11a
181
(K11a
181
)
A knot diagram
1
Linearized knot diagam
7 1 9 8 11 2 3 4 5 6 10
Solving Sequence
2,6
7 1 3
8,11
5 4 10 9
c
6
c
1
c
2
c
7
c
5
c
4
c
10
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
13
+ 2u
11
+ 3u
9
− u
7
− 4u
3
+ u
2
+ 2a + u + 1,
u
14
− u
13
+ 4u
12
− 4u
11
+ 9u
10
− 9u
9
+ 11u
8
− 11u
7
+ 10u
6
− 10u
5
+ 6u
4
− 5u
3
+ 4u
2
− 2u + 1i
I
u
2
= h−u
9
− 2u
7
− u
6
− 2u
5
− u
4
− u
3
− u
2
+ b − 1, u
11
+ u
9
+ 2u
8
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 2a + u − 1,
u
12
+ 3u
10
+ 2u
9
+ 4u
8
+ 4u
7
+ 3u
6
+ 4u
5
+ u
4
+ 2u
3
+ u
2
+ u + 2i
I
u
3
= h−u
9
− 4u
7
+ u
6
− 6u
5
+ 3u
4
− 3u
3
+ 3u
2
+ b + u + 1, −u
8
− 3u
6
− 3u
4
+ a + u + 1,
u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1i
I
u
4
= h−u
4
− u
3
− 2u
2
+ b − a − u − 1, 2u
4
a + 2u
3
a + u
4
+ 4u
2
a + a
2
+ 3au + 2u
2
+ 2a − u,
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
5
= hb − u, −2u
4
− 2u
3
− 2u
2
+ a − u, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
6
= hb + u, a + 2u − 1, u
2
+ 1i
* 6 irreducible components of dim
C
= 0, with total 53 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hb−u, u
13
+2u
11
+3u
9
−u
7
−4u
3
+u
2
+2a+u+1, u
14
−u
13
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−
1
2
u
13
− u
11
+ ··· −
1
2
u −
1
2
u
a
5
=
−
1
2
u
13
+ u
12
+ ··· −
3
2
u +
3
2
u
2
a
4
=
−u
5
+ u
4
− 2u
3
+ u
2
− u + 1
−
1
2
u
13
− 2u
11
+ ··· +
1
2
u +
1
2
a
10
=
−
1
2
u
13
− u
11
+ ··· −
3
2
u −
1
2
u
a
9
=
−
1
2
u
13
− u
11
+ ··· −
1
2
u −
1
2
u
5
+ u
3
+ u
a
9
=
−
1
2
u
13
− u
11
+ ··· −
1
2
u −
1
2
u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
13
+ 4u
12
−14u
11
+ 12u
10
−26u
9
+ 24u
8
−20u
7
+ 20u
6
−10u
5
+ 20u
4
−2u
3
−6u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
14
− u
13
+ ··· − 2u + 1
c
2
, c
11
u
14
+ 7u
13
+ ··· + 4u + 1
c
3
, c
4
, c
8
u
14
+ 2u
13
+ ··· + 3u + 2
c
7
, c
9
u
14
− 2u
13
+ ··· − 12u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
14
+ 7y
13
+ ··· + 4y + 1
c
2
, c
11
y
14
+ 3y
13
+ ··· + 28y
2
+ 1
c
3
, c
4
, c
8
y
14
+ 12y
13
+ ··· + 11y + 4
c
7
, c
9
y
14
− 10y
13
+ ··· + 496y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460484 + 0.954971I
a = 1.80473 + 1.22926I
b = −0.460484 + 0.954971I
−1.77357 − 5.35695I −6.00056 + 9.03526I
u = −0.460484 − 0.954971I
a = 1.80473 − 1.22926I
b = −0.460484 − 0.954971I
−1.77357 + 5.35695I −6.00056 − 9.03526I
u = −0.628671 + 0.622459I
a = 0.748022 + 0.456292I
b = −0.628671 + 0.622459I
5.80501 − 1.28126I 3.72038 + 3.33843I
u = −0.628671 − 0.622459I
a = 0.748022 − 0.456292I
b = −0.628671 − 0.622459I
5.80501 + 1.28126I 3.72038 − 3.33843I
u = 0.582308 + 0.988094I
a = −1.26996 + 1.41625I
b = 0.582308 + 0.988094I
3.60332 + 8.26243I −0.67488 − 8.53661I
u = 0.582308 − 0.988094I
a = −1.26996 − 1.41625I
b = 0.582308 − 0.988094I
3.60332 − 8.26243I −0.67488 + 8.53661I
u = 0.799677 + 0.138430I
