11a
44
(K11a
44
)
1
Arc Sequences
4 1 8 2 11 9 3 6 7 5 10
Solving Sequence
1,4
2 3
5,7 8,10
9 6 11
c
1
c
2
c
4
c
7
c
9
c
6
c
11
c
3
, c
5
, c
8
, c
10
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
= ha, u 1, d + 1, cb + 1i
I
u
2
= ha, c, u 1, d + 1, b + 1i
I
u
3
= ha, d, b 1, c 1, u 1i
I
u
4
= ha + u, u
2
+ d, u
3
+ b u, 2u
4
2u
3
+ c + 2u + 1, u
6
+ u
5
u
4
2u
3
+ u + 1i
I
u
5
= hd
12
+ 9d
11
+ 34d
10
+ 68d
9
+ 73d
8
+ 33d
7
5d
6
+ d
5
+ 25d
4
+ 23d
3
+ 2d
2
4d + 1,
22d
11
148d
10
+ ··· + 69a + 40, 56d
11
+ 452d
10
+ ··· + 69b 14,
10d
11
61d
10
+ ··· + 69c 101,
22d
11
+ 148d
10
+ 374d
9
+ 370d
8
88d
7
523d
6
408d
5
+ 46d
4
+ 182d
3
77d
2
126d + 69u 40i
I
u
6
= hu
2
+ d, u
17
+ u
16
+ ··· + 2b + 1, u
18
2u
17
+ ··· + 4c 4, u
19
+ 2u
18
+ ··· + 3u + 1,
u
18
+ 2u
17
+ ··· + 2a + 3i
I
u
7
= hu
10
3u
8
2u
7
+ 2u
6
+ 4u
5
+ 3u
4
3u
2
+ a 3u 1, u
10
+ 2u
8
+ 2u
7
u
6
2u
5
2u
4
u
3
+ u
2
+ b + u,
u
11
3u
9
2u
8
+ 2u
7
+ 4u
6
+ 3u
5
3u
3
3u
2
+ d u,
u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1,
u
11
4u
9
2u
8
+ 6u
7
+ 6u
6
2u
5
6u
4
3u
3
+ 2u
2
+ c + 2u 1i
I
u
8
= hu
16
+ u
15
3u
14
5u
13
+ 3u
12
+ 9u
11
+ 2u
10
8u
9
6u
8
+ 2u
7
+ 5u
6
+ u
5
u
4
+ 2u
3
+ 3u
2
4u 4,
221u
15
273u
14
+ ··· + 2360a 470, 727u
15
+ 393u
14
+ ··· + 1180b 2866,
593u
15
31u
14
+ ··· + 2360c + 850, 85u
15
13u
14
+ ··· + 590d + 1152i
I
v
1
= hb, c, v 1, d + 1, a 1i
There are 9 irreducible components with 68 representations.
There are 1 irreducible components of dim
C
= 1 for 11a
44
2
I. I
u
1
= ha, u 1, d + 1, cb + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
0
1
a
5
=
1
0
a
7
=
0
b
a
8
=
0
b
a
10
=
c
1
a
9
=
c
b 1
a
6
=
c
1
a
11
=
c + 1
1
a
11
=
c + 1
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 = ···
1.64493 2.82963 0.26612I
4
II. I
u
2
= ha, c, u 1, d + 1, b + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
0
1
a
5
=
1
0
a
7
=
0
1
a
8
=
0
1
a
10
=
0
1
a
9
=
0
1
a
6
=
0
1
a
11
=
1
1
a
11
=
1
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
= ha, d, b 1, c 1, u 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
3
=
0
1
a
5
=
1
0
a
7
=
0
1
a
8
=
0
1
a
10
=
1
0
a
9
=
1
1
a
6
=
1
0
a
11
=
1
0
a
11
=
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 = 0
b = 1.00000
c = 1.00000
d = 0
0 0
8
IV.
