11a
263
(K11a
263
)
1
Arc Sequences
4 8 1 2 11 9 10 3 7 5 6
Solving Sequence
1,3
4
2,6,9
7 8 11 5 10
c
3
c
1
c
6
c
8
c
11
c
5
c
10
c
2
, c
4
, c
7
, c
9
Representation Ideals
I =
8
\
i=1
I
u
i
\
I
v
1
1
The knot diagram image is adapter from “C. Livingston and A. H. Mo ore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I
u
1
= hc, u 1, b + 1, da + 1i
I
u
2
= ha, c, u 1, d + 1, b + 1i
I
u
3
= hb, c, u 1, a + 1, d + 1i
I
u
4
= hb u, u
6
+ u
5
4u
4
3u
3
+ 4u
2
+ 2a + 2u + 1, u
7
+ u
6
4u
5
3u
4
+ 4u
3
+ 2u
2
+ 2d + u,
u
8
+ u
7
5u
6
4u
5
+ 8u
4
+ 3u
3
3u
2
+ 4u 1, u
7
2u
6
+ 5u
5
+ 9u
4
7u
3
10u
2
+ 2c + u 3i
I
u
5
= hb u, u
10
5u
8
+ u
7
+ 7u
6
5u
5
+ 6u
3
4u
2
+ d, u
10
u
9
+ 5u
8
+ 3u
7
9u
6
+ 6u
4
6u
3
+ c + 3u,
u
9
+ 2u
8
3u
7
6u
6
+ 3u
5
+ 2u
4
4u
3
+ 4u
2
+ a + 4u + 1,
u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1i
I
u
6
= h3a
5
+ 9a
4
+ 11a
3
+ 4a + 4u + 5, a
6
+ 2a
5
+ 2a
4
a
3
+ 4a
2
a + 1, a
5
5a
4
9a
3
6a
2
+ 4b + 2a 5,
a
5
5a
4
9a
3
6a
2
+ 4c 2a 5, a
5
+ 5a
4
+ 9a
3
+ 6a
2
+ 4d + 2a + 9i
I
u
7
= hu
9
5u
7
+ u
6
+ 7u
5
5u
4
+ 6u
2
+ a 4u, u
10
5u
8
+ u
7
+ 7u
6
5u
5
+ 6u
3
4u
2
+ d,
u
10
u
9
+ 5u
8
+ 3u
7
9u
6
+ 6u
4
6u
3
+ c + 3u,
u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1,
u
10
+ u
9
4u
8
3u
7
+ 5u
6
+ u
5
2u
4
+ 2u
3
+ u
2
+ b + u 1i
I
u
8
= hu
11
3u
9
+ 2u
8
+ 3u
7
4u
6
+ 2u
4
u
3
3u
2
+ 4,
20u
10
17u
9
+ 52u
8
13u
7
56u
6
+ 41u
5
6u
4
+ 28u
3
+ 18u
2
+ 86a 15u + 41,
3u
10
+ 34u
9
+ 25u
8
60u
7
17u
6
+ 90u
5
+ 12u
4
142u
3
+ 7u
2
+ 172b + 159u 82,
27u
10
+ 134u
9
+ 53u
8
368u
7
+ 191u
6
+ 294u
5
236u
4
+ 98u
3
+ 63u
2
+ 344c 117u 222,
109u
10
146u
9
163u
8
+ 460u
7
185u
6
174u
5
+ 252u
4
230u
3
+ 147u
2
+ 172d 273u + 170i
I
v
1
= ha, d, b 1, v 1, c + 1i
There are 9 irreducible components with 50 representations.
