11a
195
(K11a
195
)
1
Arc Sequences
7 1 11 10 9 2 3 6 5 4 8
Solving Sequence
2,6
7 1 3 8 9 5 11 4 10
c
6
c
1
c
2
c
7
c
8
c
5
c
11
c
3
c
10
c
4
, c
9
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
6
=
0
u
a
7
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
7
2u
5
2u
3
u
7
u
5
+ u
a
9
=
u
7
2u
5
2u
3
u
9
+ u
7
+ u
5
+ u
a
5
=
u
15
4u
13
8u
11
8u
9
4u
7
u
17
+ 3u
15
+ 5u
13
+ 4u
11
+ 3u
9
+ 2u
7
+ 2u
5
+ u
a
11
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
u
4
a
4
=
u
20
+ 5u
18
+ 13u
16
+ 20u
14
+ 20u
12
+ 13u
10
+ 7u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
u
20
+ 4u
18
+ 8u
16
+ 8u
14
+ 3u
12
2u
10
2u
8
+ u
4
a
10
=
u
23
6u
21
18u
19
32u
17
36u
15
24u
13
8u
11
u
7
2u
5
2u
3
u
25
+ 5u
23
+ ··· + 3u
5
+ u
a
10
=
u
23
6u
21
18u
19
32u
17
36u
15
24u
13
8u
11
u
7
2u
5
2u
3
u
25
+ 5u
23
+ ··· + 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 = 0.802038 0.253607I
16.0177 4.2821I 0.13314 + 2.02711I
u = 0.802038 + 0.253607I
16.0177 + 4.2821I 0.13314 2.02711I
u = 0.605138 0.306508I
0.20618 1.65739I 4.39967 + 5.42760I
u = 0.605138 + 0.306508I
0.20618 + 1.65739I 4.39967 5.42760I
u = 0.552254 1.161766I
18.6999 + 9.3134I 3.16767 5.53584I
u = 0.552254 + 1.161766I
18.6999 9.3134I 3.16767 + 5.53584I
u = 0.542697 0.732391I
3.09394 + 2.15610I 1.13399 4.05651I
u = 0.542697 + 0.732391I
3.09394 2.15610I 1.13399 + 4.05651I
u = 0.514778 1.096235I
2.03162 + 6.10006I 0.39307 8.69218I
u = 0.514778 + 1.096235I
2.03162 6.10006I 0.39307 + 8.69218I
u = 0.356074 1.044640I
3.16465 + 0.96048I 3.09934 + 0.95175I
u = 0.356074 + 1.044640I
3.16465 0.96048I 3.09934 0.95175I
u = 0.285406 1.191604I
18.9562 0.8960I 5.38672 0.41726I
u = 0.285406 + 1.191604I
18.9562 + 0.8960I 5.38672 + 0.41726I
u = 0.297666 1.141551I
9.26319 + 0.26212I 5.31196 + 0.01260I
u = 0.297666 + 1.141551I
9.26319 0.26212I 5.31196 0.01260I
u = 0.471387 0.491921I
0.833642 0.761088I 8.16561 + 5.13707I
u = 0.471387 + 0.491921I
0.833642 + 0.761088I 8.16561 5.13707I
u = 0.476758 1.045336I
0.84040 3.21915I 4.62809 + 2.59939I
u = 0.476758 + 1.045336I
0.84040 + 3.21915I 4.62809 2.59939I
u = 0.537219 1.138146I
7.64978 8.20022I 2.78707 + 6.68979I
u = 0.537219 + 1.138146I
7.64978 + 8.20022I 2.78707 6.68979I
u = 0.637657 0.776072I
13.35512 2.46006I 0.85027 + 3.10858I
u = 0.637657 + 0.776072I
13.35512 + 2.46006I 0.85027 3.10858I
u = 0.737696 0.258677I
5.09746 + 3.38991I 0.31521 3.08376I
u = 0.737696 + 0.258677I
5.09746 3.38991I 0.31521 + 3.08376I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
26
+ u
25
+ ··· + u + 1)
c
2
(u
26
+ 13u
25
+ ··· + u + 1)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
26
+ u
25
+ ··· + u + 1)
c
7
(u
26
+ u
25
+ ··· + 15u + 13)
c
11
(u
26
+ 5u
25
+ ··· + 13u + 7)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
26
+ 13y
25
+ ··· + y + 1)
c
2
(y
26
+ y
25
+ ··· + 13y + 1)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
26
+ 37y
25
+ ··· + y + 1)
c
7
(y
26
11y
25
+ ··· 771y + 169)
c
11
(y
26
7y
25
+ ··· + 209y + 49)
5