11a
263
(K11a
263
)
A knot diagram
1
Linearized knot diagam
4 8 1 2 11 9 10 3 7 5 6
Solving Sequence
2,8
3
5,9,10
11 4 1 7 6
c
2
c
8
c
10
c
4
c
1
c
7
c
6
c
3
, c
5
, c
9
, c
11
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−9u
7
+ 12u
6
+ 5u
5
− 62u
4
+ 26u
3
− 24u
2
+ 92d − 64u + 16,
5u
7
+ u
6
− 13u
5
+ 37u
4
+ 6u
3
− 48u
2
+ 92c + 56u + 32,
− 3u
7
+ 4u
6
− 6u
5
− 13u
4
+ 24u
3
− 8u
2
+ 46b − 6u − 10,
4u
7
− 13u
6
+ 8u
5
+ 25u
4
− 78u
3
+ 26u
2
+ 92a + 8u − 48, u
8
− u
7
− u
6
+ 5u
5
− 4u
4
+ 8u
2
+ 4u − 4i
I
u
2
= h−2u
10
+ 3u
9
+ 2u
8
− 2u
7
− 2u
6
− u
5
− 10u
4
+ 21u
3
− 16u
2
+ 4d + 10u,
− u
7
+ 2u
5
+ u
4
− u
3
− u
2
+ 2c − 4u + 2,
− 2u
10
+ 2u
9
+ 3u
8
− 2u
7
− 2u
6
+ 2u
5
− 9u
4
+ 12u
3
− 7u
2
+ 4b + 2,
2u
10
− 3u
9
− 3u
8
+ 4u
7
+ 2u
6
− 3u
5
+ 9u
4
− 15u
3
+ 11u
2
+ 4a − 6,
u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2i
I
u
3
= hu
10
− u
9
− 2u
8
+ u
6
+ u
5
+ 7u
4
− 7u
3
+ 2u
2
+ 4d − 2u − 4, u
10
− 3u
8
+ 3u
6
+ 2u
4
− 2u
3
− 3u
2
+ 4c + 6u − 2,
u
8
− 2u
6
− u
5
+ u
4
+ u
3
+ 4u
2
+ 2b − 2u,
− 2u
9
+ 3u
8
+ 2u
7
− 2u
6
− 2u
5
− u
4
− 10u
3
+ 21u
2
+ 4a − 16u + 10,
u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2i
I
u
4
= hu
10
− u
9
− 2u
8
+ u
6
+ u
5
+ 7u
4
− 7u
3
+ 2u
2
+ 4d − 2u − 4, u
10
− 3u
8
+ 3u
6
+ 2u
4
− 2u
3
− 3u
2
+ 4c + 6u − 2,
− 2u
10
+ 2u
9
+ 3u
8
− 2u
7
− 2u
6
+ 2u
5
− 9u
4
+ 12u
3
− 7u
2
+ 4b + 2,
2u
10
− 3u
9
− 3u
8
+ 4u
7
+ 2u
6
− 3u
5
+ 9u
4
− 15u
3
+ 11u
2
+ 4a − 6,
u
11
− 2u
10
− u
9
+ 3u
8
+ u
7
− 2u
6
+ 4u
5
− 11u
4
+ 9u
3
− u
2
− 2u + 2i
I
u
5
= h−a
2
c − ca + d − a − 1, −a
2
c + c
2
− ca − a − 1, a
2
+ b + a, a
3
+ 2a
2
+ a + 1, 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 50 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−9u
7
+ 12u
6
+ · · · + 92d + 16, 5u
7
+ u
6
+ · · · + 92c + 32, −3u
7
+
4u
6
+ · · · + 46b − 10, 4u
7
− 13u
6
+ · · · + 92a − 48, u
8
− u
7
+ · · · + 4u − 4i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
−0.0434783u
7
+ 0.141304u
6
+ ··· − 0.0869565u + 0.521739
0.0652174u
7
− 0.0869565u
6
+ ··· + 0.130435u + 0.217391
a
9
=
−u
−u
3
+ u
a
10
=
−0.0543478u
7
− 0.0108696u
6
+ ··· − 0.608696u − 0.347826
0.0978261u
7
− 0.130435u
6
+ ··· + 0.695652u − 0.173913
a
11
=
−0.108696u
7
− 0.0217391u
6
+ ··· − 0.217391u − 0.695652
0.173913u
7
− 0.0652174u
6
+ ··· + 0.347826u − 0.0869565
a
4
=
0.0217391u
7
+ 0.0543478u
6
+ ··· + 0.0434783u + 0.739130
0.0652174u
7
− 0.0869565u
6
+ ··· + 0.130435u + 0.217391
a
1
=
0.0217391u
7
+ 0.0543478u
6
+ ··· + 0.0434783u + 0.739130
0.0760870u
7
+ 0.0652174u
6