There are 1 irreducible components of dim
C
= 1 for 11a
263
2
I. I
u
1
= hc, u 1, b + 1, da + 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
1
a
4
=
1
1
a
2
=
0
1
a
6
=
a
1
a
9
=
0
d
a
7
=
a
d 1
a
8
=
0
d
a
11
=
a + 1
1
a
5
=
1
0
a
10
=
a
1
a
10
=
a
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
4.93480 10.99148 5.92212I
4
II. I
u
2
= ha, c, u 1, d + 1, b + 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
1
a
4
=
1
1
a
2
=
0
1
a
6
=
0
1
a
9
=
0
1
a
7
=
0
1
a
8
=
0
1
a
11
=
1
1
a
5
=
1
0
a
10
=
0
1
a
10
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
c = 0
d = 1.00000
3.28987 12.0000
6
III. I
u
3
= hb, c, u 1, a + 1, d + 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
1
a
4
=
1
1
a
2
=
0
1
a
6
=
1
0
a
9
=
0
1
a
7
=
1
1
a
8
=
0
1
a
11
=
1
0
a
5
=
1
0
a
10
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
3.28987 12.0000
8
IV. I
u
4
= hb u, u
6
+ u
5
+ · · · + 2a + 1, u
7
+ u
6
+ · · · + 2d + u, u
8
+ u
7
+
· · · + 4u 1, u
7
2u
6
+ · · · + 2c 3i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
2
=
u
2
+ 1
u
2
a
6
=
1
2
u
6
1
2
u
5
+ ··· u
1
2
u
a
9
=
1
2
u
7
+ u
6
+ ···
1
2
u +
3
2
1
2
u
7
1
2
u
6
+ ··· u
2
1
2
u
a
7
=
1
2
u
7
1
2
u
6
+ ···
1
2
u 1
1
2
u
6
+
1
2
u
5
+ ··· u +
1
2
a
8
=
1
2
u
7
+ u
6
+ ···
1
2
u +
3
2
1
2
u
6
+
1
2
u
5
+ ··· + u
1
2
a
11
=
1
2
u
7
+
1
2
u
6
+ ··· +
1
2
u + 1
u
2
a
5
=
u
3
2u
u
3
+ u
a
10
=
1
2
u
7
+
1
2
u
6
+ ··· +
1
2
u + 1
u
4
2u
2
a
10
=
1
2
u
7
+
1
2
u
6
+ ··· +
1
2
u + 1
u
4
2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.67197
a = 0.190462
b = 1.67197
c = 1.03628
d = 0.318446
17.5248 22.0160
u = 1.50879 0.39741I
a = 0.10075 + 1.41246I
b = 1.50879 0.39741I
c = 0.984897 0.284625I
d = 0.71334 2.09107I
16.0437 13.7204I 19.7312 + 6.7283I
u = 1.50879 + 0.39741I
a = 0.10075 1.41246I
b = 1.50879 + 0.39741I
c = 0.984897 + 0.284625I
d = 0.71334 + 2.09107I
16.0437 + 13.7204I 19.7312 6.7283I
u = 0.186694 0.577706I
a = 0.32268 + 1.48983I
b = 0.186694 0.577706I
c = 1.11546 0.96149I
d = 0.800440 + 0.464559I
1.02858 + 1.92389I 7.30727 5.93806I
u = 0.186694 + 0.577706I
a = 0.32268 1.48983I
b = 0.186694 + 0.577706I
c = 1.11546 + 0.96149I
d = 0.800440 0.464559I
1.02858 1.92389I 7.30727 + 5.93806I
u = 0.282608
a = 0.896884
b = 0.282608
c = 1.80440
d = 0.253467
0.633408 16.3408
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.51678 0.24068I
