43
− u
42
+ ··· − 5u − 2
c
10
u
43
+ 11u
42
+ ··· + 12u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
43
+ 23y
42
+ ··· + 2y −1
c
2
y
43
− 5y
42
+ ··· + 14y −1
c
3
y
43
+ 7y
42
+ ··· − 926y −25
c
4
, c
5
, c
8
c
9
y
43
− 49y
42
+ ··· + 2y −1
c
7
, c
11
y
43
− 33y
42
+ ··· + 125y −4
c
10
y
43
− y
42
+ ··· − 18y −1
8
