11a
43
(K11a
43
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 11 9 3 6 8 5 10
Solving Sequence
3,7
4
1,8
2
5,10
9 6 11
c
3
c
7
c
2
c
4
c
9
c
6
c
11
c
1
, c
5
, c
8
, c
10
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h−u
9
− 2u
8
− 3u
7
− 2u
6
− 3u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 4d, u
9
+ u
8
+ u
7
− u
6
+ u
5
− 3u
4
− 2u
3
+ 4c + 4u,
− u
9
− 2u
8
− 3u
7
− 2u
6
− u
5
+ 4u
3
+ 4u
2
+ 4b, u
9
+ u
8
+ u
7
− u
6
− u
5
− 3u
4
− 2u
3
− 2u
2
+ 4a + 4u,
u
11
+ u
10
+ 2u
9
+ u
8
+ 2u
7
− 3u
6
− 3u
5
− 4u
4
− 4u
2
+ 4u + 4i
I
u
2
= h3u
15
+ 3u
14
+ ··· + 4d − 4, 2u
16
+ u
15
+ ··· + 4c + 2,
u
14
+ 2u
12
+ 3u
10
+ 2u
9
+ 2u
8
+ 2u
7
+ u
6
+ 6u
5
+ 5u
4
+ 4u
3
+ 4b + 4, 2u
15
+ 4u
14
+ ··· + 4a + 10,
u
17
+ 2u
16
+ ··· − 2u − 2i
I
u
3
= h3u
15
+ 3u
14
+ ··· + 4d − 4, 2u
16
+ u
15
+ ··· + 4c + 2,
− u
15
− u
14
− 3u
13
− 2u
12
− 5u
11
− 3u
10
− 7u
9
− 2u
8
− 5u
7
− 3u
6
− 10u
5
− 11u
4
− 7u
3
− 2u
2
+ 4b + 2u + 4,
− 2u
16
− 3u
15
+ ··· + 4a − 2, u
17
+ 2u
16
+ ··· − 2u − 2i
I
u
4
= h2u
16
+ 5u
15
+ ··· + 4d + 14u,
− u
15
− 2u
13
− 5u
11
− 2u
10
− 6u
9
− 2u
8
− 7u
7
− 8u
6
− 9u
5
− 6u
4
− 2u
3
− 6u
2
+ 4c − 12u − 4,
− u
15
− u
14
− 3u
13
− 2u
12
− 5u
11
− 3u
10
− 7u
9
− 2u
8
− 5u
7
− 3u
6
− 10u
5
− 11u
4
− 7u
3
− 2u
2
+ 4b + 2u + 4,
− 2u
16
− 3u
15
+ ··· + 4a − 2, u
17
+ 2u
16
+ ··· − 2u − 2i
I
u
5
= h−2a
2
cu + a
2
c + cau + a
2
u − 4ca − 2cu − a
2
+ 2au + 2d + 5c + a − u + 1,
a
2
cu + a
2
c − 4cau − a
2
u + c
2
+ 3ca + 2cu + au − 2c − 3a − u + 2, −a
2
u + a
2
− au + b − a + 2,
a
3
− 2a
2
u + 3au − u, u
2
− u + 1i
I
v
1
= ha, d, c + 1, b + 1, v + 1i
I
v
2
= hc, d + 1, b, a − 1, v + 1i
I
v
3
= ha, d + 1, c − a, b + 1, v + 1i
I
v
4
= ha, da + c + 1, dv − 1, cv + a + v, b + 1i
* 8 irreducible components of dim
C
= 0, with total 77 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h−u
9
− 2u
8
+ · · · + 4u
2
+ 4d, u
9
+ u
8
+ · · · + 4c + 4u, −u
9
− 2u
8
+
· · · + 4u
2
+ 4b, u
9
+ u
8
+ · · · + 4a + 4u, u
11
+ u
10
+ · · · + 4u + 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
1
=
−
1
4
u
9
−
1
4
u
8
+ ··· +
1
2
u
2
− u
1
4
u
9
+
1
2
u
8
+ ··· − u
3
− u
2
a
8
=
−u
u
a
2
=
−
1
4
u
9
−
1
4
u
8
+ ··· +
1
2
u
2
+ 1
1
4
u
9
+
1
4
u
7
+
1
4
u
5
a
5
=
1
4
u
8
+
1
2
u
7
+ ··· −
1
2
u
2
− u
1
4
u
10
+
1
4
u
9
+ ··· −
1
2
u
4
+ u
2
a
10
=
−
1
4
u
9
−
1
4
u
8
+ ··· +
1
2
u
3
− u
1
4
u
9
+
1
2
u
8
+ ··· −
1
2
u
3
− u
2
a
9
=
1
4
u
10
+
1
4
u
9
+ ··· −
1
2
u
3
− u
−
1
4
u
10
−
1
4
u
9
+ ··· +
1
2
u
3
− u
2
a
6
=
−
1
4
u
8
−
1
2
u
7
+ ··· + u
2
+ u
−
1
4
u
10
−
1
4
u
9
+ ··· +
1
2
u
3
− u
2
a
11
=
1
2
u
6
+
1
2
u
4
+
1
2
u
2
− u
1
2
u
8
+
1
2
u
7
+ ··· −
1
2
u
3
− u
2
a
11
=
1
2
u
6
+
1
2
u
4
+
1
2
u
2
− u
1
2
u
8
+
1
2
u
7
+ ··· −
1
2
u
3
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
10
− 3u
9
− 4u
8
− 5u
7
− 4u
6
− u
5
+ 3u
4
+ 4u
3
+ 2u
2
+ 4u − 10
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
10
u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
+ 4u
4
− 2u
2
+ 2u + 1
c
2
, c
9
, c
11
u
11
+ 5u
10
+ ··· + 8u + 1
c
3
, c
7
u
11
+ u
10
+ 2u
9
+ u
8
+ 2u
7
− 3u
6
− 3u
5
− 4u
