12a
0574
(K12a
0574
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 12 6 4 5 1 8
Solving Sequence
4,10
5 11
2,6
7 9 3 1 8 12
c
4
c
10
c
5
c
6
c
9
c
3
c
1
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
24
− 5u
23
+ ··· + b + 5, 5u
24
− 7u
23
+ ··· + 2a + 4, u
25
− 3u
24
+ ··· + 9u
2
− 2i
I
u
2
= hu
17
a − u
17
+ ··· + b + a, 2u
17
a + 2u
17
+ ··· + a
2
+ 2, u
18
+ 2u
17
+ ··· + u + 1i
I
u
3
= hb − u + 1, 3a − 2u + 3, u
2
− 3i
I
u
4
= hb, a + 1, u + 1i
I
u
5
= hb + 2, a + 1, u − 1i
I
u
6
= hb + 1, a, u − 1i
I
u
7
= hb + 1, a + 1, u − 1i
I
v
1
= ha, b + 1, v + 1i
* 8 irreducible components of dim
C
= 0, with total 68 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
= h4u
24
−5u
23
+· · ·+b+5, 5u
24
−7u
23
+· · ·+2a+4, u
25
−3u
24
+· · ·+9u
2
−2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−
5
2
u
24
+
7
2
u
23
+ ··· −
3
2
u − 2
−4u
24
+ 5u
23
+ ··· − 3u − 5
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−
5
2
u
24
+
7
2
u
23
+ ··· −
3
2
u − 2
−3u
24
+ 4u
23
+ ··· − 2u − 3
a
9
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
1
=
−
9
2
u
24
+
13
2
u
23
+ ··· −
7
2
u − 5
−7u
24
+ 9u
23
+ ··· − 5u − 9
a
8
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
12
=
5
2
u
24
−
7
2
u
23
+ ··· +
1
2
u + 3
4u
24
− 5u
23
+ ··· + 4u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
24
− 8u
23
− 118u
22
+ 104u
21
+ 738u
20
− 568u
19
− 2532u
18
+
1728u
17
+ 5122u
16
− 3322u
15
− 6024u
14
+ 4356u
13
+ 3552u
12
− 3876u
11
− 116u
10
+
1936u
9
− 1222u
8
− 156u
7
+ 670u
6
− 304u
5
− 22u
4
+ 112u
3
− 56u
2
+ 16u − 4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
25
+ 11u
24
+ ··· + 16u + 1
c
2
, c
6
, c
7
c
12
u
25
− u
24
+ ··· − 2u − 1
c
3
, c
4
, c
5
c
9
, c
10
u
25
− 3u
24
+ ··· + 9u
2
− 2
c
8
u
25
− 15u
24
+ ··· − 272u + 142
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
25
+ 13y
24
+ ··· + 88y −1
c
2
, c
6
, c
7
c
12
y
25
− 11y
24
+ ··· + 16y −1
c
3
, c
4
, c
5
c
9
, c
10
y
25
− 33y
24
+ ··· + 36y −4
c
8
y
25
− 9y
24
+ ··· + 269092y −20164
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014520 + 0.347002I
a = −0.043435 + 0.313283I
b = 1.26937 + 1.85429I
−4.53390 + 11.98000I −18.3056 − 9.4054I
u = −1.014520 − 0.347002I
a = −0.043435 − 0.313283I
b = 1.26937 − 1.85429I
−4.53390 − 11.98000I −18.3056 + 9.4054I
u = −0.875840 + 0.298355I
a = 0.324656 + 0.199831I
b = −0.824925 − 0.525750I
−0.08743 + 1.64240I −12.36047 − 1.45966I