+ ··· − 0.347826u + 0.0869565
a
7
=
−0.0217391u
7
− 0.0543478u
6
+ ··· − 0.0434783u + 0.260870
−0.0652174u
7
+ 0.0869565u
6
+ ··· + 0.869565u − 0.217391
a
6
=
−0.0434783u
7
+ 0.141304u
6
+ ··· − 0.0869565u + 0.521739
0.0652174u
7
− 0.0869565u
6
+ ··· + 0.130435u + 0.217391
a
6
=
−0.0434783u
7
+ 0.141304u
6
+ ··· − 0.0869565u + 0.521739
0.0652174u
7
− 0.0869565u
6
+ ··· + 0.130435u + 0.217391
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1
23
u
7
−
9
23
u
6
+
25
23
u
5
−
11
23
u
4
−
8
23
u
3
+
110
23
u
2
−
136
23
u −
334
23
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
8
− u
7
− 5u
6
+ 4u
5
+ 8u
4
− 3u
3
− 3u
2
− 4u − 1
c
2
, c
8
u
8
+ u
7
− u
6
− 5u
5
− 4u
4
+ 8u
2
− 4u − 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
8
− 11y
7
+ 49y
6
− 108y
5
+ 108y
4
− 15y
3
− 31y
2
− 10y + 1
c
2
, c
8
y
8
− 3y
7
+ 3y
6
− y
5
− 96y
3
+ 96y
2
− 80y + 16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.763708 + 0.464906I
a = 0.494536 + 0.909342I
b = 0.186694 − 0.577706I
c = 0.514343 − 0.443344I
d = −0.800440 − 0.464559I
1.02858 + 1.92389I −7.30727 − 5.93806I
u = −0.763708 − 0.464906I
a = 0.494536 − 0.909342I
b = 0.186694 + 0.577706I
c = 0.514343 + 0.443344I
d = −0.800440 + 0.464559I
1.02858 − 1.92389I −7.30727 + 5.93806I
u = 0.50215 + 1.40047I
a = −1.123050 + 0.278329I
b = 1.51678 − 0.24068I
c = −0.191820 + 1.014270I
d = −0.95373 − 1.43303I
−13.1698 + 5.8977I −19.7832 − 3.0693I
u = 0.50215 − 1.40047I
a = −1.123050 − 0.278329I
b = 1.51678 + 0.24068I
c = −0.191820 − 1.014270I
d = −0.95373 + 1.43303I
−13.1698 − 5.8977I −19.7832 + 3.0693I
u = 0.509938
a = 0.497054
b = 0.282608
c = −0.554200
d = 0.253467
−0.633408 −16.3410
u = 1.37290 + 0.82084I
a = 0.288086 + 1.350870I
b = −1.50879 − 0.39741I
c = 0.937075 − 0.270804I
d = −0.71334 + 2.09107I
−16.0437 − 13.7204I −19.7312 + 6.7283I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37290 − 0.82084I
a = 0.288086 − 1.350870I
b = −1.50879 + 0.39741I
c = 0.937075 + 0.270804I
d = −0.71334 − 2.09107I
−16.0437 + 13.7204I −19.7312 − 6.7283I
u = −1.73262
a = 0.183795
b = −1.67197
c = −0.964994
d = −0.318446
17.5248 −22.0160
7
II. I
u
2
= h−2u
10
+ 3u
9
+ · · · + 4d + 10u, −u
7
+ 2u
5
+ · · · + 2c + 2, −2u
10
+
2u
9
+ · · · + 4b + 2, 2u
10
− 3u
9
+ · · · + 4a − 6, u
11
− 2u
10
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
−
1
2
u
10
+
3
4
u
9
+ ··· −
11
4
u
2
+
3
2
1
2
u
10
−
1
2
u
9
+ ··· +
7
4
u
2
−
1
2
a
9
=
−u
−u
3
+ u
a
10
=
1
2
u
7
− u
5
+ ··· + 2u − 1
1
2
u
10
−
3
4
u
9
+ ··· + 4u
2
−
5
2
u
a
11
=
1
2
u
7
− u
5
+
1
2
u
3
+
3
2
u − 1
1
2
u
