11n
136
(K11n
136
)
A knot diagram
1
Linearized knot diagam
6 1 9 7 10 2 4 1 5 9 4
Solving Sequence
4,9 1,3
2 8 7 5 6 11 10
c
3
c
2
c
8
c
7
c
4
c
6
c
11
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h83u
11
− 937u
10
+ ··· + 244b − 1872, −234u
11
+ 2491u
10
+ ··· + 244a + 6946,
u
12
− 11u
11
+ 57u
10
− 189u
9
+ 459u
8
− 868u
7
+ 1293u
6
− 1499u
5
+ 1327u
4
− 863u
3
+ 374u
2
− 88u + 8i
I
u
2
= h−6u
14
− 27u
13
+ ··· + 8b − 31, −93u
14
a + 31u
14
+ ··· − 303a + 110, u
15
+ 5u
14
+ ··· + 8u + 3i
I
u
3
= hu
5
+ 2u
4
+ u
3
+ 2u
2
+ b + u + 1, −u
5
− u
4
+ u
3
− 2u
2
+ a, u
6
+ 2u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 1i
I
u
4
= hau + b + 1, u
2
a + a
2
− au − 1, u
3
− u
2
− 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 55 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
= h83u
11
− 937u
10
+ · · · + 244b − 1872, −234u
11
+ 2491u
10
+ · · · +
244a + 6946, u
12
− 11u
11
+ · · · − 88u + 8i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
0.959016u
11
− 10.2090u
10
+ ··· + 186.193u − 28.4672
−0.340164u
11
+ 3.84016u
10
+ ··· − 55.9262u + 7.67213
a
3
=
1
−u
2
a
2
=
−1.08402u
11
+ 11.3340u
10
+ ··· − 191.693u + 29.4672
0.590164u
11
− 6.09016u
10
+ ··· + 66.9262u − 8.67213
a
8
=
−0.518443u
11
+ 6.26844u
10
+ ··· − 204.701u + 32.6148
−0.565574u
11
+ 5.06557u
10
+ ··· + 14.0082u − 4.14754
a
7
=
−1.08402u
11
+ 11.3340u
10
+ ··· − 190.693u + 28.4672
−0.565574u
11
+ 5.06557u
10
+ ··· + 14.0082u − 4.14754
a
5
=
0.485656u
11
− 5.98566u
10
+ ··· + 195.705u − 29.6885
1.16803u
11
− 11.1680u
10
+ ··· + 35.8852u − 0.934426
a
6
=
−0.309426u
11
+ 2.55943u
10
+ ··· + 27.7418u − 4.85246
0.598361u
11
− 5.59836u
10
+ ··· + 39.7377u − 4.27869
a
11
=
0.618852u
11
− 6.36885u
10
+ ··· + 130.266u − 20.7951
−0.340164u
11
+ 3.84016u
10
+ ··· − 55.9262u + 7.67213
a
10
=
0.618852u
11
− 6.36885u
10
+ ··· + 130.266u − 20.7951
−1.22541u
11
+ 11.7254u
10
+ ··· − 89.5656u + 11.1803
a
10
=
0.618852u
11
− 6.36885u
10
+ ··· + 130.266u − 20.7951
−1.22541u
11
+ 11.7254u
10
+ ··· − 89.5656u + 11.1803
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
69
61
u
11
+
679
61
u
10
−
3121
61
u
9
+
9220
61
u
8
−
20174
61
u
7
+
34320
61
u
6
−
44856
61
u
5
+
43929
61
u
4
−
31083
61
u
3
+
14067
61
u
2
−
2500
61
u −
994
61
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
12
+ u
11
+ ··· − 2u − 1
c
2
, c
10
u
12
+ 7u
11
+ ··· + 8u + 1
c
3
u
12
+ 11u
11
+ ··· + 88u + 8
c
4
, c
7
u
12
− 7u
11
+ ··· + 4u − 8
c
8
, c
11
u
12
− 2u
11
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