a = −0.192212 + 0.103093I
b = 0.799677 + 0.138430I
1.59498 − 3.95770I 0.96673 + 2.71748I
u = 0.799677 − 0.138430I
a = −0.192212 − 0.103093I
b = 0.799677 − 0.138430I
1.59498 + 3.95770I 0.96673 − 2.71748I
u = 0.492502 + 1.221530I
a = −1.29138 + 2.41020I
b = 0.492502 + 1.221530I
−9.30050 + 9.21742I −9.53627 − 6.56177I
u = 0.492502 − 1.221530I
a = −1.29138 − 2.41020I
b = 0.492502 − 1.221530I
−9.30050 − 9.21742I −9.53627 + 6.56177I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525386 + 1.228370I
a = 1.17574 + 2.34936I
b = −0.525386 + 1.228370I
−4.8439 − 13.8790I −5.49540 + 8.77072I
u = −0.525386 − 1.228370I
a = 1.17574 − 2.34936I
b = −0.525386 − 1.228370I
−4.8439 + 13.8790I −5.49540 − 8.77072I
u = 0.240054 + 0.605061I
a = −0.974923 − 0.634482I
b = 0.240054 + 0.605061I
−0.020113 + 1.303980I −0.98002 − 6.02630I
u = 0.240054 − 0.605061I
a = −0.974923 + 0.634482I
b = 0.240054 − 0.605061I
−0.020113 − 1.303980I −0.98002 + 6.02630I
6
II. I
u
2
= h−u
9
− 2u
7
− u
6
− 2u
5
− u
4
− u
3
− u
2
+ b − 1, u
11
+ u
9
+ · · · + 2a −
1, u
12
+ 3u
10
+ · · · + u + 2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−
1
2
u
11
−
1
2
u
9
+ ··· −
1
2
u +
1
2
u
9
+ 2u
7
+ u
6
+ 2u
5
+ u
4
+ u
3
+ u
2
+ 1
a
5
=
−
1
2
u
11
− u
10
+ ··· −
1
2
u −
1
2
−u
10
− 2u
8
− u
7
− 2u
6
− u
5
− u
4
− u
3
− u
2
− u − 1
a
4
=
−
1
2
u
11
−
1
2
u
9
+ ··· −
1
2
u +
1
2
−u
11
− 3u
9
− 4u
7
− u
5
− u
4
+ u
3
− 2u
2
+ u − 1
a
10
=
−
1
2
u
11
−
3
2
u
9
+ ··· −
1
2
u −
1
2
u
9
+ 2u
7
+ u
6
+ 2u
5
+ u
4
+ u
3
+ u
2
+ 1
a
9
=
1
2
u
11
+ u
10
+ ··· +
3
2
u +
1
2
u
10
+ u
9
+ 2u
8
+ 2u
7
+ 3u
6
+ u
5
+ u
4
+ u
2
+ u + 1
a
9
=
1
2
u
11
+ u
10
+ ··· +
3
2
u +
1
2
u
10
+ u
9
+ 2u
8
+ 2u
7
+ 3u
6
+ u
5
+ u
4
+ u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
10
− 4u
9
− 8u
8
− 16u
7
− 8u
6
− 16u
5
− 4u
4
− 4u
3
− 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
12
+ 3u
10
+ 2u
9
+ 4u
8
+ 4u
7
+ 3u
6
+ 4u
5
+ u
4
+ 2u
3
+ u
2
+ u + 2
c
2
, c
11
u
12
+ 6u
11
+ ··· + 3u + 4
c
3
, c
4
, c
8
(u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1)
2
c
7
, c
9
(u
6
+ 3u
5
+ 2u
4
+ u
3
+ 5u
2
+ 3u − 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
12
+ 6y
11
+ ··· + 3y + 4
c
2
, c
11
y
12
− 2y
11
+ ··· − y + 16
c
3
, c
4
, c
8
(y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
2
c
7
, c
9
(y
6
− 5y
5
+ 8y
4
− 3y
3
+ 11y
2
− 29y + 4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569850 + 0.878821I
a = 0.176883 − 0.327495I
b = 0.696319 + 0.473577I
5.07386 − 3.39374I 2.36018 + 3.51762I
u = −0.569850 − 0.878821I
a = 0.176883 + 0.327495I
b = 0.696319 − 0.473577I
5.07386 + 3.39374I 2.36018 − 3.51762I
u = −0.170932 + 1.042910I
a = −0.32398 − 1.97668I
b = −0.170932 − 1.042910I
−3.86646 −13.16287 + 0.I
u = −0.170932 − 1.042910I
a = −0.32398 + 1.97668I
b = −0.170932 + 1.042910I
−3.86646 −13.16287 + 0.I
u = −0.885163 + 0.125190I
a = −0.598885 + 1.037840I
