11n
75
(K11n
75
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 9 4 10 7 1 6
Solving Sequence
4,7
8
1,3
2
5,10
9 6 11
c
7
c
3
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
I
u
1
= h563u
12
+ 528u
11
+ ··· + 40878d + 8114, 15485u
12
+ 31932u
11
+ ··· + 490536c − 416896,
19430u
12
+ 31239u
11
+ ··· + 245268b + 104720, 1958u
12
+ 5628u
11
+ ··· + 81756a − 64396,
u
13
+ 2u
12
+ 5u
11
+ 6u
10
+ 6u
9
+ 6u
8
− u
7
− 4u
6
− 10u
5
− 12u
4
+ 24u
3
− 4u
2
+ 8i
I
u
2
= h−u
4
c + 2u
3
c − 4u
2
c + 3cu + u
2
+ d − 2c − u + 2,
3u
4
c − 9u
3
c − u
4
+ 16u
2
c + 3u
3
+ 2c
2
− 17cu − 6u
2
+ 4c + 7u − 2, u
2
+ b − u + 1,
− u
4
+ 3u
3
− 6u
2
+ 2a + 5u − 2, u
5
− 3u
4
+ 6u
3
− 7u
2
+ 4u − 2i
I
u
3
= hu
2
+ d + u + 1, c + u, −au + u
2
+ b + u + 1, u
2
a + a
2
− u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
I
u
4
= h−au + d, −2u
2
a − au + u
2
+ c − 3a + 1, −au + u
2
+ b + u + 1, u
2
a + a
2
− u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
I
u
5
= hu
2
+ d + u + 1, c + u, u
2
+ b + u + 3, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
I
v
1
= hc, d + 1, b, a + 1, v + 1i
I
v
2
= ha, d, c − 1, b + 1, v − 1i
I
v
3
= ha, d + 1, c − a, b + 1, v − 1i
I
v
4
= hc, d + 1, −av + c − v, bv + 1i
* 8 irreducible components of dim
C
= 0, with total 41 representations.
* 1 irreducible components of dim
C
= 1
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
=
h563u
12
+528u
11
+· · ·+4.09×10
4
d+8114, 1.55×10
4
u
12
+3.19×10
4
u
11
+· · ·+
4.91×10
5
c−4.17×10
5
, 1.94×10
4
u
12
+3.12×10
4
u
11
+· · ·+2.45×10
5
b+1.05×
10
5
, 1958u
12
+5628u
11
+· · ·+8.18×10
4
a−6.44×10
4
, u
13
+2u
12
+· · ·−4u
2
+8i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
1
=
−0.0239493u
12
− 0.0688390u
11
+ ··· − 0.848770u + 0.787661
−0.0792195u
12
− 0.127367u
11
+ ··· + 0.865616u − 0.426962
a
3
=
−u
u
3
+ u
a
2
=
−0.0239493u
12
− 0.0688390u
11
+ ··· − 0.848770u + 0.787661
−0.0327519u
12
− 0.0235946u
11
+ ··· + 1.05721u − 0.259439
a
5
=
0.0567012u
12
+ 0.0924336u
11
+ ··· − 0.208441u − 0.528222
−0.0327519u
12
− 0.0235946u
11
+ ··· + 1.05721u − 0.259439
a
10
=
−0.0315675u
12
− 0.0650961u
11
+ ··· − 0.166977u + 0.849879
−0.0137727u
12
− 0.0129165u
11
+ ··· + 0.119429u − 0.198493
a
9
=
−0.0177948u
12
− 0.0521797u
11
+ ··· − 0.286405u + 1.04837
−0.0137727u
12
− 0.0129165u
11
+ ··· + 0.119429u − 0.198493
a
6
=
−0.0261530u
12
− 0.0246587u
11
+ ··· + 0.204992u + 0.667074
−0.00541449u
12
− 0.0404374u
11
+ ··· − 0.371969u + 0.182804
a
11
=
−0.00615449u
12
− 0.0166593u
11
+ ··· − 0.562364u + 0.739289
−0.0654468u
12
− 0.114450u
11
+ ··· + 0.746188u − 0.228468
a
11
=
−0.00615449u
12
− 0.0166593u
11
+ ··· − 0.562364u + 0.739289
−0.0654468u
12
− 0.114450u
11
+ ··· + 0.746188u − 0.228468
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3739
13626
u
12
+
4675
13626
u
11
+
4243
4542
u
10
+
6761
13626
u
9
+
812
6813
u
8
+
59
757
u
7
−
14825
13626
u
6
+
1951
13626
u
5
+
811
757
u
4
+
10702
6813
u
3
+
80432
6813
u