4
− 4u
2
+ 4u + 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
10
y
11
− 5y
10
+ ··· + 8y −1
c
2
, c
9
, c
11
y
11
+ 7y
10
+ ··· + 40y −1
c
3
, c
7
y
11
+ 3y
10
+ ··· + 48y −16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981646 + 0.091031I
a = 0.527474 + 0.160953I
b = −0.259189 + 0.777251I
c = −0.366942 − 0.136098I
d = 0.177956 + 0.945407I
−0.38453 + 3.51380I −10.33478 − 7.33311I
u = 0.981646 − 0.091031I
a = 0.527474 − 0.160953I
b = −0.259189 − 0.777251I
c = −0.366942 + 0.136098I
d = 0.177956 − 0.945407I
−0.38453 − 3.51380I −10.33478 + 7.33311I
u = 0.360685 + 1.114550I
a = 0.621176 − 0.836924I
b = 0.410237 + 0.659760I
c = 0.074184 − 1.245440I
d = 0.569474 + 1.085660I
3.72768 − 0.41249I −4.65663 − 1.55838I
u = 0.360685 − 1.114550I
a = 0.621176 + 0.836924I
b = 0.410237 − 0.659760I
c = 0.074184 + 1.245440I
d = 0.569474 − 1.085660I
3.72768 + 0.41249I −4.65663 + 1.55838I
u = −1.053240 + 0.696446I
a = 0.436462 − 0.109397I
b = −1.04374 − 1.24892I
c = −1.44166 + 0.27329I
d = 1.58561 + 1.00769I
−5.36867 − 9.54355I −15.3185 + 7.2879I
u = −1.053240 − 0.696446I
a = 0.436462 + 0.109397I
b = −1.04374 + 1.24892I
c = −1.44166 − 0.27329I
d = 1.58561 − 1.00769I
−5.36867 + 9.54355I −15.3185 − 7.2879I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.306817 + 1.268500I
a = 0.136985 + 1.403680I
b = −0.369008 − 1.314180I
c = −0.860509 + 0.304947I
d = −0.184720 − 0.266859I
3.91373 − 8.22510I −8.34823 + 8.49377I
u = 0.306817 − 1.268500I
a = 0.136985 − 1.403680I
b = −0.369008 + 1.314180I
c = −0.860509 − 0.304947I
d = −0.184720 + 0.266859I
3.91373 + 8.22510I −8.34823 − 8.49377I
u = −0.809328 + 1.127750I
a = −0.58283 − 1.50488I
b = −1.16377 + 1.41429I
c = −0.19914 + 1.98351I
d = 1.51573 − 1.89641I
−3.9531 + 16.3093I −14.3050 − 10.3392I
u = −0.809328 − 1.127750I
a = −0.58283 + 1.50488I
b = −1.16377 − 1.41429I
c = −0.19914 − 1.98351I
d = 1.51573 + 1.89641I
−3.9531 − 16.3093I −14.3050 + 10.3392I
u = −0.573171
a = 0.721466
b = −0.149048
c = 0.588134
d = −0.328093
−0.805061 −12.0740
7
II. I
u
2
= h3u
15
+ 3u
14
+ · · · + 4d − 4, 2u
16
+ u
15
+ · · · + 4c + 2, u
14
+ 2u
12
+
· · · + 4b + 4, 2u
15
+ 4u
14
+ · · · + 4a + 10, u
17
+ 2u
16
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
1
=
−
1
2
u
15
− u
14
+ ··· − 7u −
5
2
−
1
4
u
14
−
1
2
u
12
+ ··· − u
3
− 1
a
8
=
−u
u
a
2
=
−
1
2
u
15
− u
14
+ ··· − 8u −
5
2
−
3
4
u
14
−
3
2
u
12
+ ··· − 2u
3
− 1
a
5
=
−
1
2
u
15
−
5
4
u
14
+ ··· − 7u −
7
2
−
1
4
u
16
−
1
2
u
14
+ ··· − 3u
2
− u
a
10
=
−
1
2
u
16
−
1
4
u
15
+ ··· −
1
2
u −
1
2
−
3
4
u
15
−
3
4
u
14
+ ··· +
1
2
u + 1
a
9
=
−
1
4
u
16
−
3
4
u
14
+ ··· −
3
2
u −
1
2
−
1
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
6
=
1
2
u
16
+ u
15
+ ··· +
11
4
u
2
−
1
2
−
1
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
11
=
−
1
2
u
15
− u
14
+ ··· −
15
2
u − 3
−
1
2
u
14
− u
12
+ ··· − u
3
− 1
a
11
=
−
1
2
u
15
− u
14
+ ··· −
15
2
u − 3
−
1
2
u
14
− u
12
+ ··· − u
3
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
16
+ 4u
15
+ 6u
14
+ 8u
13
+ 8u
12
+ 14u
11
+ 10u
10
+ 12u
9
+ 4u
8
+
10u
7
+ 20u
6
+ 26u
5
+ 16u