a = 0.467112 + 1.018907I
b = 1.51678 0.24068I
c = 0.180023 + 0.951886I
d = 0.95373 + 1.43303I
13.1698 + 5.8977I 19.7832 3.0693I
u = 1.51678 + 0.24068I
a = 0.467112 1.018907I
b = 1.51678 + 0.24068I
c = 0.180023 0.951886I
d = 0.95373 1.43303I
13.1698 5.8977I 19.7832 + 3.0693I
11
V. I
u
5
= hb u, u
10
5u
8
+ · · · 4u
2
+ d, u
10
u
9
+ · · · + c + 3u, u
9
+
2u
8
+ · · · + a + 1, u
11
+ 2u
10
+ · · · u 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
2
=
u
2
+ 1
u
2
a
6
=
u
9
2u
8
+ 3u
7
+ 6u
6
3u
5
2u
4
+ 4u
3
4u
2
4u 1
u
a
9
=
u
10
+ u
9
5u
8
3u
7
+ 9u
6
6u
4
+ 6u
3
3u
u
10
+ 5u
8
u
7
7u
6
+ 5u
5
6u
3
+ 4u
2
a
7
=
u
10
2u
9
+ 3u
8
+ 6u
7
3u
6
2u
5
+ 5u
4
4u
3
6u
2
u 1
u
10
5u
8
+ 2u
7
+ 8u
6
8u
5
2u
4
+ 8u
3
4u
2
+ u
a
8
=
u
10
+ u
9
5u
8
3u
7
+ 9u
6
6u
4
+ 6u
3
3u
2u
10
u
9
+ 10u
8
+ u
7
16u
6
+ 8u
5
+ 5u
4
13u
3
+ 6u
2
+ 1
a
11
=
u
10
+ 2u
9
3u
8
6u
7
+ 3u
6
+ 2u
5
4u
4
+ 4u
3
+ 4u
2
+ u + 1
u
2
a
5
=
u
3
2u
u
3
+ u
a
10
=
u
10
+ 2u
9
3u
8
6u
7
+ 3u
6
+ 2u
5
5u
4
+ 4u
3
+ 6u
2
+ u + 1
u
4
2u
2
a
10
=
u
10
+ 2u
9
3u
8
6u
7
+ 3u
6
+ 2u
5
5u
4
+ 4u
3
+ 6u
2
+ u + 1
u
4
2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.50982 0.17565I
a = 0.640009 + 0.807487I
b = 1.50982 0.17565I
c = 0.935118 0.134570I
d = 0.624556 0.992977I
11.90564 2.58451I 20.1919 + 1.0166I
u = 1.50982 + 0.17565I
a = 0.640009 0.807487I
b = 1.50982 + 0.17565I
c = 0.935118 + 0.134570I
d = 0.624556 + 0.992977I
11.90564 + 2.58451I 20.1919 1.0166I
u = 1.48612 0.29515I
a = 0.413574 + 1.254815I
b = 1.48612 0.29515I
c = 0.942990 + 0.224666I
d = 0.76197 + 1.60205I
10.05938 8.65115I 17.7857 + 5.5789I
u = 1.48612 + 0.29515I
a = 0.413574 1.254815I
b = 1.48612 + 0.29515I
c = 0.942990 0.224666I
d = 0.76197 1.60205I
10.05938 + 8.65115I 17.7857 5.5789I
u = 0.172742 0.362556I
a = 0.408469 + 1.047589I
b = 0.172742 0.362556I
c = 0.96499 + 1.35258I
d = 0.855030 + 0.431288I
1.55892 0.74196I 8.46073 + 1.11909I
u = 0.172742 + 0.362556I
a = 0.408469 1.047589I
b = 0.172742 + 0.362556I
c = 0.96499 1.35258I
d = 0.855030 0.431288I
1.55892 + 0.74196I 8.46073 1.11909I
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.399448 0.789847I
a = 0.46751 + 1.89798I
b = 0.399448 0.789847I
c = 0.977720 + 0.919514I
d = 0.602844 1.166019I
3.96110 + 4.69742I 14.9188 5.8832I
u = 0.399448 + 0.789847I
a = 0.46751 1.89798I
b = 0.399448 + 0.789847I
c = 0.977720 0.919514I
d = 0.602844 + 1.166019I