2
−
22922
6813
u +
4756
2271
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
13
− 2u
12
+ ··· + 8u − 4
c
2
u
13
+ 14u
12
+ ··· + 88u + 16
c
3
, c
7
u
13
− 2u
12
+ ··· + 4u
2
− 8
c
5
, c
6
, c
9
c
11
u
13
+ 2u
12
− 4u
10
+ 8u
8
+ 7u
7
− 7u
6
− 8u
5
+ 3u
4
+ 9u
3
− u
2
− u − 1
c
8
, c
10
u
13
− 4u
12
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
13
− 14y
12
+ ··· + 88y − 16
c
2
y
13
− 30y
12
+ ··· + 2848y − 256
c
3
, c
7
y
13
+ 6y
12
+ ··· + 64y − 64
c
5
, c
6
, c
9
c
11
y
13
− 4y
12
+ ··· − y − 1
c
8
, c
10
y
13
+ 16y
12
+ ··· − 25y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917056 + 0.260692I
a = −0.589132 − 0.469887I
b = 0.79135 + 1.65546I
c = 0.504975 + 0.125247I
d = −0.865536 + 0.462701I
1.87851 − 3.16005I 8.32269 + 6.37622I
u = 0.917056 − 0.260692I
a = −0.589132 + 0.469887I
b = 0.79135 − 1.65546I
c = 0.504975 − 0.125247I
d = −0.865536 − 0.462701I
1.87851 + 3.16005I 8.32269 − 6.37622I
u = 0.300918 + 0.625488I
a = 0.901027 − 1.049210I
b = 0.070598 − 0.355169I
c = 1.038000 − 0.500200I
d = 0.218164 − 0.376758I
−1.70980 − 0.77307I −3.13297 + 1.88722I
u = 0.300918 − 0.625488I
a = 0.901027 + 1.049210I
b = 0.070598 + 0.355169I
c = 1.038000 + 0.500200I
d = 0.218164 + 0.376758I
−1.70980 + 0.77307I −3.13297 − 1.88722I
u = −0.613875
a = 0.827092
b = −1.55872
c = 0.608171
d = −0.644275
1.13096 8.32650
u = −1.37082 + 0.38920I
a = −1.049350 − 0.162066I
b = 1.42939 − 0.72557I
c = 0.437589 − 0.166249I
d = −0.997004 − 0.758703I
−4.46546 + 5.94244I 3.19547 − 4.81410I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37082 − 0.38920I
a = −1.049350 + 0.162066I
b = 1.42939 + 0.72557I
c = 0.437589 + 0.166249I
d = −0.997004 + 0.758703I
−4.46546 − 5.94244I 3.19547 + 4.81410I
u = 0.54282 + 1.32018I
a = −0.524033 − 0.514167I
b = −1.67767 + 0.82663I
c = −0.163933 + 1.389820I
d = 1.083710 + 0.709645I
−1.53986 + 8.66555I 5.43123 − 7.16460I
u = 0.54282 − 1.32018I
a = −0.524033 + 0.514167I
b = −1.67767 − 0.82663I
c = −0.163933 − 1.389820I
d = 1.083710 − 0.709645I
−1.53986 − 8.66555I 5.43123 + 7.16460I
u = −0.79330 + 1.40153I
a = 0.258600 + 0.939751I
b = −2.03673 − 0.63977I
c = −0.397741 − 1.239110I
d = 1.23485 − 0.73165I
−7.6949 − 13.5931I 3.46569 + 7.45820I
u = −0.79330 − 1.40153I
a = 0.258600 − 0.939751I
b = −2.03673 + 0.63977I
c = −0.397741 + 1.239110I
d = 1.23485 + 0.73165I
−7.6949 + 13.5931I 3.46569 − 7.45820I
u = −0.28973 + 1.63988I
a = 0.089343 + 0.977840I
b = −0.797574 + 0.049049I
c = 0.277026 + 0.842714I
d = 0.647958 + 1.070920I
−11.70800 − 0.17366I −0.445368 − 1.147630I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28973 − 1.63988I
a = 0.089343 − 0.977840I
b = −0.797574 − 0.049049I
c = 0.277026 − 0.842714I
d = 0.647958 − 1.070920I
−11.70800 + 0.17366I −0.445368 + 1.147630I
7
II. I
u
2
= h−u
4
c + 2u
3
c + · · · − 2c + 2, 3u
4
c − u
4
+ · · · + 4c − 2, u
2
+ b − u +
1, −u
4
+ 3u
3
+ · · · + 2a − 2, u
5
− 3u
4
+ · · · + 4u − 2i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