u = −0.875840 − 0.298355I
a = 0.324656 − 0.199831I
b = −0.824925 + 0.525750I
−0.08743 − 1.64240I −12.36047 + 1.45966I
u = 1.08434
a = −0.492978
b = −0.942393
−5.05178 −16.4940
u = −1.142900 + 0.163650I
a = −0.760257 − 0.659750I
b = −1.148230 − 0.116814I
−6.80316 − 3.32641I −19.9139 + 4.3823I
u = −1.142900 − 0.163650I
a = −0.760257 + 0.659750I
b = −1.148230 + 0.116814I
−6.80316 + 3.32641I −19.9139 − 4.3823I
u = 0.748460 + 0.331609I
a = 0.182754 − 0.355577I
b = 0.439503 − 1.224670I
0.58577 − 4.17677I −12.9289 + 7.8019I
u = 0.748460 − 0.331609I
a = 0.182754 + 0.355577I
b = 0.439503 + 1.224670I
0.58577 + 4.17677I −12.9289 − 7.8019I
u = 0.489290 + 0.461642I
a = 0.494840 − 0.083674I
b = −1.112620 + 0.488193I
−1.55633 + 5.36068I −15.2414 − 2.7515I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489290 − 0.461642I
a = 0.494840 + 0.083674I
b = −1.112620 − 0.488193I
−1.55633 − 5.36068I −15.2414 + 2.7515I
u = 0.223404 + 0.580813I
a = 0.00021 + 2.17964I
b = −0.147329 − 0.569907I
−0.71018 − 8.82975I −13.3096 + 8.6436I
u = 0.223404 − 0.580813I
a = 0.00021 − 2.17964I
b = −0.147329 + 0.569907I
−0.71018 + 8.82975I −13.3096 − 8.6436I
u = 0.047295 + 0.535702I
a = 0.79115 − 1.42217I
b = 0.192529 + 0.279886I
2.69786 + 1.19945I −6.93738 − 2.54623I
u = 0.047295 − 0.535702I
a = 0.79115 + 1.42217I
b = 0.192529 − 0.279886I
2.69786 − 1.19945I −6.93738 + 2.54623I
u = −1.63846 + 0.04838I
a = −0.24414 + 2.30889I
b = −0.31656 + 2.94869I
−7.64782 + 5.42310I −15.0279 − 5.6441I
u = −1.63846 − 0.04838I
a = −0.24414 − 2.30889I
b = −0.31656 − 2.94869I
−7.64782 − 5.42310I −15.0279 + 5.6441I
u = −0.337545
a = 0.668217
b = −0.205875
−0.538410 −18.2630
u = 1.68786 + 0.06949I
a = −1.26126 + 1.27240I
b = −2.17832 + 1.75017I
−9.13866 − 3.01203I −13.72954 + 0.I
u = 1.68786 − 0.06949I
a = −1.26126 − 1.27240I
b = −2.17832 − 1.75017I
−9.13866 + 3.01203I −13.72954 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72244 + 0.09263I
a = 1.48000 − 2.81178I
b = 2.64308 − 3.71258I
−14.2211 − 13.7690I −19.5082 + 7.8820I
u = 1.72244 − 0.09263I
a = 1.48000 + 2.81178I
b = 2.64308 + 3.71258I
−14.2211 + 13.7690I −19.5082 − 7.8820I
u = −1.74758
a = −1.18512
b = −1.50038
−15.2938 −14.4450
u = 1.75336 + 0.03699I
a = −0.959572 − 0.248462I
b = −0.992169 − 0.771791I
−17.2303 + 2.5055I −21.1359 − 5.5116I
u = 1.75336 − 0.03699I
a = −0.959572 + 0.248462I
b = −0.992169 + 0.771791I
−17.2303 − 2.5055I −21.1359 + 5.5116I
7
II.
