11n
94
(K11n
94
)
A knot diagram
1
Linearized knot diagam
5 1 9 10 2 4 3 1 7 6 9
Solving Sequence
1,5
2 3
6,9
8 7 11 10 4
c
1
c
2
c
5
c
8
c
7
c
11
c
10
c
4
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h16u
18
− 65u
17
+ ··· + 39b + 33, −20u
18
+ 91u
17
+ ··· + 39a − 129, u
19
− 5u
18
+ ··· + 10u
2
− 3i
I
u
2
= hu
9
+ 2u
8
− 4u
6
− 2u
5
+ 4u
4
+ 3u
3
− u
2
+ b + 1, −u
9
− 2u
8
+ u
7
+ 5u
6
+ u
5
− 7u
4
− 3u
3
+ 4u
2
+ a + u − 2,
u
10
+ 2u
9
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
− u
3
− u
2
+ u + 1i
I
u
3
= h−2u
9
− 3u
8
− u
7
+ 5u
6
− 3u
4
− u
2
a − 2u
3
− au + 6u
2
+ b − 2u − 3, −3u
9
a + 2u
9
+ ··· − 4a + 2,
u
10
+ 2u
9
+ u
8
− 3u
7
− 2u
6
+ 2u
5
+ 3u
4
− 2u
3
− u
2
+ 2u + 1i
I
u
4
= hb − 1, a
2
− a − 1, u − 1i
I
v
1
= ha, b − 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 52 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
= h16u
18
− 65u
17
+ · · · + 39b + 33, −20u
18
+ 91u
17
+ · · · + 39a −
129, u
19
− 5u
18
+ · · · + 10u
2
− 3i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
0.512821u
18
− 2.33333u
17
+ ··· + 2.12821u + 3.30769
−0.410256u
18
+ 1.66667u
17
+ ··· − 1.76923u − 0.846154
a
8
=
0.923077u
18
− 4u
17
+ ··· + 3.89744u + 4.15385
−0.410256u
18
+ 1.66667u
17
+ ··· − 1.76923u − 0.846154
a
7
=
5
39
u
18
− u
17
+ ··· +
50
39
u +
27
13
0.153846u
18
− 0.794872u
16
+ ··· − 2.46154u − 0.307692
a
11
=
1.10256u
18
− 8u
17
+ ··· + 7.35897u + 10.4615
−3.94872u
18
+ 18.3333u
17
+ ··· − 6.15385u − 10.7692
a
10
=
−0.307692u
18
+ 2.66667u
17
+ ··· − 3.41026u − 1.38462
6.20513u
18
− 25.6667u
17
+ ··· + 0.384615u + 11.9231
a
4
=
1.41026u
18
− 5.33333u
17
+ ··· − 1.56410u + 2.84615
−1.12821u
18
+ 3.33333u
17
+ ··· + 2.38462u + 0.923077
a
4
=
1.41026u
18
− 5.33333u
17
+ ··· − 1.56410u + 2.84615
−1.12821u
18
+ 3.33333u
17
+ ··· + 2.38462u + 0.923077
(ii) Obstruction class = −1
(iii) Cusp Shapes =
389
39
u
18
−
140
3
u
17
+ ··· −
38
13
u +
356
13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
19
+ 5u
18
+ ··· − 10u
2
+ 3
c
2
u
19
+ 5u
18
+ ··· + 60u + 9
c
3
u
19
+ 8u
17
+ ··· − u + 5
c
4
, c
6
u
19
+ u
18
+ ··· + 4u + 1
c
7
u
19
+ 20u
17
+ ··· + 3u + 1
c
8
, c
11
u
19
− 18u
17
+ ··· + 13u + 1
c
9
u
19
− 14u
18
+ ··· − 30u + 3
c
10
u
19
− 21u
18
+ ··· − 1792u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
19
− 5y
18
+ ··· + 60y −9
c
2
y
19
+ 23y
18
+ ··· − 1872y −81
c
3
y
19
+ 16y