I
u
4
= ha+u, u
2
+d, u
3
+bu, 2u
4
2u
3
+c+2u+1, u
6
+u
5
u
4
2u
3
+u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
u
3
+ u
a
8
=
u
4
+ u
2
1
u
5
+ u
4
2u
3
u
2
+ u + 1
a
10
=
2u
4
+ 2u
3
2u 1
u
2
a
9
=
2u
4
+ 2u
3
u
2
2u 1
u
4
a
6
=
2u
5
2u
4
+ u
3
+ 2u
2
u
5
u
3
+ u
a
11
=
2u
4
+ 2u
3
u
2
2u 1
u
4
a
11
=
2u
4
+ 2u
3
u
2
2u 1
u
4
(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 = 1.073950 0.558752I
a = 1.073950 + 0.558752I
b = 0.84116 + 1.20014I
c = 0.78324 + 1.63778I
d = 0.84116 1.20014I
5.69302I 5.51057I
u = 1.073950 + 0.558752I
a = 1.073950 0.558752I
b = 0.84116 1.20014I
c = 0.78324 1.63778I
d = 0.84116 + 1.20014I
5.69302I 5.51057I
u = 0.428243 0.664531I
a = 0.428243 + 0.664531I
b = 0.917045 0.592379I
c = 0.319544 + 0.596907I
d = 0.258209 0.569162I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 + 0.664531I
a = 0.428243 0.664531I
b = 0.917045 + 0.592379I
c = 0.319544 0.596907I
d = 0.258209 + 0.569162I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 0.295542I
a = 1.002193 + 0.295542I
b = 0.258209 + 0.569162I
c = 0.53630 3.31128I
d = 0.917045 + 0.592379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 1.002193 0.295542I
b = 0.258209 0.569162I
c = 0.53630 + 3.31128I
d = 0.917045 0.592379I
1.89061 0.92430I 3.71672 + 0.79423I
10
V.
I
u
5
= hd
12
+9d
11
+· · ·4d+1, 22d
11
148d
10
+· · ·+69a+40, 56d
11
+452d
10
+
· · · + 69b 14, 10d
11
61d
10
+ · · · + 69c 101, 22d
11
+ 69u + · · · 126d 40i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
0.318841d
11
2.14493d
10
+ ··· + 1.82609d + 0.579710
a
2
=
1
0.275362d
11
+ 2.57971d
10
+ ··· + 0.695652d + 0.681159
a
3
=
0.275362d
11
2.57971d
10
+ ··· 0.695652d + 0.318841
0.275362d
11
+ 2.57971d
10
+ ··· + 0.695652d + 0.681159
a
5
=
0.318841d
11
+ 2.14493d
10
+ ··· 1.82609d 0.579710
0.811594d
11
6.55072d
10
+ ··· + 0.739130d + 0.202899
a
7
=
0.318841d
11
+ 2.14493d
10
+ ··· 1.82609d 0.579710
0.811594d
11
6.55072d
10
+ ··· + 0.739130d + 0.202899
a
8
=
0.376812d
11
2.89855d
10
+ ··· 0.478261d 0.405797
d
3
+ 2d
2
+ d
a
10
=
0.144928d
11
+ 0.884058d
10
+ ··· 1.73913d + 1.46377
d
a
9
=
0.420290d
11
+ 3.46377d
10
+ ··· 2.04348d + 1.14493
d
2
a
6
=
0.188406d
11
1.44928d
10
+ ··· + 0.260870d 1.20290
1.39130d
11
+ 10.0870d
10
+ ··· 5.69565d + 1.65217
a
11
=
0.420290d
11
+ 3.46377d
10
+ ··· 2.04348d + 1.14493
d
2
a
11
=
0.420290d
11
+ 3.46377d
10
+ ··· 2.04348d + 1.14493
d
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 1.073950 0.558752I
b = 0.84116 1.20014I
c = 0.109214 0.714907I
d = 1.76612 0.73243I
5.69302I 5.51057I
u = 1.073950 0.558752I
a = 1.073950 + 0.558752I
b = 0.84116 + 1.20014I
c = 0.109214 + 0.714907I
d = 1.76612 + 0.73243I
5.69302I 5.51057I
u = 0.428243 0.664531I
a = 0.428243 + 0.664531I