4
− 4u
3
− 10u
2
− 8u − 16
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
17
− 5u
15
+ ··· + 3u
2
− 4
c
2
u
17
+ 10u
16
+ ··· + 24u + 16
c
3
, c
7
u
17
+ 2u
16
+ ··· − 2u − 2
c
5
, c
6
, c
8
c
10
u
17
− 2u
16
+ ··· − u + 1
c
9
, c
11
u
17
+ 8u
16
+ ··· + 3u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
− 10y
16
+ ··· + 24y −16
c
2
y
17
− 10y
16
+ ··· + 800y −256
c
3
, c
7
y
17
+ 6y
16
+ ··· + 8y −4
c
5
, c
6
, c
8
c
10
y
17
− 8y
16
+ ··· + 3y −1
c
9
, c
11
y
17
+ 4y
16
+ ··· − 13y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742615 + 0.650908I
a = −1.40070 − 2.38570I
b = −1.30236 + 0.73752I
c = −0.757942 + 1.169930I
d = 1.088610 + 0.211420I
−6.94910 − 1.22724I −18.1485 + 0.8551I
u = −0.742615 − 0.650908I
a = −1.40070 + 2.38570I
b = −1.30236 − 0.73752I
c = −0.757942 − 1.169930I
d = 1.088610 − 0.211420I
−6.94910 + 1.22724I −18.1485 − 0.8551I
u = −0.834865 + 0.265014I
a = 0.511597 − 0.109110I
b = −0.597254 − 0.693509I
c = 0.800041 − 0.146031I
d = −0.807482 − 0.323646I
−0.670307 − 0.433874I −9.43166 − 0.87540I
u = −0.834865 − 0.265014I
a = 0.511597 + 0.109110I
b = −0.597254 + 0.693509I
c = 0.800041 + 0.146031I
d = −0.807482 + 0.323646I
−0.670307 + 0.433874I −9.43166 + 0.87540I
u = 0.976738 + 0.562668I
a = 0.583366 − 0.363840I
b = 0.537642 − 0.360420I
c = 0.879539 + 0.321552I
d = −1.09988 + 0.90044I
−2.67943 + 4.64771I −12.43915 − 4.11695I
u = 0.976738 − 0.562668I
a = 0.583366 + 0.363840I
b = 0.537642 + 0.360420I
c = 0.879539 − 0.321552I
d = −1.09988 − 0.90044I
−2.67943 − 4.64771I −12.43915 + 4.11695I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003992 + 0.842342I
a = 0.444102 − 0.000358I
b = −1.56684 − 0.00455I
c = 0.054218 − 0.565099I
d = −0.672214 + 0.818183I
−1.98005 − 1.46955I −8.36417 + 4.66528I
u = −0.003992 − 0.842342I
a = 0.444102 + 0.000358I
b = −1.56684 + 0.00455I
c = 0.054218 + 0.565099I
d = −0.672214 − 0.818183I
−1.98005 + 1.46955I −8.36417 − 4.66528I
u = −0.656745 + 1.004700I
a = 0.422901 − 0.058229I
b = −1.64195 − 0.84395I
c = −0.374228 + 1.227350I
d = 1.64609 − 1.04829I
−5.86965 + 6.57063I −15.2601 − 6.4345I
u = −0.656745 − 1.004700I
a = 0.422901 + 0.058229I
b = −1.64195 + 0.84395I
c = −0.374228 − 1.227350I
d = 1.64609 + 1.04829I
−5.86965 − 6.57063I −15.2601 + 6.4345I
u = −0.110097 + 1.246510I
a = 0.487558 + 1.065780I
b = 0.185932 − 1.001000I
c = 0.792244 − 0.317990I
d = 0.132799 + 0.325259I
4.74481 + 2.71165I −6.15758 − 3.13710I
u = −0.110097 − 1.246510I
a = 0.487558 − 1.065780I
b = 0.185932 + 1.001000I
c = 0.792244 + 0.317990I
d = 0.132799 − 0.325259I
4.74481 − 2.71165I −6.15758 + 3.13710I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578864 + 1.116300I
a = −0.25417 − 1.67482I
b = −0.84436 + 1.27067I
c = 0.33097 − 1.54877I
d = −0.92580 + 1.26344I
1.75994 + 5.51158I −7.74874 − 3.84490I
u = −0.578864 − 1.116300I
a = −0.25417 + 1.67482I
b = −0.84436 − 1.27067I
c = 0.33097 + 1.54877I
d = −0.92580 − 1.26344I
1.75994 − 5.51158I −7.74874 + 3.84490I
u = 0.718492 + 1.129370I
a = 0.527514 − 0.625770I
b = 0.827540 + 0.397027I
c = 0.03532 + 1.64508I
d = −1.31198 − 1.54232I