b = 0.508695 + 1.194490I
−1.52175 + 8.77346I −2.43784 − 5.90094I
u = −0.885163 − 0.125190I
a = −0.598885 − 1.037840I
b = 0.508695 − 1.194490I
−1.52175 − 8.77346I −2.43784 + 5.90094I
u = 0.696319 + 0.473577I
a = 0.412076 + 0.210997I
b = −0.569850 + 0.878821I
5.07386 − 3.39374I 2.36018 + 3.51762I
u = 0.696319 − 0.473577I
a = 0.412076 − 0.210997I
b = −0.569850 − 0.878821I
5.07386 + 3.39374I 2.36018 − 3.51762I
u = 0.508695 + 1.194490I
a = −0.583368 − 0.583465I
b = −0.885163 + 0.125190I
−1.52175 + 8.77346I −2.43784 − 5.90094I
u = 0.508695 − 1.194490I
a = −0.583368 + 0.583465I
b = −0.885163 − 0.125190I
−1.52175 − 8.77346I −2.43784 + 5.90094I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420932 + 1.237560I
a = 0.66727 − 1.96181I
b = 0.420932 − 1.237560I
−9.81751 −10.68183 + 0.I
u = 0.420932 − 1.237560I
a = 0.66727 + 1.96181I
b = 0.420932 + 1.237560I
−9.81751 −10.68183 + 0.I
11
III.
I
u
3
= h−u
9
−4u
7
+· · ·+b+1, −u
8
−3u
6
−3u
4
+a+u+1, u
10
−u
9
+· · ·−3u
3
+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
u
8
+ 3u
6
+ 3u
4
− u − 1
u
9
+ 4u
7
− u
6
+ 6u
5
− 3u
4
+ 3u
3
− 3u
2
− u − 1
a
5
=
u
7
+ 2u
5
− 2u
−u
9
− 3u
7
− 3u
5
+ u
a
4
=
u
5
− u
−u
7
− u
5
+ u
a
10
=
−u
9
+ u
8
− 4u
7
+ 4u
6
− 6u
5
+ 6u
4
− 3u
3
+ 3u
2
u
9
+ 4u
7
− u
6
+ 6u
5
− 3u
4
+ 3u
3
− 3u
2
− u − 1
a
9
=
u
4
+ u
2
− 1
−u
6
− 2u
4
− u
2
a
9
=
u
4
+ u
2
− 1
−u
6
− 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
+ 12u
7
+ 12u
5
− 4u
3
− 8u − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
8
u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1
c
2
u
10
+ 7u
9
+ 20u
8
+ 26u
7
+ 6u
6
− 22u
5
− 19u
4
+ 3u
3
+ 6u
2
+ 1
c
5
, c
10
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
7
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
8
y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1
c
2
y
10
− 9y
9
+ ··· + 12y + 1
c
5
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
7
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839548 + 0.070481I
a = 0.727084 + 1.100860I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 0.839548 − 0.070481I
a = 0.727084 − 1.100860I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 0.090539 + 1.215350I
a = 0.40007 − 1.64065I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.090539 − 1.215350I
a = 0.40007 + 1.64065I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.383413 + 1.200420I
a = −0.525385 − 0.755924I
b = −0.766826
−2.40108 −3.48114 + 0.I
u = 0.383413 − 1.200420I
a = −0.525385 + 0.755924I
b = −0.766826
−2.40108 −3.48114 + 0.I
u = −0.383851 + 1.270630I
a = −0.67357 − 1.92134I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.383851 − 1.270630I
a = −0.67357 + 1.92134I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.429649 + 0.392970I
a = −0.928202 − 0.336746I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.429649 − 0.392970I
