11a
166
(K11a
166
)
A knot diagram
1
Linearized knot diagam
5 1 9 8 2 11 10 4 3 7 6
Solving Sequence
2,6
5 1 3 11 7 10 8 4 9
c
5
c
1
c
2
c
11
c
6
c
10
c
7
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
+ u
28
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
+ u
28
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
12
− 3u
10
+ 3u
8
+ 2u
6
− 4u
4
+ u
2
+ 1
−u
12
+ 4u
10
− 6u
8
+ 2u
6
+ 3u
4
− 2u
2
a
4
=
−u
26
+ 7u
24
+ ··· + u
2
+ 1
u
26
− 8u
24
+ ··· − 2u
4
− u
2
a
9
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− u
9
+ 2u
7
+ 2u
3
− u
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− 3u
9
+ 10u
7
− 8u
5
+ u
3
+ u
a
9
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− u
9
+ 2u
7
+ 2u
3
− u
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− 3u
9
+ 10u
7
− 8u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
+ 36u
26
+ 4u
25
− 148u
24
− 32u
23
+ 340u
22
+ 116u
21
−
420u
20
− 228u
19
+ 116u
18
+ 220u
17
+ 444u
16
+ 16u
15
− 652u
14
− 284u
13
+ 236u
12
+
268u
11
+ 244u
10
− 20u
9
− 260u
8
− 116u
7
+ 36u
6
+ 60u
5
+ 44u
4
+ 4u
3
− 12u
2
− 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
29
+ u
28
+ ··· + u + 1
c
2
u
29
+ 17u
28
+ ··· − u + 1
c
3
, c
4
, c
8
c
9
u
29
+ u
28
+ ··· + 3u + 1
c
6
, c
7
, c
10
c
11
u
29
+ 3u
28
+ ··· + 13u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
29
− 17y
28
+ ··· − y −1
c
2
y
29
− 9y
28
+ ··· + 15y −1
c
3
, c
4
, c
8
c
9
y
29
+ 31y
28
+ ··· − y −1
c
6
, c
7
, c
10
c
11
y
29
+ 35y
28
+ ··· + 19y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.044216 + 0.891256I
−1.19736 − 5.41362I −1.89283 + 2.85739I
u = −0.044216 − 0.891256I
−1.19736 + 5.41362I −1.89283 − 2.85739I
u = 0.014032 + 0.891951I
−7.81267 + 2.24104I −5.36878 − 2.98057I
u = 0.014032 − 0.891951I
−7.81267 − 2.24104I −5.36878 + 2.98057I
u = −0.734005 + 0.485496I
7.86536 + 2.02395I 2.95308 − 3.87773I
u = −0.734005 − 0.485496I
7.86536 − 2.02395I 2.95308 + 3.87773I
u = −1.070720 + 0.330612I
−3.23942 + 1.60334I −9.34804 − 0.46623I
u = −1.070720 − 0.330612I
−3.23942 − 1.60334I −9.34804 + 0.46623I
u = 1.107090 + 0.219678I
2.42526 + 0.35195I −5.70450 + 0.24978I
u = 1.107090 − 0.219678I
2.42526 − 0.35195I −5.70450 − 0.24978I
u = 1.062230 + 0.417656I
−2.59554 − 4.95109I −6.08826 + 8.60241I
u = 1.062230 − 0.417656I
−2.59554 + 4.95109I −6.08826 − 8.60241I
u = −1.048690 + 0.483136I
4.31921 + 7.00744I −2.00654 − 7.01565I
u = −1.048690 − 0.483136I
4.31921 − 7.00744I −2.00654 + 7.01565I
u = 0.752202 + 0.327002I
0.76241 − 1.57601I 1.98704 + 6.02961I
u = 0.752202 − 0.327002I
0.76241 + 1.57601I 1.98704 − 6.02961I
u = −0.816521
−1.09235 −10.5770
u = −0.294384 + 0.610910I
6.42555 − 2.74708I 1.52354 + 2.70649I
u = −0.294384 − 0.610910I
6.42555 + 2.74708I 1.52354 − 2.70649I
u = 1.266100 + 0.442869I
−5.20867 + 0.71370I −5.45234 + 0.15330I
u = 1.266100 − 0.442869I
−5.20867 − 0.71370I −5.45234 − 0.15330I
u = −1.262540 + 0.461126I
−11.70220 + 2.55791I −8.74471 − 0.17899I
u = −1.262540 − 0.461126I
−11.70220 − 2.55791I −8.74471 + 0.17899I
u = −1.251660 + 0.491043I
−4.85401 + 10.36710I −4.91919 − 5.83597I
u = −1.251660 − 0.491043I
−4.85401 − 10.36710I −4.91919 + 5.83597I
u = 1.257970 + 0.476305I
−11.59010 − 7.12014I −8.39556 + 5.98372I
u = 1.257970 − 0.476305I
−11.59010 + 7.12014I −8.39556 − 5.98372I
u = 0.154862 + 0.499096I
−0.193043 + 1.259700I −2.25459 − 5.57928I
u = 0.154862 − 0.499096I
−0.193043 − 1.259700I −2.25459 + 5.57928I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
29
+ u
28
+ ··· + u + 1
c
2
u
29
+ 17u
28
+ ··· − u + 1
c
3
, c
4
, c
8
c
9
u
29
+ u
28
+ ··· + 3u + 1
c
6
, c
7
, c
10
c
11
u
29
+ 3u
28
+ ··· + 13u + 3
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
29
− 17y
28
+ ··· − y −1
c
2
y
29
− 9y
28
+ ··· + 15y −1
c
3
, c
4
, c
8
c
9
y
29
+ 31y
28
+ ··· − y −1
c
6
, c
7
, c
10
c
11
y
29
+ 35y
28
+ ··· + 19y −9
7