12
− 7y
11
+ ··· − 8y + 1
c
2
, c
10
y
12
+ y
11
+ ··· − 32y + 1
c
3
y
12
− 7y
11
+ ··· − 1760y + 64
c
4
, c
7
y
12
+ 5y
11
+ ··· − 656y + 64
c
8
, c
11
y
12
− 18y
11
+ ··· − 21y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302190 + 1.082960I
a = −0.173842 − 0.404485I
b = −0.385507 + 0.310495I
2.70102 − 2.45198I −9.00502 + 1.91716I
u = 0.302190 − 1.082960I
a = −0.173842 + 0.404485I
b = −0.385507 − 0.310495I
2.70102 + 2.45198I −9.00502 − 1.91716I
u = 1.48047 + 0.22618I
a = −1.025210 − 0.103256I
b = 1.49443 + 0.38475I
−1.76862 − 2.36514I −8.64736 + 0.93899I
u = 1.48047 − 0.22618I
a = −1.025210 + 0.103256I
b = 1.49443 − 0.38475I
−1.76862 + 2.36514I −8.64736 − 0.93899I
u = 0.360681
a = −0.734365
b = 0.264871
−0.612207 −16.2730
u = −0.06599 + 1.68520I
a = −0.168168 + 0.408954I
b = 0.678073 + 0.310386I
−1.13692 + 4.86316I −15.3188 − 3.9545I
u = −0.06599 − 1.68520I
a = −0.168168 − 0.408954I
b = 0.678073 − 0.310386I
−1.13692 − 4.86316I −15.3188 + 3.9545I
u = 1.60414 + 0.72863I
a = 0.881126 − 0.421215I
b = −1.72036 + 0.03367I
−9.15791 − 5.54846I −14.9776 + 4.7158I
u = 1.60414 − 0.72863I
a = 0.881126 + 0.421215I
b = −1.72036 − 0.03367I
−9.15791 + 5.54846I −14.9776 − 4.7158I
u = 0.222519
a = −5.14860
b = 1.14566
−4.93861 −18.1860
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.88759 + 0.64713I
a = 0.927570 − 0.032494I
b = −1.77190 − 0.53892I
−7.6014 − 13.7948I −13.8218 + 7.4992I
u = 1.88759 − 0.64713I
a = 0.927570 + 0.032494I
b = −1.77190 + 0.53892I
−7.6014 + 13.7948I −13.8218 − 7.4992I
6
II. I
u
2
= h−6u
14
− 27u
13
+ · · · + 8b − 31, −93u
14
a + 31u
14
+ · · · − 303a +
110, u
15
+ 5u
14
+ · · · + 8u + 3i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
a
3
4
u
14
+
27
8
u
13
+ ··· +
49
8
u +
31
8
a
3
=
1
−u
2
a
2
=
−0.375000au
14
− 0.0833333u
14
+ ··· − 2.25000a + 0.708333
3
8
u
14
a −
5
4
u
14
+ ··· +
9
4
a − 3
a
8
=
−0.750000au
14
+ 0.333333u
14
+ ··· − 3.87500a + 1.29167
−
1
4
u
14
−
9
8
u
13
+ ··· −
3
8
u − 1
a
7
=
−0.750000au
14
+ 0.0833333u
14
+ ··· − 3.87500a + 0.291667
−
1
4
u
14
−
9
8
u
13
+ ··· −
3
8
u − 1
a
5
=
5
8
u
14
a +
1
24
u
14
+ ··· +
19
8
a +
31
12
1
2
u
14
+
19
8
u
13
+ ··· +
33
8
u +
17
8
a
6
=
1
4
u
14
a −
31
24
u
14
+ ··· + 2a −
101
24
1
4
u
13
a −
1
4
u
14
+ ··· +
3
8
a −
1
8
a
11
=
3
4
u
14
+
27
8
u
13
+ ··· + a +
31
8
3
4
u
14
+
27
8
u
13
+ ··· +
49
8
u +
31
8
a
10
=
3
4
u
14
+
27
8
u
13
+ ··· + a +
31
8
1
2
u
14
+
19
8
u
13
+ ··· +
43
8
u +
11
4
a
10
=
3
4
u
14
+
27
8
u
13
+ ··· + a +
31
8
1
