11a
356
(K11a
356
)
A knot diagram
1
Linearized knot diagam
7 9 8 1 11 10 2 3 4 5 6
Solving Sequence
2,9
3 8 4 10 7 1 5 6 11
c
2
c
8
c
3
c
9
c
7
c
1
c
4
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
39
− u
38
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 39 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
39
− u
38
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
6
− 2u
4
− u
2
a
5
=
−u
16
− 7u
14
− 19u
12
− 22u
10
− 3u
8
+ 14u
6
+ 6u
4
− 2u
2
+ 1
−u
16
− 6u
14
− 14u
12
− 14u
10
− 2u
8
+ 6u
6
+ 4u
4
+ 2u
2
a
6
=
−u
15
− 6u
13
− 14u
11
− 14u
9
− 2u
7
+ 6u
5
+ 4u
3
+ 2u
−u
17
− 7u
15
− 19u
13
− 22u
11
− 3u
9
+ 14u
7
+ 6u
5
− 2u
3
+ u
a
11
=
u
38
+ 15u
36
+ ··· − 4u
2
+ 1
u
38
− u
37
+ ··· + 3u + 1
a
11
=
u
38
+ 15u
36
+ ··· − 4u
2
+ 1
u
38
− u
37
+ ··· + 3u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
37
+ 4u
36
− 60u
35
+ 56u
34
− 408u
33
+ 352u
32
− 1632u
31
+ 1284u
30
− 4136u
29
+
2900u
28
− 6488u
27
+ 3844u
26
− 4940u
25
+ 1868u
24
+ 2188u
23
− 2704u
22
+ 9160u
21
−
5360u
20
+7744u
19
−2920u
18
−468u
17
+1192u
16
−5148u
15
+2160u
14
−2700u
13
+768u
12
+
540u
11
− 24u
10
+ 756u
9
− 96u
8
+ 112u
7
− 140u
6
+ 12u
5
− 68u
4
+ 16u
3
− 4u
2
+ 4u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
39
+ u
38
+ ··· − 26u − 5
c
2
, c
3
, c
8
u
39
− u
38
+ ··· − 2u − 1
c
4
, c
6
u
39
+ 3u
38
+ ··· − 4u − 1
c
5
, c
10
, c
11
u
39
− u
38
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
39
− 37y
38
+ ··· + 276y −25
c
2
, c
3
, c
8
y
39
+ 31y
38
+ ··· + 12y −1
c
4
, c
6
y
39
+ 19y
38
+ ··· + 12y −1
c
5
, c
10
, c
11
y
39
− 33y
38
+ ··· + 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.184373 + 1.113280I
−1.87456 − 2.88869I −14.2614 + 3.8496I
u = 0.184373 − 1.113280I
−1.87456 + 2.88869I −14.2614 − 3.8496I
u = −0.870700
−12.5889 −20.2660
u = 0.859957 + 0.065950I
−8.34775 − 7.83020I −17.2097 + 5.1907I
u = 0.859957 − 0.065950I
−8.34775 + 7.83020I −17.2097 − 5.1907I
u = −0.840218 + 0.059790I
−3.40399 + 3.95494I −12.75445 − 3.98902I
u = −0.840218 − 0.059790I
−3.40399 − 3.95494I −12.75445 + 3.98902I
u = 0.814161 + 0.022766I
−5.70205 − 0.09754I −16.2351 − 0.6362I
u = 0.814161 − 0.022766I
−5.70205 + 0.09754I −16.2351 + 0.6362I
u = −0.062866 + 1.207990I
2.96167 + 1.25323I −8.48961 − 5.22711I
u = −0.062866 − 1.207990I
2.96167 − 1.25323I −8.48961 + 5.22711I
u = −0.383266 + 1.213820I
0.146925 + 0.444639I −9.41731 + 0.59689I
u = −0.383266 − 1.213820I
0.146925 − 0.444639I −9.41731 − 0.59689I
u = 0.407915 + 1.208990I
−4.82928 + 3.28352I −14.1252 − 1.7536I
u = 0.407915 − 1.208990I
−4.82928 − 3.28352I −14.1252 + 1.7536I
u = 0.366310 + 1.256220I
−1.87897 − 4.14984I −12.49254 + 4.42068I
u = 0.366310 − 1.256220I
−1.87897 + 4.14984I −12.49254 − 4.42068I
u = −0.407478 + 1.273380I
−8.63550 + 4.57833I −16.5882 − 3.2538I
u = −0.407478 − 1.273380I
−8.63550 − 4.57833I −16.5882 + 3.2538I
u = 0.362109 + 1.293340I
−1.59442 − 4.32741I −11.59101 + 2.45124I
u = 0.362109 − 1.293340I
−1.59442 + 4.32741I −11.59101 − 2.45124I
u = −0.091582 + 1.340430I
3.95422 − 0.66385I −6.81341 + 0.I
u = −0.091582 − 1.340430I
3.95422 + 0.66385I −6.81341 + 0.I
u = 0.126262 + 1.340800I
7.43974 − 3.24701I −3.23245 + 3.90104I
u = 0.126262 − 1.340800I
7.43974 + 3.24701I −3.23245 − 3.90104I
u = −0.153420 + 1.344440I
3.18314 + 7.20185I −8.30980 − 6.60092I
u = −0.153420 − 1.344440I
3.18314 − 7.20185I −8.30980 + 6.60092I
u = −0.378228 + 1.313410I
0.88961 + 8.33524I −8.46162 − 6.44444I
u = −0.378228 − 1.313410I
0.88961 − 8.33524I −8.46162 + 6.44444I
u = 0.389378 + 1.319710I
−4.01328 − 12.31500I −12.9972 + 7.6973I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389378 − 1.319710I
−4.01328 + 12.31500I −12.9972 − 7.6973I
u = −0.492543 + 0.335168I
−2.04249 + 4.99221I −14.0623 − 7.3168I
u = −0.492543 − 0.335168I
−2.04249 − 4.99221I −14.0623 + 7.3168I
u = 0.582761
−5.05980 −19.3550
u = −0.317690 + 0.458841I
−1.46078 − 1.97639I −11.86139 − 0.45941I
u = −0.317690 − 0.458841I
−1.46078 + 1.97639I −11.86139 + 0.45941I
u = 0.409039 + 0.362185I
2.19576 − 1.42469I −7.96461 + 5.04290I
u = 0.409039 − 0.362185I
2.19576 + 1.42469I −7.96461 − 5.04290I
u = −0.296485
−0.479709 −20.6440
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
39
+ u
38
+ ··· − 26u − 5
c
2
, c
3
, c
8
u
39
− u
38
+ ··· − 2u − 1
c
4
, c
6
u
39
+ 3u
38
+ ··· − 4u − 1
c
5
, c
10
, c
11
u
39
− u
38
+ ··· − 2u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
39
− 37y
38
+ ··· + 276y −25
c
2
, c
3
, c
8
y
39
+ 31y
38
+ ··· + 12y −1
c
4
, c
6
y
39
+ 19y
38
+ ··· + 12y −1
c
5
, c
10
, c
11
y
39
− 33y
38
+ ··· + 12y −1
8