b = 0.917045 0.592379I
c = 0.055560 + 1.311364I
d = 1.73203 0.37023I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 + 0.664531I
a = 0.428243 0.664531I
b = 0.917045 + 0.592379I
c = 0.055560 1.311364I
d = 1.73203 + 0.37023I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 0.295542I
a = 1.002193 + 0.295542I
b = 0.258209 + 0.569162I
c = 0.008329 0.488867I
d = 1.297233 0.443379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 1.002193 0.295542I
b = 0.258209 0.569162I
c = 0.008329 + 0.488867I
d = 1.297233 + 0.443379I
1.89061 0.92430I 3.71672 + 0.79423I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 0.428243 0.664531I
b = 0.917045 + 0.592379I
c = 1.05556 + 1.31136I
d = 0.526177 0.939391I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.428243 0.664531I
a = 0.428243 + 0.664531I
b = 0.917045 0.592379I
c = 1.05556 1.31136I
d = 0.526177 + 0.939391I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 0.295542I
a = 1.002193 + 0.295542I
b = 0.258209 + 0.569162I
c = 1.008329 + 0.488867I
d = 0.214278 0.149000I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 1.002193 0.295542I
b = 0.258209 0.569162I
c = 1.008329 0.488867I
d = 0.214278 + 0.149000I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.073950 + 0.558752I
a = 1.073950 0.558752I
b = 0.84116 1.20014I
c = 0.890786 + 0.714907I
d = 0.607288 0.467717I
5.69302I 5.51057I
u = 1.073950 0.558752I
a = 1.073950 + 0.558752I
b = 0.84116 + 1.20014I
c = 0.890786 0.714907I
d = 0.607288 + 0.467717I
5.69302I 5.51057I
13
VI. I
u
6
= hu
2
+ d, u
17
+ u
16
+ · · · + 2b + 1, u
18
2u
17
+ · · · + 4c
4, u
19
+ 2u
18
+ · · · + 3u + 1, u
18
+ 2u
17
+ · · · + 2a + 3i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
1
2
u
18
u
17
+ ··· +
1
2
u
3
2
1
2
u
17
1
2
u
16
+ ··· + u
1
2
a
8
=
u
18
3
2
u
17
+ ··· +
1
2
u 2
1
2
u
17
+ 2u
15
+ ··· +
9
2
u
2
1
a
10
=
1
4
u
18
+
1
2
u
17
+ ···
1
4
u + 1
u
2
a
9
=
1
2
u
18
+
3
4
u
17
+ ···
3
4
u +
9
4
1
2
u
18
+
3
4
u
17
+ ··· +
1
4
u +
3
4
a
6
=
1
4
u
17
1
2
u
16
+ ···
5
4
u +
1
4
u
5
u
3
+ u
a
11
=
1
4
u
18
+
1
2
u
17
+ ···
1
4
u + 1
u
4
a
11
=
1
4
u
18
+
1
2
u
17
+ ···
1
4
u + 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.219915 0.612443I
a = 1.84038 + 0.77324I
b = 1.97753 + 1.24306I
c = 1.10074 + 1.33083I
d = 1.11311 1.49426I
2.5538 15.5977I 0.09598 + 9.40344I
u = 1.219915 + 0.612443I
a = 1.84038 0.77324I
b = 1.97753 1.24306I
c = 1.10074 1.33083I
d = 1.11311 + 1.49426I
2.5538 + 15.5977I 0.09598 9.40344I
u = 1.163712 0.575900I
a = 1.49922 0.61081I
b = 1.46155 1.34018I
c = 1.02511 + 1.49171I
d = 1.02256 1.34036I
2.61225 10.89709I 3.23641 + 8.50579I
u = 1.163712 + 0.575900I
a = 1.49922 + 0.61081I
b = 1.46155 + 1.34018I
c = 1.02511 1.49171I
d = 1.02256 + 1.34036I
