11a
188
(K11a
188
)
A knot diagram
1
Linearized knot diagam
7 1 8 11 10 2 3 4 6 5 9
Solving Sequence
6,10
5 11 4 9 1 8 3 2 7
c
5
c
10
c
4
c
9
c
11
c
8
c
3
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
+ u
32
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 33 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
33
+ u
32
+ · · · − u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
u
a
1
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
8
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
3
=
−u
12
− 7u
10
− 17u
8
− 16u
6
− 4u
4
+ u
2
+ 1
−u
14
− 8u
12
− 23u
10
− 28u
8
− 14u
6
− 4u
4
+ u
2
a
2
=
−u
24
− 13u
22
+ ··· − 5u
4
+ 1
u
24
+ 14u
22
+ ··· − 30u
6
− 10u
4
a
7
=
−u
17
− 10u
15
− 39u
13
− 74u
11
− 69u
9
− 26u
7
+ 4u
5
+ 8u
3
+ u
−u
19
− 11u
17
+ ··· + 3u
3
+ u
a
7
=
−u
17
− 10u
15
− 39u
13
− 74u
11
− 69u
9
− 26u
7
+ 4u
5
+ 8u
3
+ u
−u
19
− 11u
17
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
32
− 4u
31
− 80u
30
− 76u
29
− 704u
28
− 632u
27
− 3580u
26
−
3016u
25
− 11624u
24
− 9108u
23
− 25160u
22
− 18136u
21
− 36848u
20
− 24152u
19
−
36272u
18
− 21456u
17
− 22940u
16
− 12348u
15
− 7568u
14
− 3960u
13
+ 668u
12
− 108u
11
+
1756u
10
+ 388u
9
+ 672u
8
+ 200u
7
+ 28u
6
+ 44u
5
− 28u
4
+ 32u
3
− 8u
2
+ 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
+ u
32
+ ··· + u + 1
c
2
u
33
+ 19u
32
+ ··· − 3u − 1
c
3
, c
7
, c
8
u
33
− u
32
+ ··· + u + 5
c
4
, c
5
, c
9
c
10
u
33
− u
32
+ ··· − u + 1
c
11
u
33
− 11u
32
+ ··· + 825u − 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
+ 19y
32
+ ··· − 3y −1
c
2
y
33
− 9y
32
+ ··· − 15y −1
c
3
, c
7
, c
8
y
33
− 37y
32
+ ··· + 281y −25
c
4
, c
5
, c
9
c
10
y
33
+ 39y
32
+ ··· − 3y −1
c
11
y
33
− 21y
32
+ ··· + 34353y −34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.432708 + 0.835688I
−10.12330 + 1.05032I −7.28000 + 0.76825I
u = −0.432708 − 0.835688I
−10.12330 − 1.05032I −7.28000 − 0.76825I
u = −0.467680 + 0.807931I
−9.85167 − 8.36620I −6.60862 + 7.12105I
u = −0.467680 − 0.807931I
−9.85167 + 8.36620I −6.60862 − 7.12105I
u = 0.441389 + 0.806737I
−6.24327 + 3.55068I −3.65965 − 4.08940I
u = 0.441389 − 0.806737I
−6.24327 − 3.55068I −3.65965 + 4.08940I
u = 0.410896 + 0.632341I
−1.74331 + 5.24520I −3.08967 − 9.50750I
u = 0.410896 − 0.632341I
−1.74331 − 5.24520I −3.08967 + 9.50750I
u = 0.189812 + 0.728281I
−3.26709 − 0.39865I −8.78755 − 0.39915I
u = 0.189812 − 0.728281I
−3.26709 + 0.39865I −8.78755 + 0.39915I
u = −0.643564 + 0.026463I
−7.51632 + 4.64153I −2.88542 − 3.11188I
u = −0.643564 − 0.026463I
−7.51632 − 4.64153I −2.88542 + 3.11188I
u = −0.333302 + 0.543113I
0.01425 − 1.43543I 1.18967 + 5.27444I
u = −0.333302 − 0.543113I
0.01425 + 1.43543I 1.18967 − 5.27444I
u = 0.620531
−3.83643 0.489420
u = −0.347286 + 0.367281I
0.489336 − 1.105190I 3.80448 + 5.83190I
u = −0.347286 − 0.367281I
0.489336 + 1.105190I 3.80448 − 5.83190I
u = 0.445942 + 0.189934I
−0.50516 − 2.21066I 1.15388 + 3.33162I
u = 0.445942 − 0.189934I
−0.50516 + 2.21066I 1.15388 − 3.33162I
u = −0.02425 + 1.52826I
−5.83685 − 2.02148I 0
u = −0.02425 − 1.52826I
−5.83685 + 2.02148I 0
u = −0.07256 + 1.57034I
−7.21966 − 2.79655I 0
u = −0.07256 − 1.57034I
−7.21966 + 2.79655I 0
u = 0.10256 + 1.58115I
−9.24914 + 7.07591I 0
u = 0.10256 − 1.58115I
−9.24914 − 7.07591I 0
u = 0.04854 + 1.61236I
−11.31290 + 0.47869I 0
u = 0.04854 − 1.61236I
−11.31290 − 0.47869I 0
u = 0.12471 + 1.64061I
−14.6375 + 5.7063I 0
u = 0.12471 − 1.64061I
−14.6375 − 5.7063I 0
u = −0.13328 + 1.64240I
−18.2479 − 10.6589I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13328 − 1.64240I
−18.2479 + 10.6589I 0
u = −0.11947 + 1.64926I
−18.6687 − 1.0564I 0
u = −0.11947 − 1.64926I
−18.6687 + 1.0564I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
+ u
32
+ ··· + u + 1
c
2
u
33
+ 19u
32
+ ··· − 3u − 1
c
3
, c
7
, c
8
u
33
− u
32
+ ··· + u + 5
c
4
, c
5
, c
9
c
10
u
33
− u
32
+ ··· − u + 1
c
11
u
33
− 11u
32
+ ··· + 825u − 187
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
+ 19y
32
+ ··· − 3y −1
c
2
y
33
− 9y
32
+ ··· − 15y −1
c
3
, c
7
, c
8
y
33
− 37y
32
+ ··· + 281y −25
c
4
, c
5
, c
9
c
10
y
33
+ 39y
32
+ ··· − 3y −1
c
11
y
33
− 21y
32
+ ··· + 34353y −34969
8