18
+ ··· − 109y −25
c
4
, c
6
y
19
− 7y
18
+ ··· + 16y −1
c
7
y
19
+ 40y
18
+ ··· + 7y −1
c
8
, c
11
y
19
− 36y
18
+ ··· + 39y −1
c
9
y
19
+ 38y
17
+ ··· + 42y −9
c
10
y
19
− 9y
18
+ ··· + 2162688y −262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350966 + 0.908273I
a = 0.497187 − 0.151368I
b = −0.408408 − 0.715459I
2.38098 − 2.19136I 4.02486 + 1.79521I
u = −0.350966 − 0.908273I
a = 0.497187 + 0.151368I
b = −0.408408 + 0.715459I
2.38098 + 2.19136I 4.02486 − 1.79521I
u = −0.779496 + 0.468978I
a = −0.091107 + 0.590275I
b = 0.602057 + 0.798290I
0.99904 + 3.33102I 2.55789 − 7.26755I
u = −0.779496 − 0.468978I
a = −0.091107 − 0.590275I
b = 0.602057 − 0.798290I
0.99904 − 3.33102I 2.55789 + 7.26755I
u = 1.077080 + 0.271096I
a = 0.401351 + 0.468581I
b = −0.142788 + 0.130045I
−2.28578 − 0.47591I −3.82840 + 3.46313I
u = 1.077080 − 0.271096I
a = 0.401351 − 0.468581I
b = −0.142788 − 0.130045I
−2.28578 + 0.47591I −3.82840 − 3.46313I
u = 0.761451
a = 1.02355
b = −0.185922
−1.28421 −7.36270
u = 0.898363 + 0.894383I
a = −1.77752 − 0.80237I
b = 2.15592 − 0.55152I
8.84727 − 4.55297I 5.83723 + 8.19473I
u = 0.898363 − 0.894383I
a = −1.77752 + 0.80237I
b = 2.15592 + 0.55152I
8.84727 + 4.55297I 5.83723 − 8.19473I
u = 0.956723 + 0.863236I
a = −1.21407 − 1.44574I
b = 2.09496 + 0.17987I
8.65502 − 1.95883I 4.78017 − 2.64502I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956723 − 0.863236I
a = −1.21407 + 1.44574I
b = 2.09496 − 0.17987I
8.65502 + 1.95883I 4.78017 + 2.64502I
u = −1.200480 + 0.502359I
a = −0.256728 − 0.089743I
b = −0.766723 + 0.224201I
−0.51529 + 7.49251I 1.46560 − 6.64058I
u = −1.200480 − 0.502359I
a = −0.256728 + 0.089743I
b = −0.766723 − 0.224201I
−0.51529 − 7.49251I 1.46560 + 6.64058I
u = 0.869568 + 1.036960I
a = 1.19820 + 0.93760I
b = −2.14294 − 0.19617I
10.89150 + 6.89079I 1.93588 − 3.17270I
u = 0.869568 − 1.036960I
a = 1.19820 − 0.93760I
b = −2.14294 + 0.19617I
10.89150 − 6.89079I 1.93588 + 3.17270I
u = 1.063600 + 0.913849I
a = 1.35608 + 1.04713I
b = −2.11940 + 0.59325I
10.2390 − 14.0065I 0.95958 + 7.34096I
u = 1.063600 − 0.913849I
a = 1.35608 − 1.04713I
b = −2.11940 − 0.59325I
10.2390 + 14.0065I 0.95958 − 7.34096I
u = −0.415119 + 0.278912I
a = 0.874831 + 0.733477I
b = 0.820280 − 0.072764I
1.73128 − 0.06651I 5.44854 − 0.44003I
u = −0.415119 − 0.278912I
a = 0.874831 − 0.733477I
b = 0.820280 + 0.072764I