1
=
1
2
u
4
−
3
2
u
3
+ 3u
2
−
5
2
u + 1
−u
2
+ u − 1
a
3
=
−u
u
3
+ u
a
2
=
1
2
u
4
−
3
2
u
3
+ 3u
2
−
5
2
u + 1
u
3
− 2u
2
+ 2u − 1
a
5
=
−
1
2
u
4
+
1
2
u
3
− u
2
+
1
2
u
u
3
− 2u
2
+ 2u − 1
a
10
=
c
u
4
c − 2u
3
c + 4u
2
c − 3cu − u
2
+ 2c + u − 2
a
9
=
−u
4
c + 2u
3
c − 4u
2
c + 3cu + u
2
− c − u + 2
u
4
c − 2u
3
c + 4u
2
c − 3cu − u
2
+ 2c + u − 2
a
6
=
u
4
c − 2u
3
c + 5u
2
c − 3cu − u
2
+ 3c + u − 2
−u
4
c + 2u
3
c − 5u
2
c + 3cu + u
2
− 2c − u + 2
a
11
=
u
4
c −
1
2
u
4
+ ··· + 2c −
1
2
u
−u
4
c + u
3
c + u
4
− 2u
2
c − 2u
3
+ 3u
2
− u − 1
a
11
=
u
4
c −
1
2
u
4
+ ··· + 2c −
1
2
u
−u
4
c + u
3
c + u
4
− 2u
2
c − 2u
3
+ 3u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
3
+ 6u
2
− 12u + 12
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
2
c
2
(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
2
c
3
, c
7
(u
5
+ 3u
4
+ 6u
3
+ 7u
2
+ 4u + 2)
2
c
5
, c
6
, c
9
c
11
u
10
+ u
9
− u
8
− 3u
7
+ 2u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 4
c
8
, c
10
u
10
− 3u
9
+ ··· − 40u + 16
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
c
2
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y − 1)
2
c
3
, c
7
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y − 4)
2
c
5
, c
6
, c
9
c
11
y
10
− 3y
9
+ ··· − 40y + 16
c
8
, c
10
y
10
+ 5y
9
+ ··· − 32y + 256
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.225231 + 0.702914I
a = −0.361361 − 0.587269I
b = −0.331409 + 0.386277I
c = 0.456786 + 0.020682I
d = −1.184730 + 0.098919I
2.91669 + 1.13882I 7.28192 − 6.05450I
u = 0.225231 + 0.702914I
a = −0.361361 − 0.587269I
b = −0.331409 + 0.386277I
c = 1.40917 + 2.76067I
d = 0.853320 + 0.287358I
2.91669 + 1.13882I 7.28192 − 6.05450I
u = 0.225231 − 0.702914I
a = −0.361361 + 0.587269I
b = −0.331409 − 0.386277I
c = 0.456786 − 0.020682I
d = −1.184730 − 0.098919I
2.91669 − 1.13882I 7.28192 + 6.05450I
u = 0.225231 − 0.702914I
a = −0.361361 + 0.587269I
b = −0.331409 − 0.386277I
c = 1.40917 − 2.76067I
d = 0.853320 − 0.287358I
2.91669 − 1.13882I 7.28192 + 6.05450I
u = 1.36478
a = 1.09750
b = −1.49784
c = 0.467454 + 0.220835I
d = −0.748922 + 0.826228I
−5.22495 1.71420
u = 1.36478
a = 1.09750
b = −1.49784
c = 0.467454 − 0.220835I
d = −0.748922 − 0.826228I
−5.22495 1.71420
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59238 + 1.52933I
a = −0.187388 + 0.960762I
b = 1.58033 − 0.28256I
c = 0.362296 − 0.720965I
d = 0.443519 − 1.107390I
−10.17380 + 6.99719I 0.86096 − 3.54683I
u = 0.59238 + 1.52933I
a = −0.187388 + 0.960762I
b = 1.58033 − 0.28256I
c = −0.195707 + 1.179910I
d = 1.136810 + 0.824833I
−10.17380 + 6.99719I 0.86096 − 3.54683I
u = 0.59238 − 1.52933I
a = −0.187388 − 0.960762I
b = 1.58033 + 0.28256I
c = 0.362296 + 0.720965I
d = 0.443519 + 1.107390I
−10.17380 − 6.99719I 0.86096 + 3.54683I
u = 0.59238 − 1.52933I
a = −0.187388 − 0.960762I
b = 1.58033 + 0.28256I
c = −0.195707 − 1.179910I
d = 1.136810 − 0.824833I
−10.17380 − 6.99719I 0.86096 + 3.54683I
12
III. I