2
u
14
+
19
8
u
13
+ ··· +
43
8
u +
11
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
14
+ 16u
13
−
15
2
u
12
− 115u
11
− 131u
10
+ 156u
9
+
857
2
u
8
+
263u
7
− 94u
6
− 193u
5
− 58u
4
+ 21u
3
+ 16u
2
+ 28u +
3
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
30
− u
29
+ ··· + 2u
2
+ 1
c
2
, c
10
u
30
+ 17u
29
+ ··· − 4u + 1
c
3
(u
15
− 5u
14
+ ··· + 8u − 3)
2
c
4
, c
7
(u
15
+ 3u
14
+ ··· + 5u + 1)
2
c
8
, c
11
u
30
− 2u
29
+ ··· + 66u − 79
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
30
− 17y
29
+ ··· + 4y + 1
c
2
, c
10
y
30
− 5y
29
+ ··· − 112y + 1
c
3
(y
15
− 21y
14
+ ··· − 2y −9)
2
c
4
, c
7
(y
15
+ 5y
14
+ ··· + 7y −1)
2
c
8
, c
11
y
30
− 30y
29
+ ··· − 120802y + 6241
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573512 + 0.780031I
a = −0.303879 + 1.027660I
b = −0.674810 + 0.174597I
1.85339 − 2.65754I −12.13634 + 3.34510I
u = −0.573512 + 0.780031I
a = −0.558164 − 0.454721I
b = 0.627325 + 0.826408I
1.85339 − 2.65754I −12.13634 + 3.34510I
u = −0.573512 − 0.780031I
a = −0.303879 − 1.027660I
b = −0.674810 − 0.174597I
1.85339 + 2.65754I −12.13634 − 3.34510I
u = −0.573512 − 0.780031I
a = −0.558164 + 0.454721I
b = 0.627325 − 0.826408I
1.85339 + 2.65754I −12.13634 − 3.34510I
u = 0.697369 + 0.218567I
a = −0.921356 + 0.311277I
b = 0.314929 + 1.087780I
0.330230 + 0.679087I −12.40066 − 0.76832I
u = 0.697369 + 0.218567I
a = −0.85635 − 1.29144I
b = 0.710560 − 0.015696I
0.330230 + 0.679087I −12.40066 − 0.76832I
u = 0.697369 − 0.218567I
a = −0.921356 − 0.311277I
b = 0.314929 − 1.087780I
0.330230 − 0.679087I −12.40066 + 0.76832I
u = 0.697369 − 0.218567I
a = −0.85635 + 1.29144I
b = 0.710560 + 0.015696I
0.330230 − 0.679087I −12.40066 + 0.76832I
u = −0.624643 + 0.305436I
a = 0.722934 + 0.424315I
b = 0.23544 + 1.52005I
−0.89474 − 6.09921I −15.4033 + 6.7831I
u = −0.624643 + 0.305436I
a = −0.65611 + 2.11265I
b = 0.581176 + 0.044236I
−0.89474 − 6.09921I −15.4033 + 6.7831I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624643 − 0.305436I
a = 0.722934 − 0.424315I
b = 0.23544 − 1.52005I
−0.89474 + 6.09921I −15.4033 − 6.7831I
u = −0.624643 − 0.305436I
a = −0.65611 − 2.11265I
b = 0.581176 − 0.044236I
−0.89474 + 6.09921I −15.4033 − 6.7831I
u = 0.067784 + 0.504699I
a = −0.069426 − 1.144650I
b = 0.186932 + 0.933368I
2.10570 − 2.66884I −8.49589 + 5.19452I
u = 0.067784 + 0.504699I
a = −1.86545 + 0.11984I
b = −0.572998 + 0.112628I
2.10570 − 2.66884I −8.49589 + 5.19452I
u = 0.067784 − 0.504699I
a = −0.069426 + 1.144650I
b = 0.186932 − 0.933368I