I
u
2
= hu
17
a−u
17
+· · ·+b+a, 2u
17
a+2u
17
+· · ·+a
2
+2, u
18
+2u
17
+· · ·+u+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
a
−u
17
a + u
17
+ ··· − a + u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
a
u
17
a − u
17
+ ··· + a − u
a
9
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
1
=
−u
17
a + 11u
15
a + ··· + a − 1
−2u
17
a + u
17
+ ··· − a + u
a
8
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
12
=
−u
13
− u
11
a + ··· + a − 1
u
17
a + u
17
+ ··· + 2u
2
+ a
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
15
−40u
13
+152u
11
+4u
10
−272u
9
−28u
8
+232u
7
+64u
6
−84u
5
−52u
4
+12u
2
+4u−14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
36
+ 20u
35
+ ··· + 66u + 9
c
2
, c
6
, c
7
c
12
u
36
− 10u
34
+ ··· + 11u
2
− 3
c
3
, c
4
, c
5
c
9
, c
10
(u
18
+ 2u
17
+ ··· + u + 1)
2
c
8
(u
18
+ 4u
17
+ ··· + 5u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
36
− 8y
35
+ ··· + 198y + 81
c
2
, c
6
, c
7
c
12
y
36
− 20y
35
+ ··· − 66y + 9
c
3
, c
4
, c
5
c
9
, c
10
(y
18
− 24y
17
+ ··· + 3y + 1)
2
c
8
(y
18
+ 22y
16
+ ··· − 65y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972680 + 0.237177I
a = −1.129940 − 0.718306I
b = −1.113160 + 0.114624I
−6.99539 + 3.19755I −20.6137 − 5.3239I
u = −0.972680 + 0.237177I
a = 0.005899 + 0.226891I
b = 0.94715 + 2.42519I
−6.99539 + 3.19755I −20.6137 − 5.3239I
u = −0.972680 − 0.237177I
a = −1.129940 + 0.718306I
b = −1.113160 − 0.114624I
−6.99539 − 3.19755I −20.6137 + 5.3239I
u = −0.972680 − 0.237177I
a = 0.005899 − 0.226891I
b = 0.94715 − 2.42519I
−6.99539 − 3.19755I −20.6137 + 5.3239I
u = 0.965445 + 0.329507I
a = 0.319004 − 0.279303I
b = −0.711465 + 0.510542I
−1.96003 − 6.64718I −15.2451 + 6.1969I
u = 0.965445 + 0.329507I
a = −0.001264 − 0.306149I
b = 1.05963 − 1.87946I
−1.96003 − 6.64718I −15.2451 + 6.1969I
u = 0.965445 − 0.329507I
a = 0.319004 + 0.279303I
b = −0.711465 − 0.510542I
−1.96003 + 6.64718I −15.2451 − 6.1969I
u = 0.965445 − 0.329507I
a = −0.001264 + 0.306149I
b = 1.05963 + 1.87946I
−1.96003 + 6.64718I −15.2451 − 6.1969I
u = 0.884294
a = −1.43019
b = −0.962086
−5.00473 −16.9870
u = 0.884294
a = 0.144030
b = −1.72715
−5.00473 −16.9870
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572262 + 0.347341I
a = 0.345746 + 0.427514I
b = 0.323982 + 0.688753I
0.205439 − 0.564924I −12.70794 − 1.84066I
u = −0.572262 + 0.347341I
a = 0.448687 + 0.081566I
b = −0.979928 − 0.500327I
0.205439 − 0.564924I −12.70794 − 1.84066I
u = −0.572262 − 0.347341I
a = 0.345746 − 0.427514I
b = 0.323982 − 0.688753I
0.205439 + 0.564924I −12.70794 + 1.84066I
u = −0.572262 − 0.347341I
a = 0.448687 − 0.081566I
b = −0.979928 + 0.500327I
0.205439 + 0.564924I −12.70794 + 1.84066I
u = −0.158501 + 0.549521I
a = 0.656801 + 1.100770I
b = 0.342703 − 0.177435I
1.49299 + 3.66002I −9.51029 − 4.64953I
u = −0.158501 + 0.549521I
a = 0.32363 − 2.20170I
b = −0.075367 + 0.478624I
