11a
336
(K11a
336
)
A knot diagram
1
Linearized knot diagam
8 7 1 10 11 9 2 3 4 5 6
Solving Sequence
3,7
2 8 9 1 4 10 6 11 5
c
2
c
7
c
8
c
1
c
3
c
9
c
6
c
11
c
5
c
4
, c
10
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
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
10
=
u
17
+ 8u
15
+ 25u
13
+ 36u
11
+ 19u
9
− 4u
7
− 2u
5
+ 2u
3
− 3u
−u
19
− 9u
17
− 32u
15
− 55u
13
− 43u
11
− 9u
9
− 4u
5
+ u
3
+ u
a
6
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
11
=
−u
18
− 9u
16
− 32u
14
− 55u
12
− 43u
10
− 9u
8
− 4u
4
+ u
2
+ 1
u
18
+ 8u
16
+ 25u
14
+ 36u
12
+ 19u
10
− 4u
8
− 2u
6
+ 2u
4
− 3u
2
a
5
=
u
28
+ 13u
26
+ ··· − 5u
2
+ 1
−u
28
− u
27
+ ··· + 2u − 1
a
5
=
u
28
+ 13u
26
+ ··· − 5u
2
+ 1
−u
28
− u
27
+ ··· + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
27
+ 4u
26
+ 52u
25
+ 48u
24
+ 292u
23
+ 244u
22
+ 916u
21
+
668u
20
+ 1728u
19
+ 1020u
18
+ 1952u
17
+ 764u
16
+ 1228u
15
+ 84u
14
+ 396u
13
−188u
12
+
168u
11
− 48u
10
+ 136u
9
− 56u
8
+ 4u
7
− 80u
6
− 20u
5
− 8u
4
− 12u
2
− 12u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
29
− u
28
+ ··· − u − 1
c
3
, c
6
u
29
− 5u
28
+ ··· − 11u + 11
c
4
, c
5
, c
9
c
10
, c
11
u
29
− u
28
+ ··· − u − 1
c
8
u
29
+ u
28
+ ··· − 23u − 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
29
+ 27y
28
+ ··· + 11y −1
c
3
, c
6
y
29
+ 19y
28
+ ··· + 2035y −121
c
4
, c
5
, c
9
c
10
, c
11
y
29
− 37y
28
+ ··· + 11y −1
c
8
y
29
+ 7y
28
+ ··· + 451y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.701361 + 0.346462I
−9.80284 + 6.46387I −15.7632 − 5.4182I
u = −0.701361 − 0.346462I
−9.80284 − 6.46387I −15.7632 + 5.4182I
u = 0.245640 + 1.201630I
−10.19110 − 3.45786I −15.1424 + 3.3089I
u = 0.245640 − 1.201630I
−10.19110 + 3.45786I −15.1424 − 3.3089I
u = −0.171885 + 1.229330I
−0.67138 + 2.87906I −14.7089 − 4.2830I
u = −0.171885 − 1.229330I
−0.67138 − 2.87906I −14.7089 + 4.2830I
u = −0.480158 + 0.582021I
−8.87707 − 2.41616I −13.78310 − 0.38790I
u = −0.480158 − 0.582021I
−8.87707 + 2.41616I −13.78310 + 0.38790I
u = 0.650708 + 0.354585I
−0.79370 − 4.83148I −14.1571 + 7.3194I
u = 0.650708 − 0.354585I
−0.79370 + 4.83148I −14.1571 − 7.3194I
u = 0.054580 + 1.286800I
3.32000 − 1.28636I −8.05258 + 4.98094I
u = 0.054580 − 1.286800I
3.32000 + 1.28636I −8.05258 − 4.98094I
u = 0.696889
−13.8494 −19.9990
u = −0.577927 + 0.388990I
2.04166 + 1.81994I −7.79852 − 4.33424I
u = −0.577927 − 0.388990I
2.04166 − 1.81994I −7.79852 + 4.33424I
u = 0.480305 + 0.469181I
−0.185293 + 1.088380I −12.37698 − 0.82894I
u = 0.480305 − 0.469181I
−0.185293 − 1.088380I −12.37698 + 0.82894I
u = −0.612238
−4.36553 −20.8170
u = 0.18636 + 1.44283I
5.85747 − 1.38485I −8.54073 − 1.09314I
u = 0.18636 − 1.44283I
5.85747 + 1.38485I −8.54073 + 1.09314I
u = −0.22007 + 1.44335I
7.91796 + 4.76802I −4.71364 − 3.85103I
u = −0.22007 − 1.44335I
7.91796 − 4.76802I −4.71364 + 3.85103I
u = 0.24692 + 1.44056I
4.97107 − 8.11618I −10.00612 + 6.88913I
u = 0.24692 − 1.44056I
4.97107 + 8.11618I −10.00612 − 6.88913I
u = −0.26820 + 1.44214I
−4.06372 + 9.99800I −11.72647 − 5.43335I
u = −0.26820 − 1.44214I
−4.06372 − 9.99800I −11.72647 + 5.43335I
u = −0.14976 + 1.46219I
−2.36690 − 0.23982I −10.11006 − 0.14819I
u = −0.14976 − 1.46219I
−2.36690 + 0.23982I −10.11006 + 0.14819I
u = 0.325062
−0.510553 −19.4250
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
29
− u
28
+ ··· − u − 1
c
3
, c
6
u
29
− 5u
28
+ ··· − 11u + 11
c
4
, c
5
, c
9
c
10
, c
11
u
29
− u
28
+ ··· − u − 1
c
8
u
29
+ u
28
+ ··· − 23u − 13
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
29
+ 27y
28
+ ··· + 11y −1
c
3
, c
6
y
29
+ 19y
28
+ ··· + 2035y −121
c
4
, c
5
, c
9
c
10
, c
11
y
29
− 37y
28
+ ··· + 11y −1
c
8
y
29
+ 7y
28
+ ··· + 451y −169
7