2.10570 + 2.66884I −8.49589 − 5.19452I
u = 0.067784 − 0.504699I
a = −1.86545 − 0.11984I
b = −0.572998 − 0.112628I
2.10570 + 2.66884I −8.49589 − 5.19452I
u = −1.49696 + 0.32578I
a = −0.926351 − 0.253533I
b = 1.82057 + 0.02441I
−6.55037 + 0.76607I −13.52677 − 0.03940I
u = −1.49696 + 0.32578I
a = 1.157790 + 0.268278I
b = −1.46931 − 0.07774I
−6.55037 + 0.76607I −13.52677 − 0.03940I
u = −1.49696 − 0.32578I
a = −0.926351 + 0.253533I
b = 1.82057 − 0.02441I
−6.55037 − 0.76607I −13.52677 + 0.03940I
u = −1.49696 − 0.32578I
a = 1.157790 − 0.268278I
b = −1.46931 + 0.07774I
−6.55037 − 0.76607I −13.52677 + 0.03940I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60501
a = 1.20656
b = −0.990302
−7.32542 −4.72890
u = −1.60501
a = −0.617005
b = 1.93654
−7.32542 −4.72890
u = −1.75343 + 0.35354I
a = 0.980020 − 0.156747I
b = −1.65186 + 0.31915I
−4.38929 + 7.65996I −11.60171 − 4.83891I
u = −1.75343 + 0.35354I
a = −0.940537 − 0.007624I
b = 1.66298 − 0.62132I
−4.38929 + 7.65996I −11.60171 − 4.83891I
u = −1.75343 − 0.35354I
a = 0.980020 + 0.156747I
b = −1.65186 − 0.31915I
−4.38929 − 7.65996I −11.60171 + 4.83891I
u = −1.75343 − 0.35354I
a = −0.940537 + 0.007624I
b = 1.66298 + 0.62132I
−4.38929 − 7.65996I −11.60171 + 4.83891I
u = 1.98590 + 0.14793I
a = 0.901839 − 0.019745I
b = −1.45017 + 0.51636I
−10.17640 + 2.57627I −15.0709 − 4.0254I
u = 1.98590 + 0.14793I
a = 0.706941 − 0.312672I
b = −1.79388 − 0.09420I
−10.17640 + 2.57627I −15.0709 − 4.0254I
u = 1.98590 − 0.14793I
a = 0.901839 + 0.019745I
b = −1.45017 − 0.51636I
−10.17640 − 2.57627I −15.0709 + 4.0254I
u = 1.98590 − 0.14793I
a = 0.706941 + 0.312672I
b = −1.79388 + 0.09420I
−10.17640 − 2.57627I −15.0709 + 4.0254I
12
III. I
u
3
= hu
5
+ 2u
4
+ u
3
+ 2u
2
+ b + u + 1, −u
5
− u
4
+ u
3
− 2u
2
+ a, u
6
+
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
u
5
+ u
4
− u
3
+ 2u
2
−u
5
− 2u
4
− u
3
− 2u
2
− u − 1
a
3
=
1
−u
2
a
2
=
−u
4
− 2u
3
− u
2
− 2u
−u
5
− 2u
4
− u
3
− 3u
2
− u
a
8
=
−u
5
− u
4
+ u
3
− 2u
2
+ u
u
5
+ 2u
4
+ u
3
+ 3u
2
+ 2u + 1
a
7
=
u
4
+ 2u
3
+ u
2
+ 3u + 1
u
5
+ 2u
4
+ u
3
+ 3u
2
+ 2u + 1
a
5
=
u
5
+ 2u
4
+ u
2
+ u − 1
u
5
+ u
4
− u
3
+ 2u
2
− u − 1
a
6
=
u
5
+ 2u
4
+ u
2
+ 2u
u
5
+ u
4
− 2u
3
+ u
2
− 1
a
11
=
−u
4
− 2u
3
− u − 1
−u
5
− 2u
4
− u
3
− 2u
2
− u − 1
a
10
=
−u
4
− 2u
3
− u − 1
−u
5
− 3u
4
− 3u
3
− 3u
2
− 2u − 2
a
10
=
−u
4
− 2u
3
− u − 1
−u
5
− 3u
4
− 3u
3
− 3u
2
− 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
5
+ 16u
4
+ 8u
3
+ 12u
2
+ 12u − 5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 2u
