11a
159
(K11a
159
)
1
Arc Sequences
5 1 9 7 2 11 4 10 3 8 6
Solving Sequence
2,5
6 1 3 11 7 4 8 10 9
c
5
c
1
c
2
c
11
c
6
c
4
c
7
c
10
c
9
c
3
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
55
+ u
54
+ ··· + 2u
3
+ 1i
There are 1 irreducible components with 55 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
55
+ u
54
+ · · · + 2u
3
+ 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
11
=
u
4
u
2
+ 1
u
4
a
7
=
u
7
+ 2u
5
2u
3
u
7
u
5
+ u
a
4
=
u
15
4u
13
+ 8u
11
8u
9
+ 4u
7
u
15
+ 3u
13
4u
11
+ u
9
+ 2u
7
2u
5
+ u
a
8
=
u
23
+ 6u
21
18u
19
+ 32u
17
36u
15
+ 24u
13
8u
11
u
7
+ 2u
5
2u
3
u
23
5u
21
+ 12u
19
15u
17
+ 8u
15
+ 4u
13
8u
11
+ 3u
9
+ 3u
7
3u
5
+ u
a
10
=
u
42
11u
40
+ ··· u
2
+ 1
u
42
+ 10u
40
+ ··· 2u
4
+ u
2
a
9
=
u
48
13u
46
+ ··· 6u
4
+ 1
u
50
+ 12u
48
+ ··· 2u
4
+ u
2
a
9
=
u
48
13u
46
+ ··· 6u
4
+ 1
u
50
+ 12u
48
+ ··· 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 = 1.198143 0.444267I
8.97089 1.53080I 10.56468 + 0.59783I
u = 1.198143 + 0.444267I
8.97089 + 1.53080I 10.56468 0.59783I
u = 1.192544 0.363416I
5.96663 + 0.17301I 9.26357 + 0.91884I
u = 1.192544 + 0.363416I
5.96663 0.17301I 9.26357 0.91884I
u = 1.180556 0.523653I
3.6961 14.4089I 5.44100 + 9.98572I
u = 1.180556 + 0.523653I
3.6961 + 14.4089I 5.44100 9.98572I
u = 1.161742 0.521230I
1.25671 8.17694I 0.32936 + 6.49947I
u = 1.161742 + 0.521230I
1.25671 + 8.17694I 0.32936 6.49947I
u = 1.154343 0.398075I
4.05721 1.86906I 9.08122 + 0.59288I
u = 1.154343 + 0.398075I
4.05721 + 1.86906I 9.08122 0.59288I
u = 1.132834 0.507493I
1.71452 1.81047I 3.31619 + 0.85322I
u = 1.132834 + 0.507493I
1.71452 + 1.81047I 3.31619 0.85322I
u = 0.989431 0.152646I
3.52521 0.06578I 10.04150 + 0.64430I
u = 0.989431 + 0.152646I
3.52521 + 0.06578I 10.04150 0.64430I
u = 0.821912 0.574546I
2.29946 8.58321I 0.26840 + 8.74761I
u = 0.821912 + 0.574546I
2.29946 + 8.58321I 0.26840 8.74761I
u = 0.770144 0.578763I
6.52620 2.29211I 4.76004 + 3.60647I
u = 0.770144 + 0.578763I
6.52620 + 2.29211I 4.76004 3.60647I
u = 0.769461
1.02390 10.8305
u = 0.710164 0.582211I
2.61827 + 4.00138I 0.81073 2.09093I
u = 0.710164 + 0.582211I
2.61827 4.00138I 0.81073 + 2.09093I
u = 0.252097 0.684359I
0.84076 2.75512I 0.02989 + 2.86362I
u = 0.252097 + 0.684359I
0.84076 + 2.75512I 0.02989 2.86362I
u = 0.205680 0.754383I
4.04900 + 3.40061I 3.11315 3.08609I
u = 0.205680 + 0.754383I
4.04900 3.40061I 3.11315 + 3.08609I
