11a
225
(K11a
225
)
1
Arc Sequences
7 1 10 11 8 2 6 5 3 4 9
Solving Sequence
2,7
1 3 6 8 5 9 10 11 4
c
1
c
2
c
6
c
7
c
5
c
8
c
9
c
11
c
4
c
3
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
26
u
25
+ ··· u 1i
There are 1 irreducible components with 26 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
26
u
25
+ · · · u 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
6
=
u
u
a
8
=
u
3
u
3
+ u
a
5
=
u
5
u
u
5
+ u
3
+ u
a
9
=
u
7
2u
3
u
7
+ u
5
+ 2u
3
+ u
a
10
=
u
13
+ 2u
11
+ 5u
9
+ 6u
7
+ 6u
5
+ 2u
3
+ u
u
15
+ u
13
+ 4u
11
+ 3u
9
+ 4u
7
+ 2u
5
+ 2u
3
+ u
a
11
=
u
16
u
14
5u
12
4u
10
7u
8
4u
6
2u
4
+ 1
u
16
+ 2u
14
+ 6u
12
+ 8u
10
+ 10u
8
+ 8u
6
+ 4u
4
+ 2u
2
a
4
=
u
24
3u
22
+ ··· 5u
4
+ 1
u
25
+ u
24
+ ··· u 1
a
4
=
u
24
3u
22
+ ··· 5u
4
+ 1
u
25
+ u
24
+ ··· u 1
(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 = 0.907051 0.911013I
11.16141 0.44023I 10.10436 + 1.46145I
u = 0.907051 + 0.911013I
11.16141 + 0.44023I 10.10436 1.46145I
u = 0.887317 0.951652I
11.03033 + 7.05835I 9.75996 6.21969I
u = 0.887317 + 0.951652I
11.03033 7.05835I 9.75996 + 6.21969I
u = 0.726871 0.589145I
10.74899 1.83401I 11.98633 + 0.23070I
u = 0.726871 + 0.589145I
10.74899 + 1.83401I 11.98633 0.23070I
u = 0.592242 0.916703I
9.67676 + 6.71425I 9.25508 6.45300I
u = 0.592242 + 0.916703I
9.67676 6.71425I 9.25508 + 6.45300I
u = 0.484637 0.751855I
0.26125 + 1.87689I 2.74450 3.73316I
u = 0.484637 + 0.751855I
0.26125 1.87689I 2.74450 + 3.73316I
u = 0.361497
0.783407 12.8957
u = 0.089478 0.789753I
1.41635 + 1.31903I 1.30126 6.10882I
u = 0.089478 + 0.789753I
1.41635 1.31903I 1.30126 + 6.10882I
u = 0.197517 0.899510I
5.28037 2.44629I 3.67676 + 4.11819I
u = 0.197517 + 0.899510I
5.28037 + 2.44629I 3.67676 4.11819I
u = 0.549813 0.855063I
1.89109 4.88723I 7.24553 + 8.84366I
u = 0.549813 + 0.855063I
1.89109 + 4.88723I 7.24553 8.84366I
u = 0.597139
8.17274 12.1061
u = 0.612956 0.606631I
2.67984 + 0.49611I 10.71301 1.37639I
u = 0.612956 + 0.606631I
2.67984 0.49611I 10.71301 + 1.37639I
u = 0.887776 0.927734I
8.58736 3.27967I 5.99252 + 2.35106I
u = 0.887776 + 0.927734I
8.58736 + 3.27967I 5.99252 2.35106I
u = 0.893815 0.969703I
19.5205 9.3622I 11.47654 + 4.95795I
u = 0.893815 + 0.969703I
19.5205 + 9.3622I 11.47654 4.95795I
u = 0.927899 0.905240I
19.7312 + 2.6570I 11.84579 0.35212I
u = 0.927899 + 0.905240I
19.7312 2.6570I 11.84579 + 0.35212I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
26
+ u
25
+ ··· + u 1)
c
2
, c
5
, c
7
c
8
(u
26
+ 5u
25
+ ··· 3u + 1)
c
3
, c
4
, c
9
c
10
(u
26
+ u
25
+ ··· + u 1)
c
11
(u
26
+ 9u
25
+ ··· 247u 89)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
26
+ 5y
25
+ ··· 3y + 1)
c
2
, c
5
, c
7
c
8
(y
26
+ 33y
25
+ ··· 59y + 1)
c
3
, c
4
, c
9
c
10
(y
26
31y
25
+ ··· 3y + 1)
c
11
(y
26
19y
25
+ ··· 92159y + 7921)
5