−0.88663 − 10.83370I −11.10622 + 7.41261I
u = 0.718492 − 1.129370I
a = 0.527514 + 0.625770I
b = 0.827540 − 0.397027I
c = 0.03532 − 1.64508I
d = −1.31198 + 1.54232I
−0.88663 + 10.83370I −11.10622 − 7.41261I
u = 0.463897
a = −10.6443
b = −1.19672
c = −1.52034
d = −0.100298
−4.54799 −20.6880
13
III. I
u
3
= h3u
15
+ 3u
14
+ · · · + 4d − 4, 2u
16
+ u
15
+ · · · + 4c + 2, −u
15
− u
14
+
· · · + 4b + 4, −2u
16
− 3u
15
+ · · · + 4a − 2, u
17
+ 2u
16
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
1
=
1
2
u
16
+
3
4
u
15
+ ··· −
1
2
u +
1
2
1
4
u
15
+
1
4
u
14
+ ··· −
1
2
u − 1
a
8
=
−u
u
a
2
=
1
4
u
15
+
1
2
u
13
+ ··· +
1
2
u + 1
−
1
4
u
15
−
3
4
u
13
+ ··· −
1
2
u
2
−
1
2
u
a
5
=
1
2
u
16
+ u
15
+ ··· − u −
1
2
−
3
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
10
=
−
1
2
u
16
−
1
4
u
15
+ ··· −
1
2
u −
1
2
−
3
4
u
15
−
3
4
u
14
+ ··· +
1
2
u + 1
a
9
=
−
1
4
u
16
−
3
4
u
14
+ ··· −
3
2
u −
1
2
−
1
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
6
=
1
2
u
16
+ u
15
+ ··· +
11
4
u
2
−
1
2
−
1
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
11
=
−
1
2
u
16
−
3
2
u
14
+ ··· −
5
2
u
2
−
1
2
u
−u
15
− u
14
+ ··· − 2u
2
+ 1
a
11
=
−
1
2
u
16
−
3
2
u
14
+ ··· −
5
2
u
2
−
1
2
u
−u
15
− u
14
+ ··· − 2u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
16
+ 4u
15
+ 6u
14
+ 8u
13
+ 8u
12
+ 14u
11
+ 10u
10
+ 12u
9
+ 4u
8
+
10u
7
+ 20u
6
+ 26u
5
+ 16u
4
− 4u
3
− 10u
2
− 8u − 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
u
17
− 2u
16
+ ··· − u + 1
c
2
, c
9
u
17
+ 8u
16
+ ··· + 3u + 1
c
3
, c
7
u
17
+ 2u
16
+ ··· − 2u − 2
c
5
, c
10
u
17
− 5u
15
+ ··· + 3u
2
− 4
c
11
u
17
+ 10u
16
+ ··· + 24u + 16
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
y
17
− 8y
16
+ ··· + 3y −1
c
2
, c
9
y
17
+ 4y
16
+ ··· − 13y −1
c
3
, c
7
y
17
+ 6y
16
+ ··· + 8y −4
c
5
, c
10
y
17
− 10y
16
+ ··· + 24y −16
c
11
y
17
− 10y
16
+ ··· + 800y −256
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742615 + 0.650908I
a = 0.456798 − 0.077068I
b = −1.144690 − 0.810574I
c = −0.757942 + 1.169930I
d = 1.088610 + 0.211420I
−6.94910 − 1.22724I −18.1485 + 0.8551I
u = −0.742615 − 0.650908I
a = 0.456798 + 0.077068I
b = −1.144690 + 0.810574I
c = −0.757942 − 1.169930I
d = 1.088610 − 0.211420I
−6.94910 + 1.22724I −18.1485 − 0.8551I
u = −0.834865 + 0.265014I
a = 0.636187 + 0.240948I
b = 0.130684 + 0.390145I
c = 0.800041 − 0.146031I
d = −0.807482 − 0.323646I
−0.670307 − 0.433874I −9.43166 − 0.87540I
u = −0.834865 − 0.265014I
a = 0.636187 − 0.240948I
b = 0.130684 − 0.390145I
c = 0.800041 + 0.146031I
d = −0.807482 + 0.323646I
−0.670307 + 0.433874I −9.43166 + 0.87540I
u = 0.976738 + 0.562668I
a = 0.456039 + 0.109653I
b = −0.902787 + 1.069590I
c = 0.879539 + 0.321552I
d = −1.09988 + 0.90044I
−2.67943 + 4.64771I −12.43915 − 4.11695I
u = 0.976738 − 0.562668I
a = 0.456039 − 0.109653I
b = −0.902787 − 1.069590I
c = 0.879539 − 0.321552I
d = −1.09988 − 0.90044I
−2.67943 − 4.64771I −12.43915 + 4.11695I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003992 + 0.842342I
a = 1.18580 + 1.31498I
b = −0.210717 − 0.521575I
c = 0.054218 − 0.565099I
