11a
238
(K11a
238
)
1
Arc Sequences
7 1 11 10 9 8 2 3 5 4 6
Solving Sequence
1,7
2 3 8 9 6 5 11 4 10
c
1
c
2
c
7
c
8
c
6
c
5
c
11
c
3
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
32
+ u
31
+ ··· 2u 1i
There are 1 irreducible components with 32 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
32
+ u
31
+ · · · 2u 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
9
=
u
7
2u
5
+ 2u
3
2u
u
7
+ u
5
2u
3
+ u
a
6
=
u
3
u
5
u
3
+ u
a
5
=
u
19
4u
17
+ 10u
15
18u
13
+ 23u
11
24u
9
+ 18u
7
10u
5
+ 5u
3
u
19
+ 3u
17
8u
15
+ 13u
13
17u
11
+ 17u
9
12u
7
+ 8u
5
3u
3
+ u
a
11
=
u
8
+ u
6
u
4
+ 1
u
10
+ 2u
8
3u
6
+ 2u
4
u
2
a
4
=
u
20
+ 3u
18
7u
16
+ 10u
14
10u
12
+ 7u
10
u
8
2u
6
+ 3u
4
3u
2
+ 1
u
22
+ 4u
20
+ ··· + 2u
4
+ u
2
a
10
=
u
31
6u
29
+ ··· + 2u
3
2u
u
31
+ 5u
29
+ ··· 4u
3
+ u
a
10
=
u
31
6u
29
+ ··· + 2u
3
2u
u
31
+ 5u
29
+ ··· 4u
3
+ 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 = 1.056334 0.061026I
2.61740 3.12405I 13.03032 + 4.71506I
u = 1.056334 + 0.061026I
2.61740 + 3.12405I 13.03032 4.71506I
u = 1.028398 0.706586I
11.3054 10.8467I 6.07367 + 6.73348I
u = 1.028398 + 0.706586I
11.3054 + 10.8467I 6.07367 6.73348I
u = 1.002994 0.660346I
1.07052 5.91452I 13.1301 + 6.2502I
u = 1.002994 + 0.660346I
1.07052 + 5.91452I 13.1301 6.2502I
u = 0.989901 0.536666I
8.67678 1.64389I 8.39822 + 2.78158I
u = 0.989901 + 0.536666I
8.67678 + 1.64389I 8.39822 2.78158I
u = 0.858044 0.724840I
6.28397 2.75786I 2.60459 + 3.27604I
u = 0.858044 + 0.724840I
6.28397 + 2.75786I 2.60459 3.27604I
u = 0.650134 0.810724I
12.44821 + 5.14177I 4.17146 2.01638I
u = 0.650134 + 0.810724I
12.44821 5.14177I 4.17146 + 2.01638I
u = 0.636819 0.693070I
0.007012 + 0.662924I 11.48005 1.53290I
u = 0.636819 + 0.693070I
0.007012 0.662924I 11.48005 + 1.53290I
u = 0.432503
0.576779 17.4953
u = 0.283633 0.646722I
10.54705 2.61943I 4.33176 + 2.54357I
u = 0.283633 + 0.646722I
10.54705 + 2.61943I 4.33176 2.54357I
u = 0.343359 0.506821I
1.71293 + 1.66616I 5.31847 4.81567I
u = 0.343359 + 0.506821I
1.71293 1.66616I 5.31847 + 4.81567I
u = 0.645707 0.769221I
3.20190 3.54493I 5.40363 + 3.59501I
u = 0.645707 + 0.769221I
3.20190 + 3.54493I 5.40363 3.59501I
u = 0.766364 0.598235I
1.37609 + 2.05463I 7.69647 5.64619I
u = 0.766364 + 0.598235I
1.37609 2.05463I 7.69647 + 5.64619I
u = 0.869866 0.770916I
16.1380 + 2.8994I 2.41783 2.82935I
u = 0.869866 + 0.770916I
16.1380 2.8994I 2.41783 + 2.82935I
u = 0.971964 0.621405I
0.65027 + 2.73837I 9.34927 0.96616I
u = 0.971964 + 0.621405I
0.65027 2.73837I 9.34927 + 0.96616I
u = 1.016708 0.688378I
2.09241 + 9.07761I 7.53326 8.39661I
u = 1.016708 + 0.688378I
2.09241 9.07761I 7.53326 + 8.39661I
u = 1.05287
5.13714 18.4378
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.082105 0.105469I
6.12682 + 4.72021I 11.09441 3.42797I
u = 1.082105 + 0.105469I
6.12682 4.72021I 11.09441 + 3.42797I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
7
(u
32
+ u
31
+ ··· 2u 1)
c
2
, c
6
(u
32
+ 11u
31
+ ··· + 8u + 1)
c
3
, c
4
, c
5
c
9
, c
10
(u
32
+ u
31
+ ··· + 2u 1)
c
8
, c
11
(u
32
+ u
31
+ ··· 8u 4)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
(y
32
11y
31
+ ··· 8y + 1)
c
2
, c
6
(y
32
+ 21y
31
+ ··· 8y + 1)
c
3
, c
4
, c
5
c
9
, c
10
(y
32
+ 41y
31
+ ··· 8y + 1)
c
8
, c
11
(y
32
15y
31
+ ··· 280y + 16)
5