10
−
1
2
u
9
+ ··· +
7
2
u
2
− 2u
a
4
=
1
4
u
9
−
1
2
u
7
+ ··· − u
2
+ 1
1
2
u
10
−
1
2
u
9
+ ··· +
7
4
u
2
−
1
2
a
1
=
1
4
u
9
−
1
2
u
7
+ ··· − u
2
+ 1
1
4
u
9
−
1
2
u
7
+ ··· −
1
2
u
2
+
1
2
u
a
7
=
−
1
2
u
10
+
5
4
u
9
+ ··· +
1
2
u + 1
u
10
−
3
2
u
9
+ ··· − u −
1
2
a
6
=
−
1
2
u
10
+
3
4
u
9
+ ··· +
1
2
u + 1
−
1
2
u
9
+
1
4
u
8
+ ··· − 2u +
1
2
a
6
=
−
1
2
u
10
+
3
4
u
9
+ ··· +
1
2
u + 1
−
1
2
u
9
+
1
4
u
8
+ ··· − 2u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
10
− 6u
8
− 2u
7
+ 6u
6
+ 4u
5
+ 8u
4
− 8u
3
− 10u
2
+ 8u − 16
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
10
, c
11
u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1
c
2
, c
8
u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2
c
6
, c
7
, c
9
u
11
− 3u
9
− 2u
8
+ 3u
7
+ 4u
6
− 2u
4
− u
3
+ 3u
2
− 4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
10
, c
11
y
11
− 12y
10
+ ··· − 5y −1
c
2
, c
8
y
11
− 6y
10
+ ··· + 8y −4
c
6
, c
7
, c
9
y
11
− 6y
10
+ ··· + 24y −16
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217339 + 1.116860I
a = −0.959694 − 0.121609I
b = 1.379210 + 0.103381I
c = 0.530848 − 0.577122I
d = −2.14358 + 0.93612I
−6.49548 − 2.41892I −16.9282 + 2.8895I
u = −0.217339 − 1.116860I
a = −0.959694 + 0.121609I
b = 1.379210 − 0.103381I
c = 0.530848 + 0.577122I
d = −2.14358 − 0.93612I
−6.49548 + 2.41892I −16.9282 − 2.8895I
u = 1.116820 + 0.404951I
a = 0.142488 − 1.095710I
b = 0.399448 + 0.789847I
c = 1.146260 − 0.241815I
d = −1.31237 + 1.12740I
−3.96110 − 4.69742I −14.9188 + 5.8832I
u = 1.116820 − 0.404951I
a = 0.142488 + 1.095710I
b = 0.399448 − 0.789847I
c = 1.146260 + 0.241815I
d = −1.31237 − 1.12740I
−3.96110 + 4.69742I −14.9188 − 5.8832I
u = 0.323694 + 0.583510I
a = 1.18678 − 0.80697I
b = −0.172742 + 0.362556I
c = −0.63939 + 1.57288I
d = −0.309250 − 0.329055I
−1.55892 + 0.74196I −8.46073 − 1.11909I
u = 0.323694 − 0.583510I
a = 1.18678 + 0.80697I
b = −0.172742 − 0.362556I
c = −0.63939 − 1.57288I
d = −0.309250 + 0.329055I
−1.55892 − 0.74196I −8.46073 + 1.11909I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38823 + 0.36743I
a = −0.243517 + 0.779738I
b = −1.50982 − 0.17565I
c = −0.526224 + 0.695676I
d = −1.10814 + 1.10674I
−11.90560 − 2.58451I −20.1919 + 1.0166I
u = 1.38823 − 0.36743I
a = −0.243517 − 0.779738I
b = −1.50982 + 0.17565I
c = −0.526224 − 0.695676I
d = −1.10814 − 1.10674I
−11.90560 + 2.58451I −20.1919 − 1.0166I
u = −0.552641
a = −0.218260
b = 0.780044
c = −2.03993
d = 3.71662
−4.41605 −21.4290
u = −1.33508 + 0.61220I
a = −0.016930 − 1.207730I
b = −1.48612 + 0.29515I
