11a
311
(K11a
311
)
A knot diagram
1
Linearized knot diagam
7 6 1 10 9 2 3 11 5 4 8
Solving Sequence
4,11
10 5 9 6 8 1 3 2 7
c
10
c
4
c
9
c
5
c
8
c
11
c
3
c
2
c
7
c
1
, c
6
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
4
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
8
=
u
4
+ 3u
2
+ 1
−u
4
− 2u
2
a
1
=
u
8
+ 5u
6
+ 7u
4
+ 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
3
=
u
17
+ 10u
15
+ 39u
13
+ 74u
11
+ 71u
9
+ 38u
7
+ 18u
5
+ 4u
3
+ u
−u
17
− 9u
15
− 31u
13
− 50u
11
− 37u
9
− 12u
7
− 4u
5
+ u
a
2
=
u
25
+ 14u
23
+ ··· + 10u
3
+ u
−u
27
− 15u
25
+ ··· − 3u
3
+ u
a
7
=
−u
30
− 17u
28
+ ··· + 2u
2
+ 1
u
30
+ 16u
28
+ ··· − 6u
4
− 3u
2
a
7
=
−u
30
− 17u
28
+ ··· + 2u
2
+ 1
u
30
+ 16u
28
+ ··· − 6u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
38
+ 4u
37
+ ··· − 16u
2
− 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
39
+ u
38
+ ··· + 2u + 1
c
3
u
39
− 9u
38
+ ··· − 112u + 17
c
4
, c
5
, c
9
c
10
u
39
+ u
38
+ ··· + 2u + 1
c
7
u
39
− u
38
+ ··· − 2u
2
+ 1
c
8
, c
11
u
39
+ 7u
38
+ ··· + 120u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
39
+ 35y
38
+ ··· + 4y −1
c
3
y
39
+ 7y
38
+ ··· − 2076y −289
c
4
, c
5
, c
9
c
10
y
39
+ 43y
38
+ ··· + 4y −1
c
7
y
39
− y
38
+ ··· + 4y −1
c
8
, c
11
y
39
+ 23y
38
+ ··· + 3588y −289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.574160 + 0.594650I
2.26953 − 9.16193I −4.31482 + 8.21466I
u = 0.574160 − 0.594650I
2.26953 + 9.16193I −4.31482 − 8.21466I
u = −0.568267 + 0.567303I
−2.96795 + 5.55181I −9.25872 − 7.70638I
u = −0.568267 − 0.567303I
−2.96795 − 5.55181I −9.25872 + 7.70638I
u = −0.131849 + 0.785677I
6.72383 + 4.04302I 1.83134 − 4.62679I
u = −0.131849 − 0.785677I
6.72383 − 4.04302I 1.83134 + 4.62679I
u = −0.436022 + 0.604817I
4.84305 + 1.02619I −1.08808 − 3.88143I
u = −0.436022 − 0.604817I
4.84305 − 1.02619I −1.08808 + 3.88143I
u = 0.538839 + 0.511805I
−1.18645 − 1.89478I −6.62379 + 3.07678I
u = 0.538839 − 0.511805I
−1.18645 + 1.89478I −6.62379 − 3.07678I
u = 0.560794 + 0.470702I
−1.29404 − 1.89422I −7.65532 + 4.23095I
u = 0.560794 − 0.470702I
−1.29404 + 1.89422I −7.65532 − 4.23095I
u = −0.584786 + 0.399530I
−3.45995 − 1.60136I −11.19941 + 0.98974I
u = −0.584786 − 0.399530I
−3.45995 + 1.60136I −11.19941 − 0.98974I
u = 0.604755 + 0.364312I
1.59535 + 5.13986I −6.25494 − 2.11218I
u = 0.604755 − 0.364312I
1.59535 − 5.13986I −6.25494 + 2.11218I
u = 0.101809 + 0.665055I
1.37394 − 1.42753I −1.59581 + 5.78078I
u = 0.101809 − 0.665055I
1.37394 + 1.42753I −1.59581 − 5.78078I
u = 0.11689 + 1.44352I
7.31578 + 2.67288I 0
u = 0.11689 − 1.44352I
7.31578 − 2.67288I 0
u = −0.13315 + 1.47390I
2.59124 + 0.84756I 0
u = −0.13315 − 1.47390I
2.59124 − 0.84756I 0
u = −0.474394 + 0.165911I
3.63716 + 2.05070I −5.79681 − 3.19622I
u = −0.474394 − 0.165911I
3.63716 − 2.05070I −5.79681 + 3.19622I
u = 0.15150 + 1.50620I
5.20817 − 4.40207I 0
u = 0.15150 − 1.50620I
5.20817 + 4.40207I 0
u = 0.15186 + 1.53774I
5.65303 − 4.34476I 0
u = 0.15186 − 1.53774I
5.65303 + 4.34476I 0
u = −0.16892 + 1.55091I
4.08876 + 8.22597I 0
u = −0.16892 − 1.55091I
4.08876 − 8.22597I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12882 + 1.56443I
12.14090 + 3.09884I 0
u = −0.12882 − 1.56443I
12.14090 − 3.09884I 0
u = 0.17317 + 1.56134I
9.4648 − 11.8941I 0
u = 0.17317 − 1.56134I
9.4648 + 11.8941I 0
u = 0.01653 + 1.57431I
8.97845 − 1.78659I 0
u = 0.01653 − 1.57431I
8.97845 + 1.78659I 0
u = −0.02567 + 1.59721I
14.7937 + 4.5566I 0
u = −0.02567 − 1.59721I
14.7937 − 4.5566I 0
u = 0.323111
−0.690035 −14.8490
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
39
+ u
38
+ ··· + 2u + 1
c
3
u
39
− 9u
38
+ ··· − 112u + 17
c
4
, c
5
, c
9
c
10
u
39
+ u
38
+ ··· + 2u + 1
c
7
u
39
− u
38
+ ··· − 2u
2
+ 1
c
8
, c
11
u
39
+ 7u
38
+ ··· + 120u + 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
39
+ 35y
38
+ ··· + 4y −1
c
3
y
39
+ 7y
38
+ ··· − 2076y −289
c
4
, c
5
, c
9
c
10
y
39
+ 43y
38
+ ··· + 4y −1
c
7
y
39
− y
38
+ ··· + 4y −1
c
8
, c
11
y
39
+ 23y
38
+ ··· + 3588y −289
8
