11a
203
(K11a
203
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 8 2 11 3 4 5 7
Solving Sequence
2,7
6 1 3 11 8 9 5 10 4
c
6
c
1
c
2
c
11
c
7
c
8
c
5
c
10
c
4
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− 8u
28
+ ··· + u + 1i
I
u
2
= hu − 1i
* 2 irreducible components of dim
C
= 0, with total 31 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
30
− 8u
28
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
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
8
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
16
− 4u
14
+ 8u
12
− 8u
10
+ 4u
8
a
5
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
14
− 4u
12
+ 7u
10
− 6u
8
+ 2u
6
− u
2
a
10
=
−u
25
+ 6u
23
+ ··· − 3u
5
+ u
u
25
− 7u
23
+ ··· − 2u
3
+ u
a
4
=
u
25
− 6u
23
+ ··· + 3u
5
− u
−u
27
+ 7u
25
+ ··· − u
3
+ u
a
4
=
u
25
− 6u
23
+ ··· + 3u
5
− u
−u
27
+ 7u
25
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
29
+ 32u
27
− 4u
26
− 124u
25
+ 28u
24
+ 284u
23
− 96u
22
−
400u
21
+ 192u
20
+ 300u
19
− 232u
18
− 4u
17
+ 140u
16
− 224u
15
+ 12u
14
+ 188u
13
−
84u
12
− 28u
11
+ 40u
10
− 52u
9
+ 12u
8
+ 32u
7
− 24u
6
− 8u
5
+ 8u
4
+ 4u
3
+ 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
30
− 8u
28
+ ··· + u + 1
c
2
u
30
+ 16u
29
+ ··· + 3u + 1
c
3
, c
4
, c
8
c
9
, c
10
u
30
− 20u
28
+ ··· + 3u + 1
c
5
u
30
− 6u
29
+ ··· + 23u + 41
c
7
, c
11
u
30
− 3u
29
+ ··· + 37u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
30
− 16y
29
+ ··· − 3y + 1
c
2
y
30
− 4y
29
+ ··· − 7y + 1
c
3
, c
4
, c
8
c
9
, c
10
y
30
− 40y
29
+ ··· − 3y + 1
c
5
y
30
− 16y
29
+ ··· − 36527y + 1681
c
7
, c
11
y
30
+ 27y
29
+ ··· − 3129y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887519 + 0.482432I
−1.82016 + 4.25744I −10.93711 − 7.73976I
u = −0.887519 − 0.482432I
−1.82016 − 4.25744I −10.93711 + 7.73976I
u = 0.935013 + 0.538460I
−10.87340 − 5.27966I −12.05604 + 5.65823I
u = 0.935013 − 0.538460I
−10.87340 + 5.27966I −12.05604 − 5.65823I
u = −1.09884
−14.6811 −17.7740
u = 0.778482 + 0.436098I
1.00011 − 1.87364I −3.05909 + 5.26127I
u = 0.778482 − 0.436098I
1.00011 + 1.87364I −3.05909 − 5.26127I
u = 0.113847 + 0.839746I
−15.0478 + 5.3499I −12.97012 − 2.66295I
u = 0.113847 − 0.839746I
−15.0478 − 5.3499I −12.97012 + 2.66295I
u = −0.100894 + 0.796851I
−5.17949 − 3.97369I −12.30033 + 4.02503I
u = −0.100894 − 0.796851I
−5.17949 + 3.97369I −12.30033 − 4.02503I
u = 0.523957 + 0.596828I
−9.71958 + 0.79768I −9.60193 + 0.22241I
u = 0.523957 − 0.596828I
−9.71958 − 0.79768I −9.60193 − 0.22241I
u = −1.175620 + 0.433898I
−4.54064 + 2.58760I −11.91074 + 0.31463I
u = −1.175620 − 0.433898I
−4.54064 − 2.58760I −11.91074 − 0.31463I
u = 1.178600 + 0.472961I
−4.25686 − 5.88582I −10.73071 + 7.02338I
u = 1.178600 − 0.472961I
−4.25686 + 5.88582I −10.73071 − 7.02338I
u = 1.209450 + 0.403071I
−9.06454 − 0.14928I −16.5343 − 0.4492I
u = 1.209450 − 0.403071I
−9.06454 + 0.14928I −16.5343 + 0.4492I
u = 0.064904 + 0.715291I
−1.08394 + 1.47244I −7.45106 − 4.26447I
u = 0.064904 − 0.715291I
−1.08394 − 1.47244I −7.45106 + 4.26447I
u = −0.551842 + 0.441212I
−0.931280 − 0.302386I −8.66690 + 0.70064I
u = −0.551842 − 0.441212I
−0.931280 + 0.302386I −8.66690 − 0.70064I
u = −1.236340 + 0.392586I
−19.1575 − 1.1230I −17.1562 − 0.4196I
u = −1.236340 − 0.392586I
−19.1575 + 1.1230I −17.1562 + 0.4196I
u = −1.198880 + 0.495938I
−8.40726 + 8.70507I −15.2295 − 7.1454I
u = −1.198880 − 0.495938I
−8.40726 − 8.70507I −15.2295 + 7.1454I
u = 1.212990 + 0.509772I
−18.3208 − 10.2613I −15.9531 + 5.7696I
u = 1.212990 − 0.509772I
−18.3208 + 10.2613I −15.9531 − 5.7696I
u = −0.633476
−0.803448 −13.1110
5
II. I
u
2
= hu − 1i
(i) Arc colorings
a
2
=
0
1
a
7
=
1
0
a
6
=
1
−1
a
1
=
1
0
a
3
=
−1
1
a
11
=
1
0
a
8
=
1
0
a
9
=
0
1
a
5
=
0
−1
a
10
=
1
−1
a
4
=
−1
0
a
4
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
8
, c
9
c
10
u − 1
c
2
, c
5
u + 1
c
7
, c
11
u
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
y −1
c
7
, c
11
y
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
−4.93480 −18.0000
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u − 1)(u
30
− 8u
28
+ ··· + u + 1)
c
2
(u + 1)(u
30
+ 16u
29
+ ··· + 3u + 1)
c
3
, c
4
, c
8
c
9
, c
10
(u − 1)(u
30
− 20u
28
+ ··· + 3u + 1)
c
5
(u + 1)(u
30
− 6u
29
+ ··· + 23u + 41)
c
7
, c
11
u(u
30
− 3u
29
+ ··· + 37u − 11)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)(y
30
− 16y
29
+ ··· − 3y + 1)
c
2
(y −1)(y
30
− 4y
29
+ ··· − 7y + 1)
c
3
, c
4
, c
8
c
9
, c
10
(y −1)(y
30
− 40y
29
+ ··· − 3y + 1)
c
5
(y −1)(y
30
− 16y
29
+ ··· − 36527y + 1681)
c
7
, c
11
y(y
30
+ 27y
29
+ ··· − 3129y + 121)
11