c = 0.508471 − 0.520729I
d = −0.98497 − 1.74274I
−10.05940 + 8.65115I −17.7857 − 5.5789I
u = −1.33508 − 0.61220I
a = −0.016930 + 1.207730I
b = −1.48612 − 0.29515I
c = 0.508471 + 0.520729I
d = −0.98497 + 1.74274I
−10.05940 − 8.65115I −17.7857 + 5.5789I
12
III. I
u
3
= hu
10
− u
9
+ · · · + 4d − 4, u
10
− 3u
8
+ · · · + 4c − 2, u
8
− 2u
6
+ · · · +
2b − 2u, −2u
9
+ 3u
8
+ · · · + 4a + 10, u
11
− 2u
10
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
1
2
u
9
−
3
4
u
8
+ ··· + 4u −
5
2
−
1
2
u
8
+ u
6
+ ··· − 2u
2
+ u
a
9
=
−u
−u
3
+ u
a
10
=
−
1
4
u
10
+
3
4
u
8
+ ··· −
3
2
u +
1
2
−
1
4
u
10
+
1
4
u
9
+ ··· +
1
2
u + 1
a
11
=
−
1
2
u
9
+ u
8
+ ··· −
9
2
u + 2
1
a
4
=
1
2
u
9
−
5
4
u
8
+ ··· + 5u −
5
2
−
1
2
u
8
+ u
6
+ ··· − 2u
2
+ u
a
1
=
1
2
u
9
−
5
4
u
8
+ ··· + 5u −
5
2
−
1
4
u
10
+
1
2
u
8
+ ··· + u
3
− 1
a
7
=
−
1
4
u
8
+
1
2
u
6
+ ··· +
1
2
u −
1
2
1
2
u
5
−
1
2
u
3
−
1
2
u
2
+ u
a
6
=
1
2
u
10
−
1
4
u
9
+ ··· + u −
3
2
1
2
u
10
−
1
2
u
9
+ ··· + u −
1
2
a
6
=
1
2
u
10
−
1
4
u
9
+ ··· + u −
3
2
1
2
u
10
−
1
2
u
9
+ ··· + u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
10
− 6u
8
− 2u
7
+ 6u
6
+ 4u
5
+ 8u
4
− 8u
3
− 10u
2
+ 8u − 16
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
11
− 3u
9
− 2u
8
+ 3u
7
+ 4u
6
− 2u
4
− u
3
+ 3u
2
− 4
c
2
, c
8
u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
11
− 6y
10
+ ··· + 24y −16
c
2
, c
8
y
11
− 6y
10
+ ··· + 8y −4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
11
− 12y
10
+ ··· − 5y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217339 + 1.116860I
a = 1.16746 + 1.69211I
b = −0.529187 − 0.718311I
c = 0.142356 + 1.207200I
d = 0.344399 − 1.045410I
−6.49548 − 2.41892I −16.9282 + 2.8895I
u = −0.217339 − 1.116860I
a = 1.16746 − 1.69211I
b = −0.529187 + 0.718311I
c = 0.142356 − 1.207200I
d = 0.344399 + 1.045410I
−6.49548 + 2.41892I −16.9282 − 2.8895I
u = 1.116820 + 0.404951I
a = −0.71505 + 1.26875I
b = −1.378090 − 0.194114I
c = −0.542743 − 0.510432I
d = 0.602844 − 1.166020I
−3.96110 − 4.69742I −14.9188 + 5.8832I
u = 1.116820 − 0.404951I
a = −0.71505 − 1.26875I
b = −1.378090 + 0.194114I
c = −0.542743 + 0.510432I
d = 0.602844 + 1.166020I
−3.96110 + 4.69742I −14.9188 − 5.8832I
u = 0.323694 + 0.583510I
a = −0.656040 + 0.166054I
b = 1.124760 − 0.136043I
c = −0.349546 − 0.489945I
d = 0.855030 + 0.431288I
−1.55892 + 0.74196I −8.46073 − 1.11909I
u = 0.323694 − 0.583510I
a = −0.656040 − 0.166054I
b = 1.124760 + 0.136043I
c = −0.349546 + 0.489945I
d = 0.855030 − 0.431288I
−1.55892 − 0.74196I −8.46073 + 1.11909I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38823 + 0.36743I