3.96110 4.69742I 14.9188 + 5.8832I
u = 0.780044
a = 4.76463
b = 0.780044
c = 0.708474
d = 0.120619
4.41605 21.4294
u = 1.379210 0.103381I
a = 1.49493 + 0.79079I
b = 1.379210 0.103381I
c = 0.096343 0.817001I
d = 0.344399 1.045409I
6.49548 + 2.41892I 16.9282 2.8895I
u = 1.379210 + 0.103381I
a = 1.49493 0.79079I
b = 1.379210 + 0.103381I
c = 0.096343 + 0.817001I
d = 0.344399 + 1.045409I
6.49548 2.41892I 16.9282 + 2.8895I
14
VI. I
u
6
= h3a
5
+ 4u + · · · + 4a + 5, a
6
+ 2a
5
+ · · · a + 1, a
5
+ 4b + · · · +
2a 5, a
5
+ 4c + · · · 2a 5, a
5
+ 4d + · · · + 2a + 9i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
3
4
a
5
9
4
a
4
+ ··· a
5
4
a
4
=
3
4
a
5
+
9
4
a
4
+
11
4
a
3
+ a +
5
4
3
4
a
5
9
4
a
4
+ ··· a
5
4
a
2
=
1
4
a
5
5
4
a
4
+ ···
1
2
a
5
4
1
4
a
5
+
5
4
a
4
+ ··· +
1
2
a +
9
4
a
6
=
a
1
4
a
5
+
5
4
a
4
+ ···
1
2
a +
5
4
a
9
=
1
4
a
5
+
5
4
a
4
+ ··· +
1
2
a +
5
4
1
4
a
5
5
4
a
4
+ ···
1
2
a
9
4
a
7
=
1
4
a
5
3
4
a
4
5
4
a
3
a
2
3
4
a
5
+ 3a
4
+ 4a
3
+ a
2
+ 2a + 2
a
8
=
1
4
a
5
+
5
4
a
4
+ ··· +
1
2
a +
5
4
a
5
7
2
a
4
+ ···
3
2
a
7
2
a
11
=
3
4
a
5
7
4
a
4
+ ···
3
2
a +
5
4
a
5
+
5
2
a
4
+ ··· +
5
2
a
1
2
a
5
=
3
4
a
5
+
9
4
a
4
+
11
4
a
3
+ a +
1
4
1
a
10
=
1
4
a
5
+
3
4
a
4
+
5
4
a
3
+ a
2
+
3
4
3
4
a
5
+
5
4
a
4
+ ··· + 3a
7
4
a
10
=
1
4
a
5
+
3
4
a
4
+
5
4
a
3
+ a
2
+
3
4
3
4
a
5
+
5
4
a
4
+ ··· + 3a
7
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
15
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.662359 0.562280I
a = 1.53980 1.30714I
b = 0.662359 + 0.562280I
c = 0.877439 0.744862I
d = 0.122561 + 0.744862I
4.93480 18.0000
u = 0.662359 + 0.562280I
a = 1.53980 + 1.30714I
b = 0.662359 0.562280I
c = 0.877439 + 0.744862I
d = 0.122561 0.744862I
4.93480 18.0000
u = 1.32472
a = 0.092519 0.562280I
b = 0.662359 + 0.562280I
c = 0.754878
d = 1.75488
4.93480 18.0000
u = 1.32472
a = 0.092519 + 0.562280I
b = 0.662359 0.562280I
c = 0.754878
d = 1.75488
4.93480 18.0000
u = 0.662359 0.562280I
a = 0.447279 0.744862I
b = 1.32472
c = 0.877439 0.744862I
d = 0.122561 + 0.744862I
4.93480 18.0000
u = 0.662359 + 0.562280I
a = 0.447279 + 0.744862I
b = 1.32472
c = 0.877439 + 0.744862I
d = 0.122561 0.744862I
4.93480 18.0000
16
VII. I
u
7
= hu
9
5u
7
+ · · · + a 4u, u
10
5u
8
+ · · · 4u
2
+ d, u
10
u
9
+
· · · + c + 3u, u
11
+ 2u
10
+ · · · u 1, u
10
+ u
9
+ · · · + b 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