a = −0.928202 + 0.336746I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
15
IV. I
u
4
=
h−u
4
−u
3
−2u
2
+b−a−u−1, 2u
4
a+u
4
+· · ·+a
2
+2a, u
5
+u
4
+2u
3
+u
2
+u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
−u
4
− u
3
− u
2
− 1
a
8
=
−u
3
−u
3
− u
a
11
=
a
u
4
+ u
3
+ 2u
2
+ a + u + 1
a
5
=
−u
4
a − u
3
a − u
4
− 2u
2
a − 2au − 2u
2
− a + u + 1
−au − u
2
a
4
=
−u
4
a − 2u
3
a − u
4
− 2u
2
a − 2au − u
2
− a + u + 1
−u
3
a − 2au + 1
a
10
=
−u
4
− u
3
− 2u
2
− u − 1
u
4
+ u
3
+ 2u
2
+ a + u + 1
a
9
=
−u
4
a + u
4
+ 2u
3
+ u
2
+ a + u + 1
−u
4
a + 2u
4
− u
2
a + 2u
3
+ 3u
2
+ a + 2u + 2
a
9
=
−u
4
a + u
4
+ 2u
3
+ u
2
+ a + u + 1
−u
4
a + 2u
4
− u
2
a + 2u
3
+ 3u
2
+ a + 2u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 4u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
3
, c
4
, c
5
c
8
, c
10
u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1
c
7
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
u
10
+ 7u
9
+ 20u
8
+ 26u
7
+ 6u
6
− 22u
5
− 19u
4
+ 3u
3
+ 6u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
3
, c
4
, c
5
c
8
, c
10
y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1
c
7
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
11
y
10
− 9y
9
+ ··· + 12y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.001100 − 0.646305I
b = −0.429649 + 0.392970I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.339110 + 0.822375I
a = 0.51909 − 2.25462I
b = 0.090539 − 1.215350I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.339110 − 0.822375I
a = −0.001100 + 0.646305I
b = −0.429649 − 0.392970I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.339110 − 0.822375I
a = 0.51909 + 2.25462I
b = 0.090539 + 1.215350I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.766826
a = −0.92066 + 1.20042I
b = 0.383413 + 1.200420I
−2.40108 −3.48110
u = −0.766826
a = −0.92066 − 1.20042I
b = 0.383413 − 1.200420I
−2.40108 −3.48110
u = −0.455697 + 1.200150I
a = 0.563037 − 0.657755I
b = 0.839548 + 0.070481I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.455697 + 1.200150I
a = −0.66036 − 1.99887I
b = −0.383851 − 1.270630I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.455697 − 1.200150I
a = 0.563037 + 0.657755I
b = 0.839548 − 0.070481I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −0.455697 − 1.200150I
a = −0.66036 + 1.99887I
b = −0.383851 + 1.270630I
−5.87256 + 4.40083I −6.74431 − 3.49859I
19
V. I
u
5
= hb − u, −2u
4
− 2u
3
− 2u
2
+ a − u, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
−u
4
− u
3
− u
2
− 1
a
8
=
−u
3
−u
3
− u
a
11
=
2u
4
+ 2u
3
+ 2u
2
+ u
u
a
5
=
−2u
3
− u
2
− 2u − 1
u
2
a
4
=
−u
4
− 2u
3
− u
2
− 2u − 1
−u
4
a
10
=
2u
4
+ 2u
3
+ 2u
2
u
a
9
=
u
4
+ u
2
− 1
−u
4
− u
3
− u
2
− 1
a
9
=
u
4
+ u
2
− 1
−u
4
− u
3
− u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 4u − 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
11
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