a = −0.548785 + 0.942487I
b = 0.986131 − 0.772404I
c = 1.047690 − 0.150769I
d = −0.624556 + 0.992977I
−11.90560 − 2.58451I −20.1919 + 1.0166I
u = 1.38823 − 0.36743I
a = −0.548785 − 0.942487I
b = 0.986131 + 0.772404I
c = 1.047690 + 0.150769I
d = −0.624556 − 0.992977I
−11.90560 + 2.58451I −20.1919 − 1.0166I
u = −0.552641
a = −6.72520
b = −1.12735
c = 1.41149
d = 0.120619
−4.41605 −21.4290
u = −1.33508 + 0.61220I
a = 0.115017 + 1.358080I
b = 0.360061 − 1.006500I
c = −1.003500 − 0.239081I
d = 0.76197 + 1.60205I
−10.05940 + 8.65115I −17.7857 − 5.5789I
u = −1.33508 − 0.61220I
a = 0.115017 − 1.358080I
b = 0.360061 + 1.006500I
c = −1.003500 + 0.239081I
d = 0.76197 − 1.60205I
−10.05940 − 8.65115I −17.7857 + 5.5789I
17
IV. I
u
4
= hu
10
− u
9
+ · · · + 4d − 4, u
10
− 3u
8
+ · · · + 4c − 2, −2u
10
+ 2u
9
+
· · · + 4b + 2, 2u
10
− 3u
9
+ · · · + 4a − 6, u
11
− 2u
10
+ · · · − 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
5
=
−
1
2
u
10
+
3
4
u
9
+ ··· −
11
4
u
2
+
3
2
1
2
u
10
−
1
2
u
9
+ ··· +
7
4
u
2
−
1
2
a
9
=
−u
−u
3
+ u
a
10
=
−
1
4
u
10
+
3
4
u
8
+ ··· −
3
2
u +
1
2
−
1
4
u
10
+
1
4
u
9
+ ··· +
1
2
u + 1
a
11
=
−
1
2
u
10
+
3
2
u
8
+ ··· +
5
2
u
2
−
3
2
u
1
a
4
=
1
4
u
9
−
1
2
u
7
+ ··· − u
2
+ 1
1
2
u
10
−
1
2
u
9
+ ··· +
7
4
u
2
−
1
2
a
1
=
1
4
u
9
−
1
2
u
7
+ ··· − u
2
+ 1
1
4
u
9
−
1
2
u
7
+ ··· −
1
2
u
2
+
1
2
u
a
7
=
−
1
4
u
8
+
1
2
u
6
+ ··· +
1
2
u −
1
2
1
2
u
5
−
1
2
u
3
−
1
2
u
2
+ u
a
6
=
1
2
u
10
−
1
4
u
9
+ ··· + u −
3
2
1
2
u
10
−
1
2
u
9
+ ··· + u −
1
2
a
6
=
1
2
u
10
−
1
4
u
9
+ ··· + u −
3
2
1
2
u
10
−
1
2
u
9
+ ··· + u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
10
− 6u
8
− 2u
7
+ 6u
6
+ 4u
5
+ 8u
4
− 8u
3
− 10u
2
+ 8u − 16
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
u
11
− 2u
10
− 4u
9
+ 8u
8
+ 6u
7
− 8u
6
− 7u
5
− 2u
4
+ 7u
3
+ 3u
2
− u + 1
c
2
, c
8
u
11
+ 2u
10
− u
9
− 3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
− 2u − 2
c
5
, c
10
, c
11
u
11
− 3u
9
− 2u
8
+ 3u
7
+ 4u
6
− 2u
4
− u
3
+ 3u
2
− 4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y
11
− 12y
10
+ ··· − 5y −1
c
2
, c
8
y
11
− 6y
10
+ ··· + 8y −4
c
5
, c
10
, c
11
y
11
− 6y
10
+ ··· + 24y −16
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217339 + 1.116860I
a = −0.959694 − 0.121609I
b = 1.379210 + 0.103381I
c = 0.142356 + 1.207200I
d = 0.344399 − 1.045410I
−6.49548 − 2.41892I −16.9282 + 2.8895I
u = −0.217339 − 1.116860I
a = −0.959694 + 0.121609I
b = 1.379210 − 0.103381I
c = 0.142356 − 1.207200I
d = 0.344399 + 1.045410I