2
=
u
2
+ 1
u
2
a
6
=
u
9
+ 5u
7
u
6
7u
5
+ 5u
4
6u
2
+ 4u
u
10
u
9
+ 4u
8
+ 3u
7
5u
6
u
5
+ 2u
4
2u
3
u
2
u + 1
a
9
=
u
10
+ u
9
5u
8
3u
7
+ 9u
6
6u
4
+ 6u
3
3u
u
10
+ 5u
8
u
7
7u
6
+ 5u
5
6u
3
+ 4u
2
a
7
=
u
10
5u
8
+ 2u
7
+ 7u
6
8u
5
+ u
4
+ 7u
3
6u
2
+ 3u 1
3u
10
2u
9
+ 13u
8
+ 4u
7
18u
6
+ 6u
5
+ 6u
4
13u
3
+ 2u
2
+ 2
a
8
=
u
10
+ u
9
5u
8
3u
7
+ 9u
6
6u
4
+ 6u
3
3u
2u
10
u
9
+ 10u
8
+ u
7
16u
6
+ 8u
5
+ 5u
4
13u
3
+ 6u
2
+ 1
a
11
=
u
9
5u
7
+ 2u
6
+ 8u
5
8u
4
2u
3
+ 8u
2
4u + 1
u
10
5u
8
+ u
7
+ 7u
6
5u
5
+ 6u
3
3u
2
2
a
5
=
u
3
2u
u
3
+ u
a
10
=
u
10
+ 5u
8
2u
7
7u
6
+ 8u
5
u
4
7u
3
+ 6u
2
3u + 1
3u
10
+ u
9
15u
8
u
7
+ 23u
6
10u
5
7u
4
+ 17u
3
5u
2
u 3
a
10
=
u
10
+ 5u
8
2u
7
7u
6
+ 8u
5
u
4
7u
3
+ 6u
2
3u + 1
3u
10
+ u
9
15u
8
u
7
+ 23u
6
10u
5
7u
4
+ 17u
3
5u
2
u 3
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.50982 0.17565I
a = 0.332646 + 0.696378I
b = 0.986131 0.772404I
c = 0.935118 0.134570I
d = 0.624556 0.992977I
11.90564 2.58451I 20.1919 + 1.0166I
u = 1.50982 + 0.17565I
a = 0.332646 0.696378I
b = 0.986131 + 0.772404I
c = 0.935118 + 0.134570I
d = 0.624556 + 0.992977I
11.90564 + 2.58451I 20.1919 1.0166I
u = 1.48612 0.29515I
a = 0.287300 1.135070I
b = 0.360061 + 1.006502I
c = 0.942990 + 0.224666I
d = 0.76197 + 1.60205I
10.05938 8.65115I 17.7857 + 5.5789I
u = 1.48612 + 0.29515I
a = 0.287300 + 1.135070I
b = 0.360061 1.006502I
c = 0.942990 0.224666I
d = 0.76197 1.60205I
10.05938 + 8.65115I 17.7857 5.5789I
u = 0.172742 0.362556I
a = 0.05373 2.38394I
b = 1.124760 + 0.136043I
c = 0.96499 + 1.35258I
d = 0.855030 + 0.431288I
1.55892 0.74196I 8.46073 + 1.11909I
u = 0.172742 + 0.362556I
a = 0.05373 + 2.38394I
b = 1.124760 0.136043I
c = 0.96499 1.35258I
d = 0.855030 0.431288I
1.55892 + 0.74196I 8.46073 1.11909I
18
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.399448 0.789847I
a = 0.86821 1.20232I
b = 1.378091 + 0.194114I
c = 0.977720 + 0.919514I
d = 0.602844 1.166019I
3.96110 + 4.69742I 14.9188 5.8832I
u = 0.399448 + 0.789847I
a = 0.86821 + 1.20232I
b = 1.378091 0.194114I
c = 0.977720 0.919514I
d = 0.602844 + 1.166019I
3.96110 4.69742I 14.9188 + 5.8832I
u = 0.780044
a = 0.154632
b = 1.12735
c = 0.708474
d = 0.120619
4.41605 21.4294
u = 1.379210 0.103381I
a = 0.191815 0.772355I
b = 0.529187 + 0.718311I
c = 0.096343 0.817001I
d = 0.344399 1.045409I
6.49548 + 2.41892I 16.9282 2.8895I
