11a
309
(K11a
309
)
1
Arc Sequences
7 6 1 10 9 2 3 11 4 5 8
Solving Sequence
1,7
2 6 3 4 8 11 9 10 5
c
1
c
6
c
2
c
3
c
7
c
11
c
8
c
9
c
5
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
46
u
45
+ ··· + 3u 1i
There are 1 irreducible components with 46 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
46
u
45
+ · · · + 3u 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
4
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
5
2u
3
u
u
7
3u
5
2u
3
+ u
a
11
=
u
12
+ 5u
10
+ 9u
8
+ 6u
6
u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
2u
6
4u
4
+ u
2
a
9
=
u
19
8u
17
26u
15
42u
13
31u
11
2u
9
+ 8u
7
2u
5
5u
3
u
21
9u
19
+ ··· u
3
+ u
a
10
=
u
29
+ 12u
27
+ ··· 2u
3
u
u
29
13u
27
+ ··· 3u
3
+ u
a
5
=
u
37
+ 16u
35
+ ··· + 5u
5
+ u
u
39
+ 17u
37
+ ··· 3u
5
+ u
a
5
=
u
37
+ 16u
35
+ ··· + 5u
5
+ u
u
39
+ 17u
37
+ ··· 3u
5
+ u
(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 = 0.735656 0.193124I
10.04571 + 1.08177I 15.0686 + 0.6754I
u = 0.735656 + 0.193124I
10.04571 1.08177I 15.0686 0.6754I
u = 0.720082 0.243420I
3.31119 5.72979I 10.05626 + 7.33064I
u = 0.720082 + 0.243420I
3.31119 + 5.72979I 10.05626 7.33064I
u = 0.633625
5.91200 16.5208
u = 0.508207 0.312848I
1.51039 1.50155I 2.27260 + 5.37426I
u = 0.508207 + 0.312848I
1.51039 + 1.50155I 2.27260 5.37426I
u = 0.295699 1.371024I
5.09568 2.64921I 10.39691 + 2.00509I
u = 0.295699 + 1.371024I
5.09568 + 2.64921I 10.39691 2.00509I
u = 0.28699 1.39792I
1.91287 9.38652I 5.20305 + 7.91054I
u = 0.28699 + 1.39792I
1.91287 + 9.38652I 5.20305 7.91054I
u = 0.262309 0.944898I
7.72158 4.89307I 11.69733 + 4.06237I
u = 0.262309 + 0.944898I
7.72158 + 4.89307I 11.69733 4.06237I
u = 0.232626 0.769208I
1.47350 + 1.99549I 7.38990 2.72369I
u = 0.232626 + 0.769208I
1.47350 1.99549I 7.38990 + 2.72369I
u = 0.20570 1.40316I
6.95779 4.17599I 1.17304 + 4.31736I
u = 0.20570 + 1.40316I
6.95779 + 4.17599I 1.17304 4.31736I
u = 0.197313 1.258130I
2.09433 3.02163I 10.70890 + 3.43995I
u = 0.197313 + 1.258130I
2.09433 + 3.02163I 10.70890 3.43995I
u = 0.084209 1.388933I
4.69829 + 1.24621I 1.93786 3.60564I
u = 0.084209 + 1.388933I
4.69829 1.24621I 1.93786 + 3.60564I
u = 0.05761 1.41497I
0.82034 4.36000I 6.54566 + 3.26503I
u = 0.05761 + 1.41497I
0.82034 + 4.36000I 6.54566 3.26503I
u = 0.140968 1.343297I
3.63229 + 1.96690I 5.76565 3.43589I
u = 0.140968 + 1.343297I
3.63229 1.96690I 5.76565 + 3.43589I
u = 0.16951 1.40533I
3.73352 + 1.14194I 3.26529 0.05591I
u = 0.16951 + 1.40533I
3.73352 1.14194I 3.26529 + 0.05591I
u = 0.186642 0.910074I
1.58749 + 1.92674I 8.17224 4.16982I
u = 0.186642 + 0.910074I
1.58749 1.92674I 8.17224 + 4.16982I
u = 0.23123 1.40917I
2.87934 + 7.34272I 4.77006 6.74279I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.23123 + 1.40917I
2.87934 7.34272I 4.77006 + 6.74279I
u = 0.281884 1.383072I
1.33332 + 5.27035I 6.71990 1.90933I
u = 0.281884 + 1.383072I
1.33332 5.27035I 6.71990 + 1.90933I
u = 0.29568 1.40274I
4.02180 + 12.82068I 8.97759 7.64155I
u = 0.29568 + 1.40274I
4.02180 12.82068I 8.97759 + 7.64155I
u = 0.314077 0.787630I
7.46462 5.12455I 11.02166 + 2.13659I
u = 0.314077 + 0.787630I
7.46462 + 5.12455I 11.02166 2.13659I
u = 0.407227 0.421079I
1.94572 1.01820I 6.96761 0.40643I
u = 0.407227 + 0.421079I
1.94572 + 1.01820I 6.96761 + 0.40643I
u = 0.427442
0.677522 14.9941
u = 0.597677 0.308192I
2.59332 + 4.30245I 9.29851 7.25504I
u = 0.597677 + 0.308192I
2.59332 4.30245I 9.29851 + 7.25504I
u = 0.710206 0.212604I
3.73492 + 1.67350I 11.57713 0.85623I
u = 0.710206 + 0.212604I
3.73492 1.67350I 11.57713 + 0.85623I
u = 0.739171 0.251155I
9.28633 + 9.06645I 13.6028 6.9083I
u = 0.739171 + 0.251155I
9.28633 9.06645I 13.6028 + 6.9083I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
6
(u
46
+ u
45
+ ··· 3u 1)
c
3
(u
46
+ 11u
45
+ ··· + 95u + 11)
c
4
, c
9
(u
46
+ u
45
+ ··· + u 1)
c
5
(u
46
+ 3u
45
+ ··· + 95u + 56)
c
7
(u
46
+ u
45
+ ··· + 3u 2)
c
8
, c
11
(u
46
+ 7u
45
+ ··· + 119u + 7)
c
10
(u
46
+ u
45
+ ··· + u 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
(y
46
+ 41y
45
+ ··· 5y + 1)
c
3
(y
46
+ 5y
45
+ ··· + 2679y + 121)
c
4
, c
9
(y
46
43y
45
+ ··· 5y + 1)
c
5
(y
46
15y
45
+ ··· 63233y + 3136)
c
7
(y
46
3y
45
+ ··· + 15y + 4)
c
8
, c
11
(y
46
+ 37y
45
+ ··· 1337y + 49)
c
10
(y
46
43y
45
+ ··· 5y + 1)
6