1.49299 + 3.66002I −9.51029 − 4.64953I
u = −0.158501 − 0.549521I
a = 0.656801 − 1.100770I
b = 0.342703 + 0.177435I
1.49299 − 3.66002I −9.51029 + 4.64953I
u = −0.158501 − 0.549521I
a = 0.32363 + 2.20170I
b = −0.075367 − 0.478624I
1.49299 − 3.66002I −9.51029 + 4.64953I
u = 0.184698 + 0.383796I
a = 0.515622 − 0.022033I
b = −1.164460 + 0.166059I
−3.44032 − 1.02752I −14.6811 + 6.4558I
u = 0.184698 + 0.383796I
a = 0.63653 + 3.61007I
b = −0.227517 − 0.284301I
−3.44032 − 1.02752I −14.6811 + 6.4558I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.184698 − 0.383796I
a = 0.515622 + 0.022033I
b = −1.164460 − 0.166059I
−3.44032 + 1.02752I −14.6811 − 6.4558I
u = 0.184698 − 0.383796I
a = 0.63653 − 3.61007I
b = −0.227517 + 0.284301I
−3.44032 + 1.02752I −14.6811 − 6.4558I
u = 1.62858
a = −0.74507 + 1.95151I
b = −1.21459 + 2.49051I
−7.25470 −14.0270
u = 1.62858
a = −0.74507 − 1.95151I
b = −1.21459 − 2.49051I
−7.25470 −14.0270
u = −1.70718 + 0.02414I
a = −0.860242 + 0.085930I
b = −0.559302 + 0.302376I
−14.4445 + 0.2735I −18.2189 + 1.0708I
u = −1.70718 + 0.02414I
a = −1.96468 − 1.25832I
b = −3.02809 − 1.79960I
−14.4445 + 0.2735I −18.2189 + 1.0708I
u = −1.70718 − 0.02414I
a = −0.860242 − 0.085930I
b = −0.559302 − 0.302376I
−14.4445 − 0.2735I −18.2189 − 1.0708I
u = −1.70718 − 0.02414I
a = −1.96468 + 1.25832I
b = −3.02809 + 1.79960I
−14.4445 − 0.2735I −18.2189 − 1.0708I
u = −1.70822 + 0.08549I
a = −1.22072 − 1.11193I
b = −2.18354 − 1.58992I
−11.40320 + 8.29410I −16.5396 − 4.6645I
u = −1.70822 + 0.08549I
a = 1.12540 + 2.95401I
b = 2.04448 + 3.93426I
−11.40320 + 8.29410I −16.5396 − 4.6645I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70822 − 0.08549I
a = −1.22072 + 1.11193I
b = −2.18354 + 1.58992I
−11.40320 − 8.29410I −16.5396 + 4.6645I
u = −1.70822 − 0.08549I
a = 1.12540 − 2.95401I
b = 2.04448 − 3.93426I
−11.40320 − 8.29410I −16.5396 + 4.6645I
u = 1.71227 + 0.06112I
a = −0.814985 − 0.187785I
b = −0.451319 − 0.694586I
−16.5429 − 4.3884I −20.9761 + 3.5533I
u = 1.71227 + 0.06112I
a = 1.00266 − 3.75542I
b = 1.83542 − 5.24315I
−16.5429 − 4.3884I −20.9761 + 3.5533I
u = 1.71227 − 0.06112I
a = −0.814985 + 0.187785I
b = −0.451319 + 0.694586I
−16.5429 + 4.3884I −20.9761 − 3.5533I
u = 1.71227 − 0.06112I
a = 1.00266 + 3.75542I
b = 1.83542 + 5.24315I
−16.5429 + 4.3884I −20.9761 − 3.5533I
14
III. I
u
3
= hb − u + 1, 3a − 2u + 3, u
2
− 3i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
3
a
11
=
−u
−2u
a
2
=
2
3
u − 1
u − 1
a
6
=
−2
−3
a
7
=
−
2
3
u − 1
−u − 2
a
9
=
u
u
a
3
=
−2
−3
a
1
=
2
3
u + 1
u + 2
a
8
=
−u
−2u
a
12
=
−
1
3
u + 1
−u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
(u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
2
− 3
c
6
, c
12
(u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y −3)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205
a = 0.154701
b = 0.732051
−16.4493 −24.0000
u = −1.73205