2.61225 + 10.89709I 3.23641 8.50579I
u = 0.892218 0.798617I
a = 0.118380 1.254991I
b = 0.031342 + 0.273386I
c = 0.385453 + 1.040442I
d = 0.15826 1.42508I
9.74824 5.99256I 5.35093 + 5.49640I
u = 0.892218 + 0.798617I
a = 0.118380 + 1.254991I
b = 0.031342 0.273386I
c = 0.385453 1.040442I
d = 0.15826 + 1.42508I
9.74824 + 5.99256I 5.35093 5.49640I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.713652 0.621261I
a = 0.078489 + 0.212487I
b = 0.548223 + 0.458686I
c = 0.127668 + 1.140610I
d = 0.123333 0.886728I
2.40223 3.63220I 3.52732 + 6.81616I
u = 0.713652 + 0.621261I
a = 0.078489 0.212487I
b = 0.548223 0.458686I
c = 0.127668 1.140610I
d = 0.123333 + 0.886728I
2.40223 + 3.63220I 3.52732 6.81616I
u = 0.379493 0.913957I
a = 1.49556 0.97073I
b = 1.46152 + 0.68811I
c = 0.012242 + 0.415167I
d = 0.691302 0 .693681I
7.80660 + 4.21764I 6.24313 1.77538I
u = 0.379493 + 0.913957I
a = 1.49556 + 0.97073I
b = 1.46152 0.68811I
c = 0.012242 0.415167I
d = 0.691302 + 0 .693681I
7.80660 4.21764I 6.24313 + 1.77538I
u = 0.266152
a = 1.40639
b = 0.642422
c = 1.15247
d = 0.0708367
1.20822 9.19790
u = 0.587370 0.660248I
a = 1.52616 2.19030I
b = 1.002697 + 0.800999I
c = 0.217752 0.865792I
d = 0.090924 + 0 .775620I
4.14406 + 1.22871I 4.10945 3.37998I
16
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.587370 + 0.660248I
a = 1.52616 + 2.19030I
b = 1.002697 0.800999I
c = 0.217752 + 0.865792I
d = 0.090924 0.775620I
4.14406 1.22871I 4.10945 + 3.37998I
u = 0.710407 0.203370I
a = 0.573689 + 1.178553I
b = 0.246691 0.049771I
c = 1.88912 1.55551I
d = 0.463319 + 0.288950I
1.32552 + 1.22673I 3.58366 5.47914I
u = 0.710407 + 0.203370I
a = 0.573689 1.178553I
b = 0.246691 + 0.049771I
c = 1.88912 + 1.55551I
d = 0.463319 0.288950I
1.32552 1.22673I 3.58366 + 5.47914I
u = 1.085303 0.470880I
a = 1.74507 + 0.02900I
b = 0.757420 1.122886I
c = 0.91621 1.95317I
d = 0.956154 + 1.022095I
4.29720 + 4.85510I 5.63265 5.33490I
u = 1.085303 + 0.470880I
a = 1.74507 0.02900I
b = 0.757420 + 1.122886I
c = 0.91621 + 1.95317I
d = 0.956154 1.022095I
4.29720 4.85510I 5.63265 + 5.33490I
u = 1.118985 0.584861I
a = 2.37984 0.16413I
b = 1.30952 + 1.42851I
c = 0.89551 1.52082I
d = 0.91007 + 1.30890I
0.71510 + 8.68076I 0.47305 6.48182I
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.118985 + 0.584861I
a = 2.37984 + 0.16413I
b = 1.30952 1.42851I
c = 0.89551 + 1.52082I
d = 0.91007 1.30890I
0.71510 8.68076I 0.47305 + 6.48182I
17
VII. I
u
7
= hu
10
3u
8
+ · · · + a 1, u
10
+ 2u
8
+ · · · + b + u, u
11
3u
9
+
· · · + d u, u
12
u
11
+ · · · + 2u
2
+ 1, u
11
4u
9
+ · · · + c 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
10
+ 3u
8
+ 2u
7
2u
6
4u
5
3u
4
+ 3u
2
+ 3u + 1
u
10
2u
8
2u
7
+ u
6
+ 2u
5
+ 2u
4
+ u
3
u
2
u
a
8
=
u
7