d = −0.672214 + 0.818183I
−1.98005 − 1.46955I −8.36417 + 4.66528I
u = −0.003992 − 0.842342I
a = 1.18580 − 1.31498I
b = −0.210717 + 0.521575I
c = 0.054218 + 0.565099I
d = −0.672214 − 0.818183I
−1.98005 + 1.46955I −8.36417 − 4.66528I
u = −0.656745 + 1.004700I
a = −0.46618 − 1.83030I
b = −1.01520 + 1.16025I
c = −0.374228 + 1.227350I
d = 1.64609 − 1.04829I
−5.86965 + 6.57063I −15.2601 − 6.4345I
u = −0.656745 − 1.004700I
a = −0.46618 + 1.83030I
b = −1.01520 − 1.16025I
c = −0.374228 − 1.227350I
d = 1.64609 + 1.04829I
−5.86965 − 6.57063I −15.2601 + 6.4345I
u = −0.110097 + 1.246510I
a = 0.360483 − 1.280850I
b = −0.110904 + 1.152270I
c = 0.792244 − 0.317990I
d = 0.132799 + 0.325259I
4.74481 + 2.71165I −6.15758 − 3.13710I
u = −0.110097 − 1.246510I
a = 0.360483 + 1.280850I
b = −0.110904 − 1.152270I
c = 0.792244 + 0.317990I
d = 0.132799 − 0.325259I
4.74481 − 2.71165I −6.15758 + 3.13710I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578864 + 1.116300I
a = 0.568056 + 0.689908I
b = 0.662834 − 0.498844I
c = 0.33097 − 1.54877I
d = −0.92580 + 1.26344I
1.75994 + 5.51158I −7.74874 − 3.84490I
u = −0.578864 − 1.116300I
a = 0.568056 − 0.689908I
b = 0.662834 + 0.498844I
c = 0.33097 + 1.54877I
d = −0.92580 − 1.26344I
1.75994 − 5.51158I −7.74874 + 3.84490I
u = 0.718492 + 1.129370I
a = −0.46497 + 1.57649I
b = −1.03332 − 1.36799I
c = 0.03532 + 1.64508I
d = −1.31198 − 1.54232I
−0.88663 − 10.83370I −11.10622 + 7.41261I
u = 0.718492 − 1.129370I
a = −0.46497 − 1.57649I
b = −1.03332 + 1.36799I
c = 0.03532 − 1.64508I
d = −1.31198 + 1.54232I
−0.88663 + 10.83370I −11.10622 − 7.41261I
u = 0.463897
a = 0.535599
b = −0.751807
c = −1.52034
d = −0.100298
−4.54799 −20.6880
19
IV. I
u
4
= h2u
16
+ 5u
15
+ · · · + 4d + 14u, −u
15
− 2u
13
+ · · · + 4c − 4, −u
15
−
u
14
+ · · · + 4b + 4, −2u
16
− 3u
15
+ · · · + 4a − 2, u
17
+ 2u
16
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
1
=
1
2
u
16
+
3
4
u
15
+ ··· −
1
2
u +
1
2
1
4
u
15
+
1
4
u
14
+ ··· −
1
2
u − 1
a
8
=
−u
u
a
2
=
1
4
u
15
+
1
2
u
13
+ ··· +
1
2
u + 1
−
1
4
u
15
−
3
4
u
13
+ ··· −
1
2
u
2
−
1
2
u
a
5
=
1
2
u
16
+ u
15
+ ··· − u −
1
2
−
3
4
u
16
− u
15
+ ··· +
3
2
u + 1
a
10
=
1
4
u
15
+
1
2
u
13
+ ··· + 3u + 1
−
1
2
u
16
−
5
4
u
15
+ ··· − 7u
2
−
7
2
u
a
9
=
1
2
u
11
+ u
9
+ ··· + 2u + 1
−
1
2
u
16
− u
15
+ ··· − 7u
2
−
5
2
u
a
6
=
1
2
u
16
+ u
15
+ ··· +
1
2
u − 1
−
1
2
u
16
− u
15
+ ··· − 7u
2
−
5
2
u
a
11
=
1
2
u
11
+ u
9
+ ··· +
5
2
u + 1
−
1
2
u
16
− u
15
+ ··· −
13
2
u
2
− 3u
a
11
=
1
2
u
11
+ u
9
+ ··· +
5
2
u + 1
−
1
2
u
16
− u
15
+ ··· −
13
2
u
2
− 3u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
16
+ 4u
15
+ 6u
14
+ 8u
13
+ 8u
12
+ 14u
11
+ 10u
10
+ 12u
9
+ 4u
8
+
10u
7
+ 20u
6
+ 26u
5
+ 16u
4
− 4u
3
− 10u
2
− 8u − 16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
17
− 2u
16
+ ··· − u + 1
c
2
, c
11
u
17
+ 8u
16
+ ··· + 3u + 1
c
3
, c
7
u
17
+ 2u
16
+ ··· − 2u − 2
c
6
, c
8
u
17
− 5u
15
+ ··· + 3u
2
− 4
c
9
u
17
+ 10u
16
+ ··· + 24u + 16
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
17
− 8y
16
+ ··· + 3y −1
c
2
, c
11
y
17
+ 4y
16
+ ··· − 13y −1
