11a
110
(K11a
110
)
1
Arc Sequences
5 1 9 10 2 11 3 4 8 7 6
Solving Sequence
3,9
4 8 10 5 7 11 6 1 2
c
3
c
8
c
9
c
4
c
7
c
10
c
6
c
11
c
2
c
1
, c
5
Representation Ideals
I = I
u
1
I
u
1
= hu
48
u
47
+ ··· 2u
4
+ 1i
There are 1 irreducible components with 48 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
48
u
47
+ · · · 2u
4
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
5
=
u
6
u
4
+ 1
u
8
2u
6
2u
4
a
7
=
u
3
u
3
+ u
a
11
=
u
11
+ 2u
9
+ 2u
7
+ u
3
u
11
3u
9
4u
7
u
5
+ u
3
+ u
a
6
=
u
19
4u
17
8u
15
8u
13
5u
11
2u
9
2u
7
u
3
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
u
9
4u
7
2u
5
+ u
3
+ u
a
1
=
u
27
+ 6u
25
+ ··· + 4u
7
+ u
3
u
27
7u
25
+ ··· + u
3
+ u
a
2
=
u
41
+ 10u
39
+ ··· + 5u
5
u
u
43
+ 11u
41
+ ··· + u
3
+ u
a
2
=
u
41
+ 10u
39
+ ··· + 5u
5
u
u
43
+ 11u
41
+ ··· + u
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 = 0.772806 0.221383I
3.41452 + 3.72023I 1.09842 2.42491I
u = 0.772806 + 0.221383I
3.41452 3.72023I 1.09842 + 2.42491I
u = 0.738142 0.112136I
0.72805 + 4.58119I 0.34102 6.39238I
u = 0.738142 + 0.112136I
0.72805 4.58119I 0.34102 + 6.39238I
u = 0.617891 0.758063I
9.75907 + 2.28164I 5.95721 0.00795I
u = 0.617891 + 0.758063I
9.75907 2.28164I 5.95721 + 0.00795I
u = 0.613199 0.790716I
9.66500 7.07748I 5.61612 + 6.50457I
u = 0.613199 + 0.790716I
9.66500 + 7.07748I 5.61612 6.50457I
u = 0.531503 1.162886I
0.65137 8.58815I 2.17259 + 5.82135I
u = 0.531503 + 1.162886I
0.65137 + 8.58815I 2.17259 5.82135I
u = 0.523229 0.254780I
1.66920 0.31218I 6.04929 + 0.55460I
u = 0.523229 + 0.254780I
1.66920 + 0.31218I 6.04929 0.55460I
u = 0.488613 1.173547I
3.78897 9.13187I 3.52711 + 9.35882I
u = 0.488613 + 1.173547I
3.78897 + 9.13187I 3.52711 9.35882I
u = 0.465850 1.112228I
0.77690 3.72476I 1.95300 + 3.66807I
u = 0.465850 + 1.112228I
0.77690 + 3.72476I 1.95300 3.66807I
u = 0.399698 1.174710I
4.41403 + 0.70127I 5.15173 2.65109I
u = 0.399698 + 1.174710I
4.41403 0.70127I 5.15173 + 2.65109I
u = 0.324148 1.165865I
0.763972 + 0.284532I 4.14710 + 0.31000I
u = 0.324148 + 1.165865I
0.763972 0.284532I 4.14710 0.31000I
u = 0.311936 0.791100I
0.31404 1.44403I 2.46816 + 4.79849I
u = 0.311936 + 0.791100I
0.31404 + 1.44403I 2.46816 4.79849I
u = 0.088497 0.893701I
1.28610 1.69703I 6.44180 + 4.95354I
u = 0.088497 + 0.893701I
1.28610 + 1.69703I 6.44180 4.95354I
u = 0.296764 1.154119I
3.06688 + 3.96905I 0.33044 3.72206I
u = 0.296764 + 1.154119I
3.06688 3.96905I 0.33044 + 3.72206I
u = 0.318286 1.184978I
2.57490 5.01368I 1.05837 + 2.89086I
u = 0.318286 + 1.184978I
2.57490 + 5.01368I 1.05837 2.89086I
u = 0.428568 1.169496I
5.44153 + 3.53716I 7.56794 3.98603I
u = 0.428568 + 1.169496I
5.44153 3.53716I 7.56794 + 3.98603I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.456057 0.854553I
1.89118 + 4.83513I 2.88338 8.66489I
u = 0.456057 + 0.854553I
1.89118 4.83513I 2.88338 + 8.66489I
u = 0.466825 1.168189I
5.17049 + 4.81347I 6.85493 3.77558I
u = 0.466825 + 1.168189I
5.17049 4.81347I 6.85493 + 3.77558I
u = 0.466952 0.624404I
2.55221 0.92643I 6.15695 + 0.73591I
u = 0.466952 + 0.624404I
2.55221 + 0.92643I 6.15695 0.73591I
u = 0.536875 1.169141I
4.07278 + 13.47165I 0.85454 8.79515I
u = 0.536875 + 1.169141I
4.07278 13.47165I 0.85454 + 8.79515I
u = 0.537615 1.154107I
4.66901 + 4.18367I 1.84394 2.73999I
u = 0.537615 + 1.154107I
4.66901 4.18367I 1.84394 + 2.73999I
u = 0.602160 0.773225I
5.99169 + 2.35954I 2.55512 3.34973I
u = 0.602160 + 0.773225I
5.99169 2.35954I 2.55512 + 3.34973I
u = 0.703484 0.051909I
2.02079 0.49000I 3.99733 + 0.21349I
u = 0.703484 + 0.051909I
2.02079 + 0.49000I 3.99733 0.21349I
u = 0.769743 0.245615I
7.33658 + 0.70647I 5.00756 0.86082I
u = 0.769743 + 0.245615I
7.33658 0.70647I 5.00756 + 0.86082I
u = 0.792184 0.220376I
6.86889 8.53427I 4.08301 + 5.43363I
u = 0.792184 + 0.220376I
6.86889 + 8.53427I 4.08301 5.43363I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
48
+ u
47
+ ··· + 4u
3
+ 1)
c
2
(u
48
+ 27u
47
+ ··· + 28u
3
+ 1)
c
3
, c
8
(u
48
+ u
47
+ ··· 2u
4
+ 1)
c
4
, c
7
(u
48
+ u
47
+ ··· 44u + 17)
c
6
, c
10
, c
11
(u
48
+ 3u
47
+ ··· + 8u + 1)
c
9
(u
48
+ 25u
47
+ ··· 4u
2
+ 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
48
27y
47
+ ··· 28y
3
+ 1)
c
2
(y
48
11y
47
+ ··· + 308y
2
+ 1)
c
3
, c
8
(y
48
+ 25y
47
+ ··· 4y
2
+ 1)
c
4
, c
7
(y
48
31y
47
+ ··· + 2620y + 289)
c
6
, c
10
, c
11
(y
48
+ 49y
47
+ ··· + 56y + 1)
c
9
(y
48
3y
47
+ ··· 8y + 1)
6