2u
5
u
4
+ u
2
+ 2u + 1
u
7
+ u
6
+ u
5
u
2
u
a
10
=
u
11
+ 4u
9
+ 2u
8
6u
7
6u
6
+ 2u
5
+ 6u
4
+ 3u
3
2u
2
2u + 1
u
11
+ 3u
9
+ 2u
8
2u
7
4u
6
3u
5
+ 3u
3
+ 3u
2
+ u
a
9
=
2u
11
+ 7u
9
+ 4u
8
8u
7
10u
6
u
5
+ 6u
4
+ 6u
3
+ u
2
u + 1
u
9
u
7
2u
6
u
5
+ u
4
+ 2u
3
+ 2u
2
+ u
a
6
=
2u
11
8u
9
3u
8
+ 10u
7
+ 9u
6
7u
4
7u
3
+ 2u 1
u
8
+ 2u
6
+ u
5
u
3
2u
2
u
a
11
=
u
9
4u
7
2u
6
+ 5u
5
+ 6u
4
4u
2
3u
u
9
+ 3u
7
+ 2u
6
3u
5
4u
4
+ 2u
2
+ u
a
11
=
u
9
4u
7
2u
6
+ 5u
5
+ 6u
4
4u
2
3u
u
9
+ 3u
7
+ 2u
6
3u
5
4u
4
+ 2u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
18
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.155020 0.191936I
a = 0.689693 0.627483I
b = 0.15460 + 3.71488I
c = 0.197010 + 0.389313I
d = 0.917045 + 0.592379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.155020 + 0.191936I
a = 0.689693 + 0.627483I
b = 0.15460 3.71488I
c = 0.197010 0.389313I
d = 0.917045 0.592379I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.895235 0.524661I
a = 0.492029 0.347410I
b = 0.103539 0.942817I
c = 1.032251 0.761198I
d = 0.258209 + 0.569162I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.895235 + 0.524661I
a = 0.492029 + 0.347410I
b = 0.103539 + 0.942817I
c = 1.032251 + 0.761198I
d = 0.258209 0.569162I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.282166 0.828798I
a = 0.98800 1.35129I
b = 1.16959 + 0.91104I
c = 0.79119 1.36688I
d = 0.84116 + 1.20014I
5.69302I 5.51057I
u = 0.282166 + 0.828798I
a = 0.98800 + 1.35129I
b = 1.16959 0.91104I
c = 0.79119 + 1.36688I
d = 0.84116 1.20014I
5.69302I 5.51057I
19
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.152828 0.487477I
a = 0.56945 2.05973I
b = 0.101098 + 0.828455I
c = 1.03484 + 2.04495I
d = 0.917045 0.592379I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.152828 + 0.487477I
a = 0.56945 + 2.05973I
b = 0.101098 0.828455I
c = 1.03484 2.04495I
d = 0.917045 + 0.592379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.323479 0.139870I
a = 0.147997 + 0.445691I
b = 1.18901 0.78206I
c = 0.627522 + 0.462745I
d = 0.258209 + 0.569162I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.323479 + 0.139870I
a = 0.147997 0.445691I
b = 1.18901 + 0.78206I
c = 0.627522 0.462745I
d = 0.258209 0.569162I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.356115 0.270046I
a = 0.427109 0.970037I
b = 1.01075 + 1.59090I
c = 0.317192 0.547993I
d = 0.84116 1.20014I
5.69302I 5.51057I
u = 1.356115 + 0.270046I
a = 0.427109 + 0.970037I
b = 1.01075 1.59090I
c = 0.317192 + 0.547993I
d = 0.84116 + 1.20014I
5.69302I 5.51057I
20
VIII. I
u
8
= hu
16
+ u
15
+ · · · 4u 4, 221u
15
273u
14
+ · · · + 2360a
470, 727u
15
+ 393u
14
+ · · · + 1180b 2866, 593u
15
31u
14
+ · · · + 2360c +
850, 85u
15
13u
14