1.73128 + 0.06651I 5.44854 + 0.44003I
6
II. I
u
2
= hu
9
+ 2u
8
− 4u
6
− 2u
5
+ 4u
4
+ 3u
3
− u
2
+ b + 1, −u
9
− 2u
8
+ · · · +
a − 2, u
10
+ 2u
9
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
u
9
+ 2u
8
− u
7
− 5u
6
− u
5
+ 7u
4
+ 3u
3
− 4u
2
− u + 2
−u
9
− 2u
8
+ 4u
6
+ 2u
5
− 4u
4
− 3u
3
+ u
2
− 1
a
8
=
2u
9
+ 4u
8
− u
7
− 9u
6
− 3u
5
+ 11u
4
+ 6u
3
− 5u
2
− u + 3
−u
9
− 2u
8
+ 4u
6
+ 2u
5
− 4u
4
− 3u
3
+ u
2
− 1
a
7
=
u
9
+ 2u
8
− u
7
− 5u
6
− u
5
+ 6u
4
+ 3u
3
− 3u
2
− u + 1
−u
8
− u
7
+ u
6
+ 3u
5
− 3u
3
− u
2
+ u
a
11
=
−u
9
− u
8
+ 2u
7
+ 3u
6
− 3u
5
− 4u
4
+ 2u
3
+ 3u
2
− 2u
u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
5
+ 4u
4
− 2u
2
a
10
=
u
8
+ u
7
− u
6
− 3u
5
+ u
4
+ 3u
3
+ u
2
− u + 1
−u
9
− u
8
+ u
7
+ 2u
6
− u
5
− 2u
4
+ u
3
− 2u − 1
a
4
=
−2u
9
− 2u
8
+ 3u
7
+ 6u
6
− 3u
5
− 8u
4
+ 4u
2
− u − 1
u
9
+ u
8
− u
7
− 3u
6
+ 3u
4
+ 2u
3
a
4
=
−2u
9
− 2u
8
+ 3u
7
+ 6u
6
− 3u
5
− 8u
4
+ 4u
2
− u − 1
u
9
+ u
8
− u
7
− 3u
6
+ 3u
4
+ 2u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
9
+ 13u
8
− u
7
− 23u
6
− 11u
5
+ 23u
4
+ 15u
3
− 3u
2
+ u + 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 2u
9
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
− u
3
− u
2
+ u + 1
c
2
u
10
+ 4u
9
+ ··· + 3u + 1
c
3
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 3u
6
+ u
5
+ 3u
4
+ u
3
+ u
2
+ 1
c
4
, c
6
u
10
+ u
8
− u
7
+ 3u
6
− u
5
+ 3u
4
− 2u
3
+ 3u
2
− u + 1
c
5
u
10
− 2u
9
+ 4u
7
− 2u
6
− 4u
5
+ 4u
4
+ u
3
− u
2
− u + 1
c
7
u
10
+ u
9
+ 3u
8
− 8u
6
+ 3u
5
+ 9u
4
+ 6u
3
+ 9u
2
+ 4u + 1
c
8
u
10
+ 5u
9
+ 11u
8
+ 18u
7
+ 23u
6
+ 21u
5
+ 19u
4
+ 11u
3
+ 7u
2
+ 2u + 1
c
9
u
10
+ 5u
9
+ 11u
8
+ 10u
7
− 5u
6
− 23u
5
− 21u
4
+ u
3
+ 18u
2
+ 15u + 5
c
10
u
10
+ 3u
9
− 11u
7
− 14u
6
+ 4u
5
+ 20u
4
+ 14u
3
+ 5u
2
+ 2u + 1
c
11
u
10
− 5u
9
+ 11u
8
− 18u
7
+ 23u
6
− 21u
5
+ 19u
4
− 11u
3
+ 7u
2
− 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
− 4y
9
+ ··· − 3y + 1
c
2
y
10
+ 8y
9
+ ··· + 13y + 1
c
3
y
10
+ 5y
9
+ 11y
8
+ 18y
7
+ 23y
6
+ 21y
5
+ 19y
4
+ 11y
3
+ 7y
2
+ 2y + 1
c
4
, c
6
y
10
+ 2y
9
+ 7y
8
+ 11y
7
+ 19y
6
+ 21y
5
+ 23y
4
+ 18y
3
+ 11y
2
+ 5y + 1
c
7
y
10
+ 5y
9
+ ··· + 2y + 1
c
8
, c
11
y
10
− 3y
9
+ ··· + 10y + 1
c
9
y
10
− 3y
9
+ ··· − 45y + 25
c
10
y
10
− 9y
9
+ ··· + 6y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.032960 + 0.512793I
a = −0.926519 − 0.444783I
b = −0.031024 + 0.608247I