c
3
, c
7
y
17
+ 6y
16
+ ··· + 8y −4
c
6
, c
8
y
17
− 10y
16
+ ··· + 24y −16
c
9
y
17
− 10y
16
+ ··· + 800y −256
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742615 + 0.650908I
a = 0.456798 − 0.077068I
b = −1.144690 − 0.810574I
c = −1.59606 + 0.84314I
d = 3.08014 − 0.53548I
−6.94910 − 1.22724I −18.1485 + 0.8551I
u = −0.742615 − 0.650908I
a = 0.456798 + 0.077068I
b = −1.144690 + 0.810574I
c = −1.59606 − 0.84314I
d = 3.08014 + 0.53548I
−6.94910 + 1.22724I −18.1485 − 0.8551I
u = −0.834865 + 0.265014I
a = 0.636187 + 0.240948I
b = 0.130684 + 0.390145I
c = 0.126137 + 0.313566I
d = 0.284217 + 0.647378I
−0.670307 − 0.433874I −9.43166 − 0.87540I
u = −0.834865 − 0.265014I
a = 0.636187 − 0.240948I
b = 0.130684 − 0.390145I
c = 0.126137 − 0.313566I
d = 0.284217 − 0.647378I
−0.670307 + 0.433874I −9.43166 + 0.87540I
u = 0.976738 + 0.562668I
a = 0.456039 + 0.109653I
b = −0.902787 + 1.069590I
c = −1.248760 − 0.438489I
d = 1.50245 − 0.07666I
−2.67943 + 4.64771I −12.43915 − 4.11695I
u = 0.976738 − 0.562668I
a = 0.456039 − 0.109653I
b = −0.902787 − 1.069590I
c = −1.248760 + 0.438489I
d = 1.50245 + 0.07666I
−2.67943 − 4.64771I −12.43915 + 4.11695I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003992 + 0.842342I
a = 1.18580 + 1.31498I
b = −0.210717 − 0.521575I
c = −0.00520 + 2.80579I
d = 0.008617 − 0.945710I
−1.98005 − 1.46955I −8.36417 + 4.66528I
u = −0.003992 − 0.842342I
a = 1.18580 − 1.31498I
b = −0.210717 + 0.521575I
c = −0.00520 − 2.80579I
d = 0.008617 + 0.945710I
−1.98005 + 1.46955I −8.36417 − 4.66528I
u = −0.656745 + 1.004700I
a = −0.46618 − 1.83030I
b = −1.01520 + 1.16025I
c = −1.54709 + 2.16200I
d = 1.70703 − 0.63228I
−5.86965 + 6.57063I −15.2601 − 6.4345I
u = −0.656745 − 1.004700I
a = −0.46618 + 1.83030I
b = −1.01520 − 1.16025I
c = −1.54709 − 2.16200I
d = 1.70703 + 0.63228I
−5.86965 − 6.57063I −15.2601 + 6.4345I
u = −0.110097 + 1.246510I
a = 0.360483 − 1.280850I
b = −0.110904 + 1.152270I
c = −0.654988 − 0.910006I
d = −0.154907 + 0.832377I
4.74481 + 2.71165I −6.15758 − 3.13710I
u = −0.110097 − 1.246510I
a = 0.360483 + 1.280850I
b = −0.110904 − 1.152270I
c = −0.654988 + 0.910006I
d = −0.154907 − 0.832377I
4.74481 − 2.71165I −6.15758 + 3.13710I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578864 + 1.116300I
a = 0.568056 + 0.689908I
b = 0.662834 − 0.498844I
c = 0.119127 + 1.123250I
d = 1.08705 − 0.99233I
1.75994 + 5.51158I −7.74874 − 3.84490I
u = −0.578864 − 1.116300I
a = 0.568056 − 0.689908I
b = 0.662834 + 0.498844I
c = 0.119127 − 1.123250I
d = 1.08705 + 0.99233I
1.75994 − 5.51158I −7.74874 + 3.84490I
u = 0.718492 + 1.129370I
a = −0.46497 + 1.57649I
b = −1.03332 − 1.36799I
c = −0.64982 − 1.72842I
d = 1.23193 + 1.36601I
−0.88663 − 10.83370I −11.10622 + 7.41261I
u = 0.718492 − 1.129370I
a = −0.46497 − 1.57649I
b = −1.03332 + 1.36799I
c = −0.64982 + 1.72842I
d = 1.23193 − 1.36601I
−0.88663 + 10.83370I −11.10622 − 7.41261I
u = 0.463897
a = 0.535599
b = −0.751807
c = 2.91332
d = −5.49303
−4.54799 −20.6880
25
V. I
u
5
= h−2a
2
cu + cau + · · · + a + 1, a
2
cu − 4cau + · · · − 3a + 2, −a
2
u −