4
+ 2u
2
+ u − 1
c
2
, c
10
u
6
+ 4u
5
+ 8u
4
+ 10u
3
+ 8u
2
+ 5u + 1
c
3
u
6
+ 2u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 1
c
4
u
6
− u
5
+ 2u
4
− 3u
3
+ u
2
− 2u + 1
c
6
, c
9
u
6
− 2u
4
+ 2u
2
− u − 1
c
7
u
6
+ u
5
+ 2u
4
+ 3u
3
+ u
2
+ 2u + 1
c
8
, c
11
u
6
− u
5
− u
4
+ 2u
3
− 3u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
6
− 4y
5
+ 8y
4
− 10y
3
+ 8y
2
− 5y + 1
c
2
, c
10
y
6
− 10y
3
− 20y
2
− 9y + 1
c
3
y
6
− 2y
5
− 7y
4
− 7y
3
+ 3y + 1
c
4
, c
7
y
6
+ 3y
5
− 7y
3
− 7y
2
− 2y + 1
c
8
, c
11
y
6
− 3y
5
− y
4
+ 4y
3
+ 3y
2
+ 2y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.392638 + 0.978074I
a = 0.742271 + 0.355591I
b = −0.056351 + 0.865615I
0.69572 + 5.66603I −8.99565 − 5.65371I
u = 0.392638 − 0.978074I
a = 0.742271 − 0.355591I
b = −0.056351 − 0.865615I
0.69572 − 5.66603I −8.99565 + 5.65371I
u = −0.788940
a = 1.81768
b = −1.43404
−4.14809 −6.86750
u = 0.015196 + 0.750196I
a = −0.759470 + 0.678272I
b = −0.520377 − 0.559444I
3.09094 − 3.67876I −6.55000 + 7.14850I
u = 0.015196 − 0.750196I
a = −0.759470 − 0.678272I
b = −0.520377 + 0.559444I
3.09094 + 3.67876I −6.55000 − 7.14850I
u = −2.02673
a = −0.783279
b = 1.58749
−10.0050 −16.0410
16
IV. I
u
4
= hau + b + 1, u
2
a + a
2
− au − 1, u
3
− u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
a
−au − 1
a
3
=
1
−u
2
a
2
=
au − u
2
+ u + 1
−au − u
2
a
8
=
−a + u
−u
2
+ u
a
7
=
−u
2
− a + 2u
−u
2
+ u
a
5
=
u
2
a − au + u − 1
u − 1
a
6
=
u
2
a − au − u
2
− a + u
u
2
a − u
2
− a + 2u
a
11
=
−au + a − 1
−au − 1
a
10
=
−au + a − 1
−au + u
2
+ a − 1
a
10
=
−au + a − 1
−au + u
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4u − 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 2u
4
− u
3
+ 2u
2
− 1
c
2
, c
10
u
6
+ 4u
5
+ 8u
4
+ 11u
3
+ 8u
2
+ 4u + 1
c
3
(u
3
− u
2
− 1)
2
c
4
(u
3
+ u + 1)
2
c
6
, c
9
u
6
− 2u
4
+ u
3
+ 2u
2
− 1
c
7
(u
3
+ u − 1)
2
c
8
, c
11
u
6
− 3u
5
+ 2u
4
+ u
3
− 3u
2
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
6
− 4y
5
+ 8y
4
− 11y
3
+ 8y
2
− 4y + 1
c
2
, c
10
y
6
− 8y
4
− 23y
3
− 8y
2
+ 1
c
3
(y
3
− y
2
− 2y −1)
2
c
4
, c
7
(y
3
+ 2y
2
+ y −1)
2
c
8
, c
11
y
6
− 5y
5
+ 4y
4
− 3y
3
+ y
2
+ 2y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.232786 + 0.792552I
a = −0.669484 + 0.462841I
b = −0.789021 + 0.638344I
2.21137 − 1.58317I −8.77306 − 1.69425I
u = −0.232786 + 0.792552I
a = 1.010650 + 0.698701I
b = −0.210979 − 0.638344I
2.21137 − 1.58317I −8.77306 − 1.69425I
u = −0.232786 − 0.792552I
a = −0.669484 − 0.462841I