−6.49548 + 2.41892I −16.9282 − 2.8895I
u = 1.116820 + 0.404951I
a = 0.142488 − 1.095710I
b = 0.399448 + 0.789847I
c = −0.542743 − 0.510432I
d = 0.602844 − 1.166020I
−3.96110 − 4.69742I −14.9188 + 5.8832I
u = 1.116820 − 0.404951I
a = 0.142488 + 1.095710I
b = 0.399448 − 0.789847I
c = −0.542743 + 0.510432I
d = 0.602844 + 1.166020I
−3.96110 + 4.69742I −14.9188 − 5.8832I
u = 0.323694 + 0.583510I
a = 1.18678 − 0.80697I
b = −0.172742 + 0.362556I
c = −0.349546 − 0.489945I
d = 0.855030 + 0.431288I
−1.55892 + 0.74196I −8.46073 − 1.11909I
u = 0.323694 − 0.583510I
a = 1.18678 + 0.80697I
b = −0.172742 − 0.362556I
c = −0.349546 + 0.489945I
d = 0.855030 − 0.431288I
−1.55892 − 0.74196I −8.46073 + 1.11909I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38823 + 0.36743I
a = −0.243517 + 0.779738I
b = −1.50982 − 0.17565I
c = 1.047690 − 0.150769I
d = −0.624556 + 0.992977I
−11.90560 − 2.58451I −20.1919 + 1.0166I
u = 1.38823 − 0.36743I
a = −0.243517 − 0.779738I
b = −1.50982 + 0.17565I
c = 1.047690 + 0.150769I
d = −0.624556 − 0.992977I
−11.90560 + 2.58451I −20.1919 − 1.0166I
u = −0.552641
a = −0.218260
b = 0.780044
c = 1.41149
d = 0.120619
−4.41605 −21.4290
u = −1.33508 + 0.61220I
a = −0.016930 − 1.207730I
b = −1.48612 + 0.29515I
c = −1.003500 − 0.239081I
d = 0.76197 + 1.60205I
−10.05940 + 8.65115I −17.7857 − 5.5789I
u = −1.33508 − 0.61220I
a = −0.016930 + 1.207730I
b = −1.48612 − 0.29515I
c = −1.003500 + 0.239081I
d = 0.76197 − 1.60205I
−10.05940 − 8.65115I −17.7857 + 5.5789I
22
V. I
u
5
=
h−a
2
c−ca+d−a−1, −a
2
c+c
2
−ca −a−1, a
2
+b +a, a
3
+2a
2
+a +1, u+1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
−1
a
3
=
1
1
a
5
=
a
−a
2
− a
a
9
=
1
0
a
10
=
c
a
2
c + ca + a + 1
a
11
=
ca + a
2
+ c + a + 1
1
a
4
=
−a
2
−a
2
− a
a
1
=
−a
2
a
a
7
=
−a
2
c − ca − a − 1
−c
a
6
=
−a
2
c − ca − c − a − 1
−c
a
6
=
−a
2
c − ca − c − a − 1
−c
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
(u
3
− u − 1)
2
c
2
, c
8
(u − 1)
6
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
(y
3
− 2y
2
+ y −1)
2
c
2
, c
8
(y −1)
6
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.122561 + 0.744862I
b = 0.662359 − 0.562280I
c = 0.662359 + 0.562280I
d = 0.122561 + 0.744862I
−4.93480 −18.0000
u = −1.00000
a = −0.122561 + 0.744862I
b = 0.662359 − 0.562280I
c = −1.32472
d = 1.75488
−4.93480 −18.0000
u = −1.00000
a = −0.122561 − 0.744862I
b = 0.662359 + 0.562280I
c = 0.662359 − 0.562280I
d = 0.122561 − 0.744862I
−4.93480 −18.0000
u = −1.00000
a = −0.122561 − 0.744862I
b = 0.662359 + 0.562280I
c = −1.32472
d = 1.75488