−1.82490 + 7.04514I −4.29839 − 6.63243I
u = −1.032960 − 0.512793I
a = −0.926519 + 0.444783I
b = −0.031024 − 0.608247I
−1.82490 − 7.04514I −4.29839 + 6.63243I
u = 1.081750 + 0.414901I
a = 0.291782 + 0.133729I
b = 0.431318 + 0.661100I
−2.42349 + 0.47280I −4.60679 − 3.67832I
u = 1.081750 − 0.414901I
a = 0.291782 − 0.133729I
b = 0.431318 − 0.661100I
−2.42349 − 0.47280I −4.60679 + 3.67832I
u = −0.620721 + 0.483253I
a = 0.78365 + 1.55026I
b = −0.186622 − 0.818442I
−0.43993 − 2.89386I −0.09413 + 2.87221I
u = −0.620721 − 0.483253I
a = 0.78365 − 1.55026I
b = −0.186622 + 0.818442I
−0.43993 + 2.89386I −0.09413 − 2.87221I
u = 0.517593 + 0.494789I
a = −0.808469 − 0.682785I
b = 0.250433 − 1.183290I
−0.42431 − 4.26902I −1.08356 + 8.09272I
u = 0.517593 − 0.494789I
a = −0.808469 + 0.682785I
b = 0.250433 + 1.183290I
−0.42431 + 4.26902I −1.08356 − 8.09272I
u = −0.945660 + 0.933377I
a = −1.34045 + 0.96068I
b = 2.03589 + 0.22886I
8.40249 + 3.42159I 1.58287 − 2.15087I
u = −0.945660 − 0.933377I
a = −1.34045 − 0.96068I
b = 2.03589 − 0.22886I
8.40249 − 3.42159I 1.58287 + 2.15087I
10
III.
I
u
3
= h−2u
9
−3u
8
+· · ·+b−3, −3u
9
a+2u
9
+· · ·−4a+2, u
10
+2u
9
+· · ·+2u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
a
2u
9
+ 3u
8
+ u
7
− 5u
6
+ 3u
4
+ u
2
a + 2u
3
+ au − 6u
2
+ 2u + 3
a
8
=
−2u
9
− 3u
8
− u
7
+ 5u
6
− 3u
4
− u
2
a − 2u
3
− au + 6u
2
+ a − 2u − 3
2u
9
+ 3u
8
+ u
7
− 5u
6
+ 3u
4
+ u
2
a + 2u
3
+ au − 6u
2
+ 2u + 3
a
7
=
−u
9
− 2u
8
− u
7
+ 3u
6
+ 2u
5
− u
3
a − u
4
− u
2
a − 2u
3
+ 2u
2
+ a − 1
3u
9
+ 5u
8
+ ··· + 2u + 4
a
11
=
u
9
a + u
9
+ ··· + 2a + 1
−u
9
a − 2u
9
+ ··· − a − 3
a
10
=
u
9
a + u
9
+ ··· + 2a + 1
−u
9
a − 2u
9
+ ··· − a − 3
a
4
=
2u
9
+ 3u
8
+ ··· − a + 3
−u
9
a − 2u
9
+ ··· − a − 3
a
4
=
2u
9
+ 3u
8
+ ··· − a + 3
−u
9
a − 2u
9
+ ··· − a − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11u
9
− 17u
8
+ 37u
6
+ 3u
5
− 35u
4
− 20u
3
+ 38u
2
− 3u − 23
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
c
2
(u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
2
c
3
u
20
+ 2u
19
+ ··· − 301u + 457
c
4
, c
6
u
20
+ 2u
19
+ ··· − 5u + 5
c
7
u
20
+ 12u
18
+ ··· − 989u + 1201
c
8
, c
11
u
20
− 3u
19
+ ··· + 410u + 55
c
9
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
2
c
10
(u + 1)
20
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
2
c
2
(y
10
+ 14y
9
+ ··· − 6y + 1)
2
c
3
y
20
+ 12y
19