+ · · · + 590d + 1152i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
0.0936441u
15
+ 0.115678u
14
+ ··· 0.674153u + 0.199153
0.616102u
15
0.333051u
14
+ ··· 0.478814u + 2.42881
a
8
=
0.114831u
15
0.0699153u
14
+ ··· 0.693644u + 0.0686441
0.639831u
15
0.0449153u
14
+ ··· 0.0686441u + 3.01864
a
10
=
0.251271u
15
+ 0.0131356u
14
+ ··· + 0.0351695u 0.360169
0.144068u
15
+ 0.0220339u
14
+ ··· + 0.0525424u 1.95254
a
9
=
0.146610u
15
+ 0.0483051u
14
+ ··· + 0.622881u 0.172881
0.502542u
15
+ 0.0262712u
14
+ ··· + 0.0703390u 2.72034
a
6
=
0.127966u
15
+ 0.0110169u
14
+ ··· + 0.626271u + 0.423729
0.529661u
15
0.239831u
14
+ ··· 0.687288u + 2.13729
a
11
=
0.107203u
15
0.00889831u
14
+ ··· 0.0173729u + 0.592373
0.427119u
15
+ 0.0135593u
14
+ ··· + 0.0169492u 2.41695
a
11
=
0.107203u
15
0.00889831u
14
+ ··· 0.0173729u + 0.592373
0.427119u
15
+ 0.0135593u
14
+ ··· + 0.0169492u 2.41695
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
21
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.157569 0.635502I
a = 1.48614 0.93475I
b = 1.57665 0.90527I
c = 0.826549 0.740811I
d = 0.863672 + 0 .522607I
5.44991 9.88301I 3.28252 + 6.06963I
u = 1.157569 + 0.635502I
a = 1.48614 + 0.93475I
b = 1.57665 + 0.90527I
c = 0.826549 + 0.740811I
d = 0.863672 0 .522607I
5.44991 + 9.88301I 3.28252 6.06963I
u = 1.076279 0.402850I
a = 0.985091 0.001978I
b = 0.32411 2.07852I
c = 0.081976 + 0.594679I
d = 1.43403 + 0.66344I
4.77492 2.26376I 6.05872 + 4.53378I
u = 1.076279 + 0.402850I
a = 0.985091 + 0.001978I
b = 0.32411 + 2.07852I
c = 0.081976 0.594679I
d = 1.43403 0.66344I
4.77492 + 2.26376I 6.05872 4.53378I
u = 0.783583
a = 0.489574
b = 2.20354
c = 0.437368
d = 1.26855
2.57083 2.16015
u = 0.754559 0.841472I
a = 0.760920 + 0.848566I
b = 0.636148 0.242515I
c = 0.891409 0.994087I
d = 0.138717 + 1 .269881I
10.1546 6.33746
22
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.754559 + 0.841472I
a = 0.760920 0.848566I
b = 0.636148 + 0.242515I
c = 0.891409 + 0.994087I
d = 0.138717 1 .269881I
10.1546 6.33746
u = 0.270006 0.967768I
a = 1.64151 + 1.62176I
b = 1.56027 1.09581I
c = 0.70037 1.27972I
d = 0.93610 + 1.47128I
5.44991 + 9.88301I 3.28252 6.06963I
u = 0.270006 + 0.967768I
a = 1.64151 1.62176I
b = 1.56027 + 1.09581I
c = 0.70037 + 1.27972I
d = 0.93610 1.47128I
5.44991 9.88301I 3.28252 + 6.06963I
u = 0.365525 0.776365I
a = 0.90049 + 2.82232I
b = 0.50994 1.48491I
c = 0.89340 + 1.33041I
d = 0.664034 1.131195I
2.93531 3.55755I 2.52739 + 2.62489I
u = 0.365525 + 0.776365I
a = 0.90049 2.82232I
b = 0.50994 + 1.48491I
c = 0.89340 1.33041I
d = 0.664034 + 1.131195I
2.93531 + 3.55755I 2.52739 2.62489I
u = 0.993914 0.569061I
a = 2.16175 0.50363I
b = 1.27697 0.76242I
c = 0.940155 + 0.746855I
d = 0.469134 0 .567562I