u
3
=
hu
2
+d+u+1, c+u, −au+u
2
+b+u+1, u
2
a+a
2
−u
2
+a−1, u
3
+u
2
+2u+1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
1
=
a
au − u
2
− u − 1
a
3
=
−u
−u
2
− u − 1
a
2
=
a
u
2
a + au − u
2
− u − 1
a
5
=
−u
2
a − au + u
2
− a + u + 1
u
2
a + au − u
2
− u − 1
a
10
=
−u
−u
2
− u − 1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
6
=
0
−u
a
11
=
a
u
2
a + au − u
2
− u − 1
a
11
=
a
u
2
a + au − u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
11
u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1
c
2
u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1
c
3
, c
7
, c
8
(u
3
− u
2
+ 2u − 1)
2
c
6
, c
9
(u
3
+ u
2
− 1)
2
c
10
u
6
− 5u
5
+ 8u
4
− 6u
3
+ 8u
2
− 8u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1
c
2
, c
10
y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1
c
3
, c
7
, c
8
(y
3
+ 3y
2
+ 2y − 1)
2
c
6
, c
9
(y
3
− y
2
+ 2y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.103733 + 1.107850I
b = −0.592989 − 0.847544I
c = 0.215080 − 1.307140I
d = 0.877439 − 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = 0.558626 − 0.545571I
b = 1.47043 + 0.10268I
c = 0.215080 − 1.307140I
d = 0.877439 − 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 0.103733 − 1.107850I
b = −0.592989 + 0.847544I
c = 0.215080 + 1.307140I
d = 0.877439 + 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.558626 + 0.545571I
b = 1.47043 − 0.10268I
c = 0.215080 + 1.307140I
d = 0.877439 + 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.569840
a = 0.665586
b = −1.13416
c = 0.569840
d = −0.754878
1.11345 9.01950
u = −0.569840
a = −1.99030
b = 0.379278
c = 0.569840
d = −0.754878
1.11345 9.01950
16
IV. I
u
4
= h−au + d, −2u
2
a + u
2
+ · · · − 3a + 1, −au + u
2
+ b + u + 1, u
2
a +
a
2
− u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
1
=
a
au − u
2
− u − 1
a
3
=
−u
−u
2
− u − 1
a
2
=
a
u
2
a + au − u
2
− u − 1
a
5
=
−u
2
a − au + u
2
− a + u + 1
u
2
a + au − u
2
− u − 1
a
10
=
2u
2
a + au − u
2
+ 3a − 1
au
a
9
=
2u
2
a − u
2
+ 3a − 1
au
a
6
=
2u
2
a + 2au − u
2
+ 4a − u − 2
−au − a + u + 1
a
11
=
2u
2
a − u
2
+ 3a − 1
−u
2
a + au − u − 1
a
11
=
2u
2
a − u
2
+ 3a − 1
−u
2
a + au − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1
c
2
u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1
c
3
, c
7
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
5
, c
11
(u
3
+ u
2
− 1)
2
c
8
u
6
− 5u
5
+ 8u
4
− 6u
3
+ 8u
2
− 8u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1
c
2
, c
8
y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1
c
3
, c
7
, c
10
(y
3
+ 3y
2
+ 2y − 1)
2
c
5
, c
11
(y
3
− y
2
+ 2y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.103733 + 1.107850I
b = −0.592989 − 0.847544I
c = 0.404090 − 0.016796I
d = −1.47043 − 0.10268I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = 0.558626 − 0.545571I
b = 1.47043 + 0.10268I
c = 0.460426 + 0.958773I
d = 0.592989 + 0.847544I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 0.103733 − 1.107850I
