11a
77
(K11a
77
)
1
Arc Sequences
6 1 11 9 2 3 4 10 5 8 7
Solving Sequence
1,6
2 3 7 5 11 4 8 10 9
c
1
c
2
c
6
c
5
c
11
c
3
c
7
c
10
c
9
c
4
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
65
u
64
+ ··· + 3u 1i
There are 1 irreducible components with 65 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
65
u
64
+ · · · + 3u 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
7
=
u
5
2u
3
u
u
5
+ u
3
+ u
a
5
=
u
u
3
+ u
a
11
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
u
10
2u
8
3u
6
2u
4
u
2
a
4
=
u
18
+ 5u
16
+ 12u
14
+ 17u
12
+ 15u
10
+ 9u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
18
4u
16
9u
14
12u
12
11u
10
6u
8
2u
6
u
2
a
8
=
u
31
+ 8u
29
+ ··· + 12u
7
+ 4u
5
u
31
7u
29
+ ··· 4u
7
+ u
a
10
=
u
52
+ 13u
50
+ ··· + u
2
+ 1
u
52
12u
50
+ ··· 2u
8
u
4
a
9
=
u
56
13u
54
+ ··· + u
4
+ 1
u
58
+ 14u
56
+ ··· + 2u
4
+ u
2
a
9
=
u
56
13u
54
+ ··· + u
4
+ 1
u
58
+ 14u
56
+ ··· + 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 = 0.758291 0.320143I
2.33998 4.47857I 3.88200 + 2.31592I
u = 0.758291 + 0.320143I
2.33998 + 4.47857I 3.88200 2.31592I
u = 0.695956 0.327319I
0.19197 2.46276I 3.81248 + 3.42438I
u = 0.695956 + 0.327319I
0.19197 + 2.46276I 3.81248 3.42438I
u = 0.684044 0.204074I
3.96704 1.98381I 1.83545 + 2.52797I
u = 0.684044 + 0.204074I
3.96704 + 1.98381I 1.83545 2.52797I
u = 0.661128 0.499003I
2.30161 3.09152I 10.04446 + 3.08842I
u = 0.661128 + 0.499003I
2.30161 + 3.09152I 10.04446 3.08842I
u = 0.643068 0.639899I
0.15648 + 8.12741I 7.24544 7.96091I
u = 0.643068 + 0.639899I
0.15648 8.12741I 7.24544 + 7.96091I
u = 0.642935 0.580003I
5.09135 + 2.55649I 13.39578 4.21201I
u = 0.642935 + 0.580003I
5.09135 2.55649I 13.39578 + 4.21201I
u = 0.565027 1.031629I
0.74043 + 7.86664I 6.95687 8.47685I
u = 0.565027 + 1.031629I
0.74043 7.86664I 6.95687 + 8.47685I
u = 0.563129 1.128905I
4.71040 + 9.46363I 0.71218 5.96163I
u = 0.563129 + 1.128905I
4.71040 9.46363I 0.71218 + 5.96163I
u = 0.560390 0.925994I
0.68502 3.40527I 5.84550 + 1.97177I
u = 0.560390 + 0.925994I
0.68502 + 3.40527I 5.84550 1.97177I
u = 0.558826 0.982733I
3.90580 + 2.15177I 11.37394 2.20893I
u = 0.558826 + 0.982733I
3.90580 2.15177I 11.37394 + 2.20893I
u = 0.548456 1.110996I
2.07374 + 7.24801I 0.44286 6.94914I
u = 0.548456 + 1.110996I
2.07374 7.24801I 0.44286 + 6.94914I
u = 0.512781 1.127881I
6.57059 + 6.52849I 1.42353 6.24475I
u = 0.512781 + 1.127881I
6.57059 6.52849I 1.42353 + 6.24475I
u = 0.334950 1.134059I
7.77271 + 1.28375I 3.33892 0.93529I
u = 0.334950 + 1.134059I
7.77271 1.28375I 3.33892 + 0.93529I
u = 0.285066 1.094866I
3.86299 + 0.19977I 3.23482 + 0.27466I
u = 0.285066 + 1.094866I
3.86299 0.19977I 3.23482 0.27466I
u = 0.248337 1.135168I
6.81733 1.64607I 2.42168 + 0.12311I
u = 0.248337 + 1.135168I
6.81733 + 1.64607I 2.42168 0.12311I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.074336 0.892519I
