11a
210
(K11a
210
)
1
Arc Sequences
7 1 11 10 8 2 6 3 5 4 9
Solving Sequence
2,6
7 8 1 3 9 5 10 4 11
c
6
c
7
c
1
c
2
c
8
c
5
c
9
c
4
c
11
c
3
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
36
u
35
+ ··· + u
2
+ 1i
There are 1 irreducible components with 36 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
36
u
35
+ · · · + u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
9
=
u
11
2u
9
4u
7
4u
5
3u
3
u
11
u
9
2u
7
u
5
+ u
3
+ u
a
5
=
u
3
u
5
+ u
3
+ u
a
10
=
u
19
+ 2u
17
+ 6u
15
+ 8u
13
+ 9u
11
+ 6u
9
4u
5
3u
3
u
21
+ 3u
19
+ 9u
17
+ 16u
15
+ 24u
13
+ 25u
11
+ 21u
9
+ 10u
7
+ 3u
5
+ u
3
+ u
a
4
=
u
35
+ 4u
33
+ ··· 12u
7
+ u
3
u
35
u
34
+ ··· u
2
1
a
11
=
u
20
+ 3u
18
+ 9u
16
+ 16u
14
+ 24u
12
+ 25u
10
+ 21u
8
+ 10u
6
+ 3u
4
+ u
2
+ 1
u
20
+ 2u
18
+ 6u
16
+ 8u
14
+ 9u
12
+ 6u
10
4u
6
3u
4
a
11
=
u
20
+ 3u
18
+ 9u
16
+ 16u
14
+ 24u
12
+ 25u
10
+ 21u
8
+ 10u
6
+ 3u
4
+ u
2
+ 1
u
20
+ 2u
18
+ 6u
16
+ 8u
14
+ 9u
12
+ 6u
10
4u
6
3u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.864621 0.837762I
5.68597 2.74218I 3.17354 + 3.44962I
u = 0.864621 + 0.837762I
5.68597 + 2.74218I 3.17354 3.44962I
u = 0.848700 0.906287I
1.85163 + 3.15004I 1.82117 2.61659I
u = 0.848700 + 0.906287I
1.85163 3.15004I 1.82117 + 2.61659I
u = 0.816934 0.964209I
5.28964 + 8.99184I 2.24371 8.34910I
u = 0.816934 + 0.964209I
5.28964 8.99184I 2.24371 + 8.34910I
u = 0.794983 0.895936I
2.43227 + 2.98822I 1.17573 2.50595I
u = 0.794983 + 0.895936I
2.43227 2.98822I 1.17573 + 2.50595I
u = 0.628869 0.181121I
7.26818 3.72706I 0.04242 + 2.40123I
u = 0.628869 + 0.181121I
7.26818 + 3.72706I 0.04242 2.40123I
u = 0.433324 0.431478I
0.721812 + 0.963189I 5.72873 5.37633I
u = 0.433324 + 0.431478I
0.721812 0.963189I 5.72873 + 5.37633I
u = 0.354870 0.979895I
9.75368 + 7.25706I 5.64963 6.88942I
u = 0.354870 + 0.979895I
9.75368 7.25706I 5.64963 + 6.88942I
u = 0.331446 0.848238I
0.55346 + 2.03006I 1.12004 4.04451I
u = 0.331446 + 0.848238I
0.55346 2.03006I 1.12004 + 4.04451I
u = 0.165304 0.967098I
10.84153 1.55360I 8.17260 0.38654I
u = 0.165304 + 0.967098I
10.84153 + 1.55360I 8.17260 + 0.38654I
u = 0.182299 0.889376I
3.00780 + 0.17019I 7.29367 0.75206I
u = 0.182299 + 0.889376I
3.00780 0.17019I 7.29367 + 0.75206I
u = 0.353084 0.933340I
2.03776 5.19435I 3.33716 + 9.21025I
u = 0.353084 + 0.933340I
2.03776 + 5.19435I 3.33716 9.21025I
u = 0.530434 0.230060I
0.07417 + 1.89235I 3.15479 4.52320I
u = 0.530434 + 0.230060I
0.07417 1.89235I 3.15479 + 4.52320I
u = 0.584466 0.612192I
5.61681 2.13861I 0.19816 + 3.36808I
u = 0.584466 + 0.612192I
5.61681 + 2.13861I 0.19816 3.36808I
u = 0.726012 0.899380I
5.85535 2.75781I 2.67910 + 3.05381I
u = 0.726012 + 0.899380I
5.85535 + 2.75781I 2.67910 3.05381I
u = 0.813169 0.978946I
2.30348 11.52243I 0.68183 + 6.92390I
u = 0.813169 + 0.978946I
2.30348 + 11.52243I 0.68183 6.92390I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.821327 0.945037I
6.48998 5.15115I 5.34177 + 2.63886I
u = 0.821327 + 0.945037I
6.48998 + 5.15115I 5.34177 2.63886I
u = 0.853521 0.859582I
6.75859 1.08065I 5.91547 + 2.62482I
u = 0.853521 + 0.859582I
6.75859 + 1.08065I 5.91547 2.62482I
u = 0.874739 0.820043I
1.80521 + 5.25682I 0.24993 2.11060I
u = 0.874739 + 0.820043I
1.80521 5.25682I 0.24993 + 2.11060I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
36
+ u
35
+ ··· + u
2
+ 1)
c
2
, c
5
, c
7
(u
36
+ 9u
35
+ ··· + 2u + 1)
c
3
, c
4
, c
9
c
10
(u
36
+ u
35
+ ··· + 2u + 1)
c
8
(u
36
+ u
35
+ ··· + 24u + 5)
c
11
(u
36
+ 9u
35
+ ··· 8u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
36
+ 9y
35
+ ··· + 2y + 1)
c
2
, c
5
, c
7
(y
36
+ 37y
35
+ ··· + 18y + 1)
c
3
, c
4
, c
9
c
10
(y
36
+ 41y
35
+ ··· + 2y + 1)
c
8
(y
36
3y
35
+ ··· 6y + 25)
c
11
(y
36
+ y
35
+ ··· 30y + 1)
5