b = −0.592989 + 0.847544I
c = 0.404090 + 0.016796I
d = −1.47043 + 0.10268I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.558626 + 0.545571I
b = 1.47043 − 0.10268I
c = 0.460426 − 0.958773I
d = 0.592989 − 0.847544I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.569840
a = 0.665586
b = −1.13416
c = 0.725017
d = −0.379278
1.11345 9.01950
u = −0.569840
a = −1.99030
b = 0.379278
c = −7.45405
d = 1.13416
1.11345 9.01950
20
V. I
u
5
= hu
2
+ d + u + 1, c + u, u
2
+ b + u + 3, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
1
=
u
2
+ 1
−u
2
− u − 3
a
3
=
−u
−u
2
− u − 1
a
2
=
u
2
+ 1
−u
2
− 2
a
5
=
1
−u
2
− 2
a
10
=
−u
−u
2
− u − 1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
6
=
0
−u
a
11
=
u
2
+ 1
−u
2
− 2
a
11
=
u
2
+ 1
−u
2
− 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
u
3
+ u
2
− 1
c
2
u
3
+ u
2
+ 2u + 1
c
3
, c
7
, c
8
c
10
u
3
− u
2
+ 2u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
y
3
− y
2
+ 2y − 1
c
2
, c
3
, c
7
c
8
, c
10
y
3
+ 3y
2
+ 2y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.662359 − 0.562280I
b = −1.122560 − 0.744862I
c = 0.215080 − 1.307140I
d = 0.877439 − 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = −0.662359 + 0.562280I
b = −1.122560 + 0.744862I
c = 0.215080 + 1.307140I
d = 0.877439 + 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.569840
a = 1.32472
b = −2.75488
c = 0.569840
d = −0.754878
1.11345 9.01950
24
VI. I
v
1
= hc, d + 1, b, a + 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
1
=
−1
0
a
3
=
−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
25
(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
9
u − 1
c
6
, c
8
, c
10
c
11
u + 1
26
(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
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = −1.00000
b = 0
c = 0
d = −1.00000
3.28987 12.0000
28
VII. I
v
2
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
3
=
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 = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u − 1
c
2
, c
4
, c
5
c
10
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
30
(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
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 1.00000
d = 0
0 0
32
VIII. I
v
3
= ha, d + 1, c − a, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
3
=
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 = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u − 1
c
2
, c
4
, c
6
c
8
u + 1
c
3
, c
5
, c
7
c
10
, c
11
u
34
(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
35
(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
0 0
36
IX. I
v
4
= hc, d + 1, −av + c − v, bv + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
1
=
−1
b
a
3
=
v
0
a
2
=
v − 1
b
a
5
=
1
−b
a
10
=
0
−1
a
9
=
1
−1
a
6
=
0
1
a
11
=
−1
b − 1
a
11
=
−1
b − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −b
2
− v
2
+ 8
(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.