a = −2.15470
b = −2.73205
−16.4493 −24.0000
18
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
−1
a
5
=
1
1
a
11
=
1
0
a
2
=
−1
0
a
6
=
0
1
a
7
=
−1
1
a
9
=
−1
−1
a
3
=
0
−1
a
1
=
−1
1
a
8
=
−1
0
a
12
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
, c
11
, c
12
u − 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−6.57974 −24.0000
22
V. I
u
5
= hb + 2, a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
1
a
11
=
−1
0
a
2
=
−1
−2
a
6
=
0
1
a
7
=
−1
−1
a
9
=
1
1
a
3
=
0
−1
a
1
=
−1
−1
a
8
=
1
0
a
12
=
−2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
23
(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
11
, c
12
u − 1
c
2
, c
7
, c
9
c
10
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −2.00000
−6.57974 −24.0000
26
VI. I
u
6
= hb + 1, a, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
1
a
11
=
−1
0
a
2
=
0
−1
a
6
=
0
1
a
7
=
0
1
a
9
=
1
1
a
3
=
0
−1
a
1
=
0
−1
a
8
=
1
0
a
12
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
c
3
, c
4
, c
5
c
7
, c
9
, c
10
c
12
u − 1
c
8
, c
11
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−4.93480 −18.0000
30
VII. I
u
7
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
5
=
1
1
a
11
=
−1
0
a
2
=
−1
−1
a
6
=
0
1
a
7
=
−1
0
a
9
=
1
1
a
3
=
0
−1
a
1
=
−1
0
a
8
=
1
0
a
12
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
9
c
10
u − 1
c
7
, c
11
, c
12
u
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
9
, c
10
y −1
c
7
, c
11
, c
12
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−4.93480 −18.0000
34
VIII. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
−1
0
a
5
=
1
0
a
11
=
−1
0
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
9
=
−1
0
a
3
=
1
0
a
1
=
−1
−1
a
8
=
−1
0
a
12
=
−2
−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
7
c
11
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
12
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
38
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
5
(u + 1)(u
25
+ 11u
24
+ ··· + 16u + 1)
· (u
36
+ 20u
35
+ ··· + 66u + 9)
c
2
, c
7
u(u − 1)
4
(u + 1)
2
(u
25
− u
24
+ ··· − 2u − 1)
· (u
36
− 10u
34
+ ··· + 11u
2
− 3)
c
3
, c
4
, c
5
c
9
, c
10
u(u − 1)
3
(u + 1)(u
2
− 3)(u
18
+ 2u
17
+ ··· + u + 1)
2
· (u
25
− 3u
24
+ ··· + 9u
2
− 2)
c
6
, c
12
u(u − 1)
3
(u + 1)
3
(u
25
− u
24
+ ··· − 2u − 1)
· (u
36
− 10u
34
+ ··· + 11u
2
− 3)
c
8
u(u − 1)(u + 1)
3
(u
2
− 3)(u
18
+ 4u
17
+ ··· + 5u − 1)
2
· (u
25
− 15u
24
+ ··· − 272u + 142)
39
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y(y −1)
6
(y
25
+ 13y
24
+ ··· + 88y −1)(y
36
− 8y
35
+ ··· + 198y + 81)
c
2
, c
6
, c
7
c
12
y(y −1)
6
(y
25
− 11y
24
+ ··· + 16y −1)(y
36
− 20y
35
+ ··· − 66y + 9)
c
3
, c
4
, c
5
c
9
, c
10
y(y −3)
2
(y −1)
4
(y
18
− 24y
17
+ ··· + 3y + 1)
2
· (y
25
− 33y
24
+ ··· + 36y −4)
c
8
y(y −3)
2
(y −1)
4
(y
18
+ 22y
16
+ ··· − 65y + 1)
2
· (y
25
− 9y
24
+ ··· + 269092y −20164)
40