2.93531 + 3.55755I 2.52739 2.62489I
23
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.993914 + 0.569061I
a = 2.16175 + 0.50363I
b = 1.27697 + 0.76242I
c = 0.940155 0.746855I
d = 0.469134 + 0 .567562I
2.93531 3.55755I 2.52739 + 2.62489I
u = 1.12630
a = 0.340604
b = 0.439006
c = 0.304284
d = 0.614002
2.57083 2.16015
u = 1.227616 0.270214I
a = 0.754892 + 0.491159I
b = 0.408126 1.151443I
c = 0.232685 0.497052I
d = 0.996088 0.867158I
4.77492 2.26376I 6.05872 + 4.53378I
u = 1.227616 + 0.270214I
a = 0.754892 0.491159I
b = 0.408126 + 1.151443I
c = 0.232685 + 0.497052I
d = 0.996088 + 0.867158I
4.77492 + 2.26376I 6.05872 4.53378I
24
IX. I
v
1
= hb, c, v 1, d + 1, a 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
2
=
1
0
a
3
=
1
0
a
5
=
1
0
a
7
=
1
0
a
8
=
1
0
a
10
=
0
1
a
9
=
1
1
a
6
=
0
1
a
11
=
1
1
a
11
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
25
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
26
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
u(u 1)
3
(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
c
2
, c
11
u(u + 1)
3
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
(u
12
+ 9u
11
+ ··· 4u + 1)(u
16
+ 7u
15
+ ··· + 40u + 16)
(u
19
+ 8u
18
+ ··· + 19u + 1)
c
3
, c
7
u
4
(u
6
+ u
5
u
4
2u
3
+ u + 1)
5
(u
8
3u
7
+ 3u
6
+ 2u
5
8u
4
+ 9u
3
3u
2
2u + 2)
2
(u
19
+ 2u
18
+ ··· + 4u
2
8)
c
4
u(u 1)
2
(u + 1)(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
c
5
u(u + 1)
3
(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
c
6
u(u 1)(u + 1)
2
(u
6
u
5
u
4
+ 2u
3
u + 1)
(u
8
+ u
7
4u
6
3u
5
+ 5u
4
+ u
3
u
2
+ 3u 1)
2
(u
12
+ u
11
4u
10
2u
9
+ 7u
8
u
7
5u
6
+ 5u
5
u
4
3u
3
+ 2u
2
+ 1)
2
(u
19
+ 2u
18
+ ··· 8u 4)
c
8
, c
9
u(u 1)
3
(u
6
u
5
u
4
+ 2u
3
u + 1)
(u
8
+ u
7
4u
6
3u
5
+ 5u
4
+ u
3
u
2
+ 3u 1)
2
(u
12
+ u
11
4u
10
2u
9
+ 7u
8
u
7
5u
6
+ 5u
5
u
4
3u
3
+ 2u
2
+ 1)
2
(u
19
+ 2u
18
+ ··· 8u 4)
c
10
u(u 1)(u + 1)
2
(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
27
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
, c
5
c
10
y(y 1)
3
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
3
(y
12
9y
11
+ ··· + 4y + 1)(y
16
7y
15
+ ··· 40y + 16)
(y
19
8y
18
+ ··· + 19y 1)
c
2
, c
11
y(y 1)
3
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
(y
12
13y
11
+ ··· 12y + 1)(y
16
+ y
15
+ ··· 544y + 256)
(y
19
+ 12y
18
+ ··· + 195y 1)
c
3
, c
7
y
4
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
5
(y
8
3y
7
+ 5y
6
4y
5
+ 2y
4
13y
3
+ 13y
2
16y + 4)
2
(y
19
6y
18
+ ··· + 64y 64)
c
6
, c
8
, c
9
y(y 1)
3
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
8
9y
7
+ 32y
6
53y
5
+ 31y
4
+ 15y
3
15y
2
7y + 1)
2
(1 + 4y + 2y
2
23y
3
+ 25y
4
y
5
5y
6
33y
7
+ 73y
8
68y
9
+ 34y
10
9y
11
+ y
12
)
2
(y
19
18y
18
+ ··· + 88y 16)
28