37
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
1.64493 7.74988 + 0.34499I
38
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
3
+ u
2
− 1)(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
2
· ((u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
2
)(u
13
− 2u
12
+ ··· + 8u − 4)
c
2
u(u + 1)
2
(u
3
+ u
2
+ 2u + 1)(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
2
· ((u
6
+ 5u
5
+ ··· + 8u + 1)
2
)(u
13
+ 14u
12
+ ··· + 88u + 16)
c
3
, c
7
u
3
(u
3
− u
2
+ 2u − 1)
5
(u
5
+ 3u
4
+ 6u
3
+ 7u
2
+ 4u + 2)
2
· (u
13
− 2u
12
+ ··· + 4u
2
− 8)
c
4
u(u + 1)
2
(u
3
+ u
2
− 1)(u
5
− u
4
− 3u
3
+ 2u
2
+ 2u + 1)
2
· ((u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
2
)(u
13
− 2u
12
+ ··· + 8u − 4)
c
5
, c
11
u(u − 1)(u + 1)(u
3
+ u
2
− 1)
3
(u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
· (u
10
+ u
9
− u
8
− 3u
7
+ 2u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 4)
· (u
13
+ 2u
12
− 4u
10
+ 8u
8
+ 7u
7
− 7u
6
− 8u
5
+ 3u
4
+ 9u
3
− u
2
− u − 1)
c
6
u(u + 1)
2
(u
3
+ u
2
− 1)
3
(u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
· (u
10
+ u
9
− u
8
− 3u
7
+ 2u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 4)
· (u
13
+ 2u
12
− 4u
10
+ 8u
8
+ 7u
7
− 7u
6
− 8u
5
+ 3u
4
+ 9u
3
− u
2
− u − 1)
c
8
, c
10
u(u + 1)
2
(u
3
− u
2
+ 2u − 1)
3
(u
6
− 5u
5
+ 8u
4
− 6u
3
+ 8u
2
− 8u + 1)
· (u
10
− 3u
9
+ ··· − 40u + 16)(u
13
− 4u
12
+ ··· − u − 1)
c
9
u(u − 1)
2
(u
3
+ u
2
− 1)
3
(u
6
− u
5
− 2u
4
+ 2u
2
+ 2u − 1)
· (u
10
+ u
9
− u
8
− 3u
7
+ 2u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 4)
· (u
13
+ 2u
12
− 4u
10
+ 8u
8
+ 7u
7
− 7u
6
− 8u
5
+ 3u
4
+ 9u
3
− u
2
− u − 1)
39
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y(y − 1)
2
(y
3
− y
2
+ 2y − 1)(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
· ((y
6
− 5y
5
+ ··· − 8y + 1)
2
)(y
13
− 14y
12
+ ··· + 88y − 16)
c
2
y(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
5
− 15y
4
+ ··· − 28y − 1)
2
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
2
· (y
13
− 30y
12
+ ··· + 2848y − 256)
c
3
, c
7
y
3
(y
3
+ 3y
2
+ 2y − 1)
5
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y − 4)
2
· (y
13
+ 6y
12
+ ··· + 64y − 64)
c
5
, c
6
, c
9
c
11
y(y − 1)
2
(y
3
− y
2
+ 2y − 1)
3
(y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1)
· (y
10
− 3y
9
+ ··· − 40y + 16)(y
13
− 4y
12
+ ··· − y − 1)
c
8
, c
10
y(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
· (y
10
+ 5y
9
+ ··· − 32y + 256)(y
13
+ 16y
12
+ ··· − 25y − 1)
40