u = 1.379210 + 0.103381I
a = 0.191815 + 0.772355I
b = 0.529187 0.718311I
c = 0.096343 + 0.817001I
d = 0.344399 + 1.045409I
6.49548 2.41892I 16.9282 + 2.8895I
19
VIII. I
u
8
=
hu
11
3u
9
+· · ·3u
2
+4, 20u
10
17u
9
+· · ·+86a + 41, 3u
10
+34u
9
+· · ·+
172b82, 27u
10
+134u
9
+· · ·+344c222, 109u
10
146u
9
+· · ·+172d+170i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
2
=
u
2
+ 1
u
2
a
6
=
0.232558u
10
+ 0.197674u
9
+ ··· + 0.174419u 0.476744
0.0174419u
10
0.197674u
9
+ ··· 0.924419u + 0.476744
a
9
=
0.0784884u
10
0.389535u
9
+ ··· + 0.340116u + 0.645349
0.633721u
10
+ 0.848837u
9
+ ··· + 1.58721u 0.988372
a
7
=
0.0377907u
10
+ 0.238372u
9
+ ··· 0.00290698u 0.633721
0.441860u
10
0.674419u
9
+ ··· 1.41860u + 1.74419
a
8
=
0.0784884u
10
0.389535u
9
+ ··· + 0.340116u + 0.645349
0.715116u
10
+ 1.10465u
9
+ ··· + 1.90116u 2.54651
a
11
=
0.0784884u
10
+ 0.110465u
9
+ ··· 0.159884u + 1.14535
0.197674u
10
0.0930233u
9
+ ··· + 0.476744u 1.06977
a
5
=
u
3
2u
u
3
+ u
a
10
=
0.0377907u
10
0.238372u
9
+ ··· + 0.00290698u + 0.633721
0.279070u
10
+ 0.162791u
9
+ ··· + 0.790698u 0.627907
a
10
=
0.0377907u
10
0.238372u
9
+ ··· + 0.00290698u + 0.633721
0.279070u
10
+ 0.162791u
9
+ ··· + 0.790698u 0.627907
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
20
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.378091 0.194114I
a = 0.312076 0.890070I
b = 0.399448 + 0.789847I
c = 0.835232 0.176201I
d = 1.31237 1.12740I
3.96110 4.69742I 14.9188 + 5.8832I
u = 1.378091 + 0.194114I
a = 0.312076 + 0.890070I
b = 0.399448 0.789847I
c = 0.835232 + 0.176201I
d = 1.31237 + 1.12740I
3.96110 + 4.69742I 14.9188 5.8832I
u = 1.12735
a = 0.106994
b = 0.780044
c = 0.490213
d = 3.71662
4.41605 21.4294
u = 0.529187 0.718311I
a = 0.714410 1.005770I
b = 1.379210 + 0.103381I
c = 0.863352 0.938610I
d = 2.14358 0.93612I
6.49548 2.41892I 16.9282 + 2.8895I
u = 0.529187 + 0.718311I
a = 0.714410 + 1.005770I
b = 1.379210 0.103381I
c = 0.863352 + 0.938610I
d = 2.14358 + 0.93612I
6.49548 + 2.41892I 16.9282 2.8895I
u = 0.360061 1.006502I
a = 1.17102 1.17596I
b = 1.48612 + 0.29515I
c = 0.959920 0.983061I
d = 0.98497 + 1.74274I
10.05938 + 8.65115I 17.7857 5.5789I
21
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.360061 + 1.006502I
a = 1.17102 + 1.17596I
b = 1.48612 0.29515I
c = 0.959920 + 0.983061I
d = 0.98497 1.74274I
10.05938 8.65115I 17.7857 + 5.5789I