−4.93480 −18.0000
u = −1.00000
a = −1.75488
b = −1.32472
c = 0.662359 + 0.562280I
d = 0.122561 + 0.744862I
−4.93480 −18.0000
u = −1.00000
a = −1.75488
b = −1.32472
c = 0.662359 − 0.562280I
d = 0.122561 − 0.744862I
−4.93480 −18.0000
26
VI. I
v
1
= ha, d, c + 1, b − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
10
=
−1
0
a
11
=
−1
−1
a
4
=
1
1
a
1
=
0
−1
a
7
=
−1
0
a
6
=
−1
0
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u − 1
c
2
, c
6
, c
7
c
8
, c
9
u
c
3
, c
4
, c
10
c
11
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
10
, c
11
y −1
c
2
, c
6
, c
7
c
8
, c
9
y
29
(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
30
VII. I
v
2
= hc, d + 1, b, a − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
1
0
a
9
=
−1
0
a
10
=
0
−1
a
11
=
1
−1
a
4
=
1
0
a
1
=
1
0
a
7
=
−1
1
a
6
=
0
1
a
6
=
0
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
2
, c
3
c
4
, c
8
u
c
5
, c
9
u + 1
c
6
, c
7
, c
10
c
11
u − 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
33
(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
34
VIII. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
−1
0
a
3
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
10
=
0
−1
a
11
=
0
−1
a
4
=
1
1
a
1
=
0
−1
a
7
=
−1
1
a
6
=
0
1
a
6
=
0
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
6
, c
7
u − 1
c
2
, c
5
, c
8
c
10
, c
11
u
c
3
, c
4
, c
9
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y −1
c
2
, c
5
, c
8
c
10
, c
11
y
37
(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
38
IX. I
v
4
= ha, da − c + 1, dv − 1, cv − a − v, b − 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
v
0
a
3
=
1
0
a
5
=
0
1
a
9
=
v
0
a
10
=
1
d
a
11
=
1
d + 1
a
4
=
1
1
a
1
=
0
−1
a
7
=
v −1
−d
a
6
=
−1
−d
a
6
=
−1
−d
(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.
39
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−4.93480 −21.2841 + 0.0228I
40
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u(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
c
2
, c
8
u
3
(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
3
, c
4
, c
9
u(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
c
5
, c
10
, c
11
u(u − 1)(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
41
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y(y − 1)
2
(y
3
− 2y
2
+ y −1)
2
· (y
8
− 11y
7
+ 49y
6
− 108y
5
+ 108y
4
− 15y
3
− 31y
2
− 10y + 1)
· ((y
11
− 12y
10
+ ··· − 5y −1)
2
)(y
11
− 6y
10
+ ··· + 24y −16)
c
2
, c
8
y
3
(y −1)
6
(y
8
− 3y
7
+ 3y
6
− y
5
− 96y
3
+ 96y
2
− 80y + 16)
· (y
11
− 6y
10
+ ··· + 8y −4)
3
42