u = 0.179481 0.793499I
0.74984 + 9.53517I 2.28321 6.87514I
u = 0.179481 + 0.793499I
0.74984 9.53517I 2.28321 + 6.87514I
u = 0.013169 0.773005I
5.44101 2.81013I 7.05601 + 3.05455I
u = 0.013169 + 0.773005I
5.44101 + 2.81013I 7.05601 3.05455I
u = 0.153879 0.692616I
0.48181 1.78744I 3.72385 + 3.38377I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.153879 + 0.692616I
0.48181 + 1.78744I 3.72385 3.38377I
u = 0.166524 0.782944I
1.91993 3.95621I 4.32723 + 2.21514I
u = 0.166524 + 0.782944I
1.91993 + 3.95621I 4.32723 2.21514I
u = 0.255316 0.531343I
0.11478 1.78039I 0.55066 + 3.60054I
u = 0.255316 + 0.531343I
0.11478 + 1.78039I 0.55066 3.60054I
u = 0.709453 0.352697I
0.95831 + 1.60933I 1.49417 5.74918I
u = 0.709453 + 0.352697I
0.95831 1.60933I 1.49417 + 5.74918I
u = 0.711973 0.542332I
1.33027 + 1.15553I 1.16546 3.23863I
u = 0.711973 + 0.542332I
1.33027 1.15553I 1.16546 + 3.23863I
u = 0.817654 0.549346I
1.02771 + 3.24584I 2.27897 4.07779I
u = 0.817654 + 0.549346I
1.02771 3.24584I 2.27897 + 4.07779I
u = 1.022777 0.213142I
2.91576 + 5.31435I 7.80390 6.55381I
u = 1.022777 + 0.213142I
2.91576 5.31435I 7.80390 + 6.55381I
u = 1.096361 0.436034I
2.45106 + 5.66045I 4.09002 7.28827I
u = 1.096361 + 0.436034I
2.45106 5.66045I 4.09002 + 7.28827I
u = 1.154880 0.344796I
0.0418156 + 0.0593950I 1.97321 + 0.28127I
u = 1.154880 + 0.344796I
0.0418156 0.0593950I 1.97321 0.28127I
u = 1.158029 0.497232I
3.34533 + 6.30811I 7.15638 6.23846I
u = 1.158029 + 0.497232I
3.34533 6.30811I 7.15638 + 6.23846I
u = 1.180004 0.516980I
4.89200 + 8.77056I 7.47137 5.34591I
u = 1.180004 + 0.516980I
4.89200 8.77056I 7.47137 + 5.34591I
u = 1.196470 0.351829I
4.89384 5.78358I 7.35010 + 3.96782I
u = 1.196470 + 0.351829I
4.89384 + 5.78358I 7.35010 3.96782I
u = 1.197311 0.455517I
8.89140 + 7.22930I 10.25643 6.47034I
u = 1.197311 + 0.455517I
8.89140 7.22930I 10.25643 + 6.47034I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
55
+ u
54
+ ··· + 2u
3
+ 1)
c
2
(u
55
+ 29u
54
+ ··· 6u
2
+ 1)
c
3
, c
9
(u
55
+ u
54
+ ··· + 2u + 1)
c
4
, c
7
(u
55
+ 5u
54
+ ··· 4u 1)
c
6
, c
11
(u
55
+ 3u
54
+ ··· + 35u + 16)
c
8
, c
10
(u
55
+ 19u
54
+ ··· + 18u
2
1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
55
29y
54
+ ··· + 6y
2
1)
c
2
(y
55
5y
54
+ ··· + 12y 1)
c
3
, c
9
(y
55
+ 19y
54
+ ··· + 18y
2
1)
c
4
, c
7
(y
55
+ 31y
54
+ ··· 92y 1)
c
6
, c
11
(y
55
+ 39y
54
+ ··· 6167y 256)
c
8
, c
10
(y
55
+ 35y
54
+ ··· + 36y 1)
6