u = 0.986131 0.772404I
a = 0.881338 0.316619I
b = 1.50982 0.17565I
c = 0.691602 + 0.914308I
d = 1.10814 1.10674I
11.90564 2.58451I 20.1919 + 1.0166I
u = 0.986131 + 0.772404I
a = 0.881338 + 0.316619I
b = 1.50982 + 0.17565I
c = 0.691602 0.914308I
d = 1.10814 + 1.10674I
11.90564 + 2.58451I 20.1919 1.0166I
u = 1.124760 0.136043I
a = 0.703518 0.468542I
b = 0.172742 + 0.362556I
c = 0.221796 + 0.545613I
d = 0.309250 + 0.329055I
1.55892 + 0.74196I 8.46073 1.11909I
u = 1.124760 + 0.136043I
a = 0.703518 + 0.468542I
b = 0.172742 0.362556I
c = 0.221796 0.545613I
d = 0.309250 0.329055I
1.55892 0.74196I 8.46073 + 1.11909I
22
IX. I
v
1
= ha, d, b 1, v 1, c + 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
1
0
a
4
=
1
0
a
2
=
1
0
a
6
=
0
1
a
9
=
1
0
a
7
=
1
1
a
8
=
1
0
a
11
=
1
1
a
5
=
1
0
a
10
=
0
1
a
10
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
23
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 1.00000
d = 0
3.28987 12.0000
24
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
, c
4
u(u 1)
3
(u
3
u + 1)
2
(u
8
+ u
7
5u
6
4u
5
+ 8u
4
+ 3u
3
3u
2
+ 4u 1)
(u
11
3u
9
+ 2u
8
+ 3u
7
4u
6
+ 2u
4
u
3
3u
2
+ 4)
(u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1)
2
c
2
, c
8
u
4
(u 1)
6
(u
8
+ u
7
u
6
5u
5
4u
4
+ 8u
2
4u 4)
(u
11
+ 2u
10
u
9
3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
2u 2)
3
c
5
u(u + 1)
3
(u
3
u + 1)
2
(u
8
+ u
7
5u
6
4u
5
+ 8u
4
+ 3u
3
3u
2
+ 4u 1)
(u
11
3u
9
+ 2u
8
+ 3u
7
4u
6
+ 2u
4
u
3
3u
2
+ 4)
(u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1)
2
c
6
, c
7
u(u 1)
2
(u + 1)(u
3
u + 1)
2
(u
8
+ u
7
5u
6
4u
5
+ 8u
4
+ 3u
3
3u
2
+ 4u 1)
(u
11
3u
9
+ 2u
8
+ 3u
7
4u
6
+ 2u
4
u
3
3u
2
+ 4)
(u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1)
2
c
9
, c
10
, c
11
u(u 1)(u + 1)
2
(u
3
u + 1)
2
(u
8
+ u
7
5u
6
4u
5
+ 8u
4
+ 3u
3
3u
2
+ 4u 1)
(u
11
3u
9
+ 2u
8
+ 3u
7
4u
6
+ 2u
4
u
3
3u
2
+ 4)
(u
11
+ 2u
10
4u
9
8u
8
+ 6u
7
+ 8u
6
7u
5
+ 2u
4
+ 7u
3
3u
2
u 1)
2
25
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y(y 1)
3
(y
3
2y
2
+ y 1)
2
(y
8
11y
7
+ 49y
6
108y
5
+ 108y
4
15y
3
31y
2
10y + 1)
(1 5y 19y
2
+ 91y
3
82y
4
+ 65y
5
162y
6
+ 226y
7
158y
8
+ 60y
9
12y
10
+ y
11
)
2
(y
11
6y
10
+ ··· + 24y 16)
c
2
, c
8
y
4
(y 1)
6
(y
8
3y
7
+ 3y
6
y
5
96y
3
+ 96y
2
80y + 16)
(4 + 8y + 7y
2
+ 51y
3
69y
4
+ 8y
5
+ 44y
6
21y
7
11y
8
+ 15y
9
6y
10
+ y
11
)
3
26