2.22679 2.52501I 1.11303 + 3.27520I
u = 0.074336 + 0.892519I
2.22679 + 2.52501I 1.11303 3.27520I
u = 0.232247 1.091922I
0.41947 + 2.11288I 4.80416 3.07590I
u = 0.232247 + 1.091922I
0.41947 2.11288I 4.80416 + 3.07590I
u = 0.237049 1.137455I
5.94902 + 7.42747I 0.69589 5.16735I
u = 0.237049 + 1.137455I
5.94902 7.42747I 0.69589 + 5.16735I
u = 0.348154 1.135213I
7.18458 7.06765I 2.06509 + 6.44159I
u = 0.348154 + 1.135213I
7.18458 + 7.06765I 2.06509 6.44159I
u = 0.355182 1.053114I
1.51926 2.99365I 3.32010 + 5.42677I
u = 0.355182 + 1.053114I
1.51926 + 2.99365I 3.32010 5.42677I
u = 0.458191
1.17985 8.77651
u = 0.502096 1.127009I
6.14634 0.74794I 0.696097 + 0.704227I
u = 0.502096 + 1.127009I
6.14634 + 0.74794I 0.696097 0.704227I
u = 0.522623 1.030148I
0.40000 3.37253I 3.73657 + 2.56528I
u = 0.522623 + 1.030148I
0.40000 + 3.37253I 3.73657 2.56528I
u = 0.529062 0.917260I
1.58337 2.03293I 3.89738 + 3.26899I
u = 0.529062 + 0.917260I
1.58337 + 2.03293I 3.89738 3.26899I
u = 0.553967 1.081516I
0.02873 3.68623I 6.08412 + 2.12264I
u = 0.553967 + 1.081516I
0.02873 + 3.68623I 6.08412 2.12264I
u = 0.560440 0.528463I
1.11205 0.99447I 6.38117 + 3.96144I
u = 0.560440 + 0.528463I
1.11205 + 0.99447I 6.38117 3.96144I
u = 0.566872 1.112853I
1.79362 9.57441I 8.04394 + 8.42502I
u = 0.566872 + 1.112853I
1.79362 + 9.57441I 8.04394 8.42502I
u = 0.568116 1.129190I
3.7395 15.2573I 2.52574 + 10.74972I
u = 0.568116 + 1.129190I
3.7395 + 15.2573I 2.52574 10.74972I
u = 0.620733 0.643139I
0.78159 2.53862I 5.40480 + 3.10900I
u = 0.620733 + 0.643139I
0.78159 + 2.53862I 5.40480 3.10900I
u = 0.674549 0.172737I
3.48204 3.70053I 2.82049 + 3.17595I
u = 0.674549 + 0.172737I
3.48204 + 3.70053I 2.82049 3.17595I
u = 0.681930 0.411486I
1.93533 1.09584I 9.59662 + 2.36982I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.681930 + 0.411486I
1.93533 + 1.09584I 9.59662 2.36982I
u = 0.738945 0.355594I
4.01245 + 4.61295I 11.51833 4.52005I
u = 0.738945 + 0.355594I
4.01245 4.61295I 11.51833 + 4.52005I
u = 0.766990 0.328520I
1.38595 + 10.22917I 5.69436 7.11928I
u = 0.766990 + 0.328520I
1.38595 10.22917I 5.69436 + 7.11928I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
65
+ u
64
+ ··· + 3u + 1)
c
2
(u
65
+ 31u
64
+ ··· + u 1)
c
3
(u
65
+ 7u
64
+ ··· + 1657u + 101)
c
4
(u
65
+ u
64
+ ··· u 1)
c
6
(u
65
+ u
64
+ ··· 191u 37)
c
7
(u
65
+ u
64
+ ··· 7u + 1)
c
8
, c
10
(u
65
+ 21u
64
+ ··· + u + 1)
c
9
(u
65
+ u
64
+ ··· u 1)
c
11
(u
65
+ 5u
64
+ ··· + 163u + 21)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
65
+ 31y
64
+ ··· + y 1)
c
2
(y
65
+ 7y
64
+ ··· + 9y 1)
c
3
(y
65
+ 19y
64
+ ··· + 722417y 10201)
c
4
(y
65
21y
64
+ ··· + y 1)
c
6
(y
65
17y
64
+ ··· + 2293y 1369)
c
7
(y
65
y
64
+ ··· + 33y 1)
c
8
, c
10
(y
65
+ 47y
64
+ ··· 7y 1)
c
9
(y
65
21y
64
+ ··· + y 1)
c
11
(y
65
+ 11y
64
+ ··· 30047y 441)
6