7
, c
9
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
, c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
9
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −2.07360 + 0.14067I
b = 0.339110 + 0.822375I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.339110 − 0.822375I
a = −2.07360 − 0.14067I
b = 0.339110 − 0.822375I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.766826
a = 0.198937
b = −0.766826
−2.40108 −3.48110
u = −0.455697 + 1.200150I
a = 1.47413 + 2.44394I
b = −0.455697 + 1.200150I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −0.455697 − 1.200150I
a = 1.47413 − 2.44394I
b = −0.455697 − 1.200150I
−5.87256 + 4.40083I −6.74431 − 3.49859I
23
VI. I
u
6
= hb + u, a + 2u − 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
1
a
1
=
−u
0
a
3
=
u
u
a
8
=
1
1
a
11
=
−2u + 1
−u
a
5
=
−u − 1
−1
a
4
=
−1
u − 1
a
10
=
−u + 1
−u
a
9
=
−u + 1
−u
a
9
=
−u + 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
u
2
+ 1
c
2
, c
11
(u + 1)
2
c
7
, c
9
u
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
(y + 1)
2
c
2
, c
11
(y −1)
2
c
7
, c
9
y
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000 − 2.00000I
b = − 1.000000I
−1.64493 −8.00000
u = − 1.000000I
a = 1.00000 + 2.00000I
b = 1.000000I
−1.64493 −8.00000
27
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(u
2
+ 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
· (u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1)
· (u
12
+ 3u
10
+ 2u
9
+ 4u
8
+ 4u
7
+ 3u
6
+ 4u
5
+ u
4
+ 2u
3
+ u
2
+ u + 2)
· (u
14
− u
13
+ ··· − 2u + 1)
c
2
, c
11
(u + 1)
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
· (u
10
+ 7u
9
+ 20u
8
+ 26u
7
+ 6u
6
− 22u
5
− 19u
4
+ 3u
3
+ 6u
2
+ 1)
· (u
12
+ 6u
11
+ ··· + 3u + 4)(u
14
+ 7u
13
+ ··· + 4u + 1)
c
3
, c
4
, c
8
(u
2
+ 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
6
+ 3u
4
+ u
3
+ 2u
2
+ 2u − 1)
2
· (u
10
− u
9
+ 4u
8
− 4u
7
+ 6u
6
− 6u
5
+ 3u
4
− 3u
3
+ 1)
2
· (u
14
+ 2u
13
+ ··· + 3u + 2)
c
7
, c
9
u
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
5
(u
6
+ 3u
5
+ 2u
4
+ u
3
+ 5u
2
+ 3u − 2)
2
· (u
14
− 2u
13
+ ··· − 12u + 8)
28
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
(y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
3
· (y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
· (y
12
+ 6y
11
+ ··· + 3y + 4)(y
14
+ 7y
13
+ ··· + 4y + 1)
c
2
, c
11
((y −1)
2
)(y
5
− y
4
+ ··· + 3y −1)
3
(y
10
− 9y
9
+ ··· + 12y + 1)
· (y
12
− 2y
11
+ ··· − y + 16)(y
14
+ 3y
13
+ ··· + 28y
2
+ 1)
c
3
, c
4
, c
8
(y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
6
+ 6y
5
+ 13y
4
+ 9y
3
− 6y
2
− 8y + 1)
2
· (y
10
+ 7y
9
+ 20y
8
+ 26y
7
+ 6y
6
− 22y
5
− 19y
4
+ 3y
3
+ 6y
2
+ 1)
2
· (y
14
+ 12y
13
+ ··· + 11y + 4)
c
7
, c
9
y
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
5
· (y
6
− 5y
5
+ 8y
4
− 3y
3
+ 11y
2
− 29y + 4)
2
· (y
14
− 10y
13
+ ··· + 496y + 64)
29