au + · · · − a + 2, a
3
− 2a
2
u + 3au − u, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u − 1
a
1
=
a
a
2
u − a
2
+ au + a − 2
a
8
=
−u
u
a
2
=
−a
2
u + a
2
− a + 2
2a
2
u − a
2
− au + 3a + 2u − 4
a
5
=
a
2
u − a
2
+ au + 2a − 2
−2a
2
u + a
2
+ au − 4a − 2u + 4
a
10
=
c
a
2
cu −
1
2
cau + ··· −
1
2
a −
1
2
a
9
=
−
1
2
a
2
cu + 2cau + ··· +
3
2
c +
3
2
a
3
2
a
2
cu −
5
2
cau + ··· − 2a −
1
2
a
6
=
−a
2
cu +
1
2
cau + ··· +
1
2
a +
1
2
3
2
a
2
cu −
5
2
cau + ··· − 2a −
1
2
a
11
=
3
2
cau +
1
2
a
2
u + ··· +
3
2
a +
1
2
−
3
2
cau −
1
2
a
2
u + ··· −
3
2
a −
3
2
a
11
=
3
2
cau +
1
2
a
2
u + ··· +
3
2
a +
1
2
−
3
2
cau −
1
2
a
2
u + ··· −
3
2
a −
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 14
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
10
(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
c
2
, c
9
, c
11
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
c
3
, c
7
(u
2
− u + 1)
6
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
10
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
c
2
, c
9
, c
11
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
c
3
, c
7
(y
2
+ y + 1)
6
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.741145 − 0.632163I
b = 0.395862 + 0.291743I
c = 0.562490 + 0.528127I
d = −1.77196 − 0.20576I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.741145 − 0.632163I
b = 0.395862 + 0.291743I
c = 0.85024 + 2.21534I
d = −1.091350 − 0.608709I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.439111 + 0.046276I
b = −1.51194 + 0.59451I
c = −0.412728 − 1.011420I
d = 0.863315 + 0.814466I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.439111 + 0.046276I
b = −1.51194 + 0.59451I
c = 0.562490 + 0.528127I
d = −1.77196 − 0.20576I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = −0.18026 + 2.31794I
b = −0.883917 − 0.886250I
c = −0.412728 − 1.011420I
d = 0.863315 + 0.814466I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = −0.18026 + 2.31794I
b = −0.883917 − 0.886250I
c = 0.85024 + 2.21534I
d = −1.091350 − 0.608709I
−3.28987 − 2.02988I −12.00000 + 3.46410I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.741145 + 0.632163I
b = 0.395862 − 0.291743I
c = 0.562490 − 0.528127I
d = −1.77196 + 0.20576I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.741145 + 0.632163I
b = 0.395862 − 0.291743I
c = 0.85024 − 2.21534I
d = −1.091350 + 0.608709I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.439111 − 0.046276I
b = −1.51194 − 0.59451I
c = −0.412728 + 1.011420I
d = 0.863315 − 0.814466I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.439111 − 0.046276I
b = −1.51194 − 0.59451I
c = 0.562490 − 0.528127I
d = −1.77196 + 0.20576I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.18026 − 2.31794I
b = −0.883917 + 0.886250I
c = −0.412728 + 1.011420I
d = 0.863315 − 0.814466I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.18026 − 2.31794I
b = −0.883917 + 0.886250I
c = 0.85024 − 2.21534I
d = −1.091350 + 0.608709I
−3.28987 + 2.02988I −12.00000 − 3.46410I
30
VI. I
v
1
= ha, d, c + 1, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
1
=
0
−1
a
8
=