b = −0.789021 − 0.638344I
2.21137 + 1.58317I −8.77306 + 1.69425I
u = −0.232786 − 0.792552I
a = 1.010650 − 0.698701I
b = −0.210979 + 0.638344I
2.21137 + 1.58317I −8.77306 + 1.69425I
u = 1.46557
a = 0.715431
b = −2.04852
−7.71260 −26.4540
u = 1.46557
a = −1.39776
b = 1.04852
−7.71260 −26.4540
20
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
1
=
0
1
a
3
=
1
0
a
2
=
1
−1
a
8
=
1
−1
a
7
=
0
−1
a
5
=
1
1
a
6
=
−1
0
a
11
=
1
1
a
10
=
2
1
a
10
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
9
u − 1
c
2
, c
8
, c
10
c
11
u + 1
c
3
u
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
y −1
c
3
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−4.93480 −18.0000
24
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
6
− 2u
4
+ 2u
2
+ u − 1)(u
6
− 2u
4
− u
3
+ 2u
2
− 1)
· (u
12
+ u
11
+ ··· − 2u − 1)(u
30
− u
29
+ ··· + 2u
2
+ 1)
c
2
, c
10
(u + 1)(u
6
+ 4u
5
+ 8u
4
+ 10u
3
+ 8u
2
+ 5u + 1)
· (u
6
+ 4u
5
+ ··· + 4u + 1)(u
12
+ 7u
11
+ ··· + 8u + 1)
· (u
30
+ 17u
29
+ ··· − 4u + 1)
c
3
u(u
3
− u
2
− 1)
2
(u
6
+ 2u
5
+ u
4
+ 3u
3
+ 2u
2
+ u + 1)
· (u
12
+ 11u
11
+ ··· + 88u + 8)(u
15
− 5u
14
+ ··· + 8u − 3)
2
c
4
(u − 1)(u
3
+ u + 1)
2
(u
6
− u
5
+ 2u
4
− 3u
3
+ u
2
− 2u + 1)
· (u
12
− 7u
11
+ ··· + 4u − 8)(u
15
+ 3u
14
+ ··· + 5u + 1)
2
c
6
, c
9
(u − 1)(u
6
− 2u
4
+ 2u
2
− u − 1)(u
6
− 2u
4
+ u
3
+ 2u
2
− 1)
· (u
12
+ u
11
+ ··· − 2u − 1)(u
30
− u
29
+ ··· + 2u
2
+ 1)
c
7
(u − 1)(u
3
+ u − 1)
2
(u
6
+ u
5
+ 2u
4
+ 3u
3
+ u
2
+ 2u + 1)
· (u
12
− 7u
11
+ ··· + 4u − 8)(u
15
+ 3u
14
+ ··· + 5u + 1)
2
c
8
, c
11
(u + 1)(u
6
− 3u
5
+ 2u
4
+ u
3
− 3u
2
+ 2u − 1)
· (u
6
− u
5
− u
4
+ 2u
3
− 3u
2
+ 2u − 1)(u
12
− 2u
11
+ ··· + 3u + 1)
· (u
30
− 2u
29
+ ··· + 66u − 79)
25
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(y −1)(y
6
− 4y
5
+ 8y
4
− 11y
3
+ 8y
2
− 4y + 1)
· (y
6
− 4y
5
+ ··· − 5y + 1)(y
12
− 7y
11
+ ··· − 8y + 1)
· (y
30
− 17y
29
+ ··· + 4y + 1)
c
2
, c
10
(y −1)(y
6
− 10y
3
− 20y
2
− 9y + 1)(y
6
− 8y
4
− 23y
3
− 8y
2
+ 1)
· (y
12
+ y
11
+ ··· − 32y + 1)(y
30
− 5y
29
+ ··· − 112y + 1)
c
3
y(y
3
− y
2
− 2y −1)
2
(y
6
− 2y
5
− 7y
4
− 7y
3
+ 3y + 1)
· (y
12
− 7y
11
+ ··· − 1760y + 64)(y
15
− 21y
14
+ ··· − 2y −9)
2
c
4
, c
7
(y −1)(y
3
+ 2y
2
+ y −1)
2
(y
6
+ 3y
5
− 7y
3
− 7y
2
− 2y + 1)
· (y
12
+ 5y
11
+ ··· − 656y + 64)(y
15
+ 5y
14
+ ··· + 7y −1)
2
c
8
, c
11
(y −1)(y
6
− 5y
5
+ 4y
4
− 3y
3
+ y
2
+ 2y + 1)
· (y
6
− 3y
5
− y
4
+ 4y
3
+ 3y
2
+ 2y + 1)(y
12
− 18y
11
+ ··· − 21y + 1)
· (y
30
− 30y
29
+ ··· − 120802y + 6241)
26
