11a
307
(K11a
307
)
1
Arc Sequences
8 7 1 11 10 2 3 4 6 5 9
Solving Sequence
3,7
8 2 1 4 9 6 10 5 11
c
7
c
2
c
1
c
3
c
8
c
6
c
9
c
5
c
11
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
41
u
40
+ ··· + u + 1i
There are 1 irreducible components with 41 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
41
u
40
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
8
=
u
u
a
2
=
1
u
2
a
1
=
u
4
+ u
2
+ 1
u
4
+ 2u
2
a
4
=
u
8
3u
6
+ u
4
+ 2u
2
+ 1
u
8
4u
6
+ 4u
4
a
9
=
u
15
+ 6u
13
12u
11
+ 6u
9
+ 6u
7
2u
5
4u
3
u
15
+ 7u
13
18u
11
+ 19u
9
4u
7
4u
5
+ u
a
6
=
u
u
3
+ u
a
10
=
u
19
8u
17
+ 24u
15
30u
13
+ 7u
11
+ 10u
9
+ 4u
7
6u
5
3u
3
u
21
9u
19
+ 33u
17
62u
15
+ 62u
13
33u
11
+ 13u
9
6u
7
+ u
5
u
3
+ u
a
5
=
u
37
+ 16u
35
+ ··· + 3u
5
u
u
39
+ 17u
37
+ ··· 2u
3
+ u
a
11
=
u
26
+ 11u
24
+ ··· + u
2
+ 1
u
26
+ 12u
24
+ ··· 2u
4
+ u
2
a
11
=
u
26
+ 11u
24
+ ··· + u
2
+ 1
u
26
+ 12u
24
+ ··· 2u
4
+ u
2
(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 = 1.42652 0.20286I
1.03962 + 4.49848I 7.12017 3.52127I
u = 1.42652 + 0.20286I
1.03962 4.49848I 7.12017 + 3.52127I
u = 1.41661 0.12778I
5.86406 0.88498I 9.39506 + 3.49005I
u = 1.41661 + 0.12778I
5.86406 + 0.88498I 9.39506 3.49005I
u = 1.41194 0.27160I
3.83065 + 9.56504I 6.30600 8.62495I
u = 1.41194 + 0.27160I
3.83065 9.56504I 6.30600 + 8.62495I
u = 1.365466 0.241449I
1.86460 + 3.44778I 2.94863 1.78570I
u = 1.365466 + 0.241449I
1.86460 3.44778I 2.94863 + 1.78570I
u = 1.11700
1.66824 7.38977
u = 1.046146 0.223939I
8.35529 + 4.56229I 0.39000 3.84475I
u = 1.046146 + 0.223939I
8.35529 4.56229I 0.39000 + 3.84475I
u = 0.681237 0.347030I
7.84552 4.44427I 1.76887 + 1.55975I
u = 0.681237 + 0.347030I
7.84552 + 4.44427I 1.76887 1.55975I
u = 0.397594 0.359864I
0.917102 + 0.596105I 8.98647 4.74096I
u = 0.397594 + 0.359864I
0.917102 0.596105I 8.98647 + 4.74096I
u = 0.280343 0.720260I
9.34338 + 8.33215I 0.86165 6.60092I
u = 0.280343 + 0.720260I
9.34338 8.33215I 0.86165 + 6.60092I
u = 0.269533 0.643764I
0.08359 + 2.56810I 5.39788 3.59460I
u = 0.269533 + 0.643764I
0.08359 2.56810I 5.39788 + 3.59460I
u = 0.141874 0.704451I
11.05977 1.01340I 3.63842 0.71701I
u = 0.141874 + 0.704451I
11.05977 + 1.01340I 3.63842 + 0.71701I
u = 0.164742 0.644372I
2.99086 0.25085I 2.71271 + 0.09233I
u = 0.164742 + 0.644372I
2.99086 + 0.25085I 2.71271 0.09233I
u = 0.278364 0.691368I
1.56642 6.05654I 1.56838 + 8.60655I
u = 0.278364 + 0.691368I
1.56642 + 6.05654I 1.56838 8.60655I
u = 0.391448 0.543944I
4.74796 1.76607I 3.33618 + 3.94184I
u = 0.391448 + 0.543944I
4.74796 + 1.76607I 3.33618 3.94184I
u = 0.587096 0.303306I
0.19628 + 2.43472I 4.58629 3.61518I
u = 0.587096 + 0.303306I
0.19628 2.43472I 4.58629 + 3.61518I
u = 1.071213 0.139228I
0.40127 2.84366I 1.98426 + 5.43463I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.071213 + 0.139228I
0.40127 + 2.84366I 1.98426 5.43463I
u = 1.338866 0.271838I
6.40559 2.51190I 1.38150 + 2.46879I
u = 1.338866 + 0.271838I
6.40559 + 2.51190I 1.38150 2.46879I
u = 1.40643 0.25423I
5.27082 5.85936I 9.90370 + 3.39056I
u = 1.40643 + 0.25423I
5.27082 + 5.85936I 9.90370 3.39056I
u = 1.41180 0.16148I
6.59801 2.64882I 11.65137 + 3.90041I
u = 1.41180 + 0.16148I
6.59801 + 2.64882I 11.65137 3.90041I
u = 1.41491 0.28413I
3.93253 11.98378I 3.64923 + 6.96576I
u = 1.41491 + 0.28413I
3.93253 + 11.98378I 3.64923 6.96576I
u = 1.43088 0.09977I
1.36673 + 3.09799I 6.14389 2.05117I
u = 1.43088 + 0.09977I
1.36673 3.09799I 6.14389 + 2.05117I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
41
+ 3u
40
+ ··· u 1)
c
2
, c
6
, c
7
(u
41
+ u
40
+ ··· + u 1)
c
3
(u
41
+ 9u
40
+ ··· + 337u + 41)
c
4
, c
5
, c
9
c
10
(u
41
+ u
40
+ ··· + 3u + 1)
c
8
(u
41
+ u
40
+ ··· + 127u + 61)
c
11
(u
41
+ 11u
40
+ ··· + 121u + 11)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
41
y
40
+ ··· + 5y 1)
c
2
, c
6
, c
7
(y
41
37y
40
+ ··· + y 1)
c
3
(y
41
+ 11y
40
+ ··· 26979y 1681)
c
4
, c
5
, c
9
c
10
(y
41
+ 47y
40
+ ··· + y 1)
c
8
(y
41
13y
40
+ ··· + 51997y 3721)
c
11
(y
41
5y
40
+ ··· 275y 121)
6