−1
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
−1
0
a
9
=
−1
0
a
6
=
−1
0
a
11
=
−1
−1
a
11
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u − 1
c
2
, c
4
, c
10
c
11
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
11
y −1
c
3
, c
6
, c
7
c
8
, c
9
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions 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
34
VII. I
v
2
= hc, d + 1, b, a − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
1
=
1
0
a
8
=
−1
0
a
2
=
1
0
a
5
=
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 = −12
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
c
5
, c
8
, c
9
c
11
u + 1
c
6
, c
10
u − 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y −1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
−3.28987 −12.0000
38
VIII. I
v
3
= ha, d + 1, c − a, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
1
=
0
−1
a
8
=
−1
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
0
−1
a
9
=
−1
−1
a
6
=
0
1
a
11
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u − 1
c
2
, c
4
, c
8
c
9
u + 1
c
3
, c
5
, c
7
c
10
, c
11
u
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y −1
c
3
, c
5
, c
7
c
10
, c
11
y
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
42
IX. I
v
4
= ha, da + c + 1, dv − 1, cv + a + v, b + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
1
=
0
−1
a
8
=
v
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
−1
d
a
9
=
v −1
d
a
6
=
1
−d
a
11
=
−1
d − 1
a
11
=
−1
d − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
− 20
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
43
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−4.93480 −19.9459 + 0.3728I
44
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u − 1)
2
(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
+ 4u
4
− 2u
2
+ 2u + 1)
· (u
17
− 5u
15
+ ··· + 3u
2
− 4)(u
17
− 2u
16
+ ··· − u + 1)
2
c
2
, c
9
, c
11
u(u + 1)
2
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
· (u
11
+ 5u
10
+ ··· + 8u + 1)(u
17
+ 8u
16
+ ··· + 3u + 1)
2
· (u
17
+ 10u
16
+ ··· + 24u + 16)
c
3
, c
7
u
3
(u
2
− u + 1)
6
· (u
11
+ u
10
+ 2u
9
+ u
8
+ 2u
7
− 3u
6
− 3u
5
− 4u
4
− 4u
2
+ 4u + 4)
· (u
17
+ 2u
16
+ ··· − 2u − 2)
3
c
4
, c
8
u(u + 1)
2
(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
+ 4u
4
− 2u
2
+ 2u + 1)
· (u
17
− 5u
15
+ ··· + 3u
2
− 4)(u
17
− 2u
16
+ ··· − u + 1)
2
c
5
, c
10
u(u − 1)(u + 1)(u
6
− 2u
4
+ u
3
+ u
2
− u + 1)
2
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
+ 4u
4
− 2u
2
+ 2u + 1)
· (u
17
− 5u
15
+ ··· + 3u
2
− 4)(u
17
− 2u
16
+ ··· − u + 1)
2
45
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
10
y(y − 1)
2
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
· (y
11
− 5y
10
+ ··· + 8y −1)(y
17
− 10y
16
+ ··· + 24y −16)
· (y
17
− 8y
16
+ ··· + 3y −1)
2
c
2
, c
9
, c
11
y(y − 1)
2
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
· (y
11
+ 7y
10
+ ··· + 40y −1)(y
17
− 10y
16
+ ··· + 800y −256)
· (y
17
+ 4y
16
+ ··· − 13y −1)
2
c
3
, c
7
y
3
(y
2
+ y + 1)
6
(y
11
+ 3y
10
+ ··· + 48y −16)
· (y
17
+ 6y
16
+ ··· + 8y −4)
3
46