+ ··· − 305391y + 208849
c
4
, c
6
y
20
+ 28y
18
+ ··· − 275y + 25
c
7
y
20
+ 24y
19
+ ··· − 10199399y + 1442401
c
8
, c
11
y
20
− 23y
19
+ ··· − 8050y + 3025
c
9
(y
10
+ 3y
9
+ ··· + 11y + 4)
2
c
10
(y −1)
20
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975430 + 0.320615I
a = 0.583170 − 0.332488I
b = −0.819443 + 0.010673I
−0.581891 + 0.600845I −1.31849 − 3.40041I
u = 0.975430 + 0.320615I
a = 1.43037 − 0.39642I
b = 0.786422 + 0.695571I
−0.581891 + 0.600845I −1.31849 − 3.40041I
u = 0.975430 − 0.320615I
a = 0.583170 + 0.332488I
b = −0.819443 − 0.010673I
−0.581891 − 0.600845I −1.31849 + 3.40041I
u = 0.975430 − 0.320615I
a = 1.43037 + 0.39642I
b = 0.786422 − 0.695571I
−0.581891 − 0.600845I −1.31849 + 3.40041I
u = 0.541733 + 0.670646I
a = −1.108000 + 0.503913I
b = 0.88831 − 1.63472I
1.08979 − 4.58635I 4.20678 + 7.42430I
u = 0.541733 + 0.670646I
a = −0.11061 + 1.52297I
b = −0.151145 + 0.151691I
1.08979 − 4.58635I 4.20678 + 7.42430I
u = 0.541733 − 0.670646I
a = −1.108000 − 0.503913I
b = 0.88831 + 1.63472I
1.08979 + 4.58635I 4.20678 − 7.42430I
u = 0.541733 − 0.670646I
a = −0.11061 − 1.52297I
b = −0.151145 − 0.151691I
1.08979 + 4.58635I 4.20678 − 7.42430I
u = −0.876556 + 1.026090I
a = −1.059400 + 0.874691I
b = 2.32466 − 0.31720I
9.46664 + 1.75340I 5.39474 + 0.85033I
u = −0.876556 + 1.026090I
a = 1.32869 − 0.69669I
b = −1.66238 − 0.33815I
9.46664 + 1.75340I 5.39474 + 0.85033I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876556 − 1.026090I
a = −1.059400 − 0.874691I
b = 2.32466 + 0.31720I
9.46664 − 1.75340I 5.39474 − 0.85033I
u = −0.876556 − 1.026090I
a = 1.32869 + 0.69669I
b = −1.66238 + 0.33815I
9.46664 − 1.75340I 5.39474 − 0.85033I
u = −0.580680 + 0.133301I
a = 1.356460 + 0.199192I
b = −0.57404 + 1.29815I
−1.56776 + 3.93250I −8.27914 − 6.71393I
u = −0.580680 + 0.133301I
a = −2.24080 + 1.97323I
b = 0.403939 + 0.912038I
−1.56776 + 3.93250I −8.27914 − 6.71393I
u = −0.580680 − 0.133301I
a = 1.356460 − 0.199192I
b = −0.57404 − 1.29815I
−1.56776 − 3.93250I −8.27914 + 6.71393I
u = −0.580680 − 0.133301I
a = −2.24080 − 1.97323I
b = 0.403939 − 0.912038I
−1.56776 − 3.93250I −8.27914 + 6.71393I
u = −1.059930 + 0.922349I
a = 1.041530 − 0.882518I
b = −1.74793 − 0.01501I
8.86503 + 5.36397I 3.49612 − 6.50559I
u = −1.059930 + 0.922349I
a = −1.22140 + 1.07135I
b = 2.05160 + 0.78425I
8.86503 + 5.36397I 3.49612 − 6.50559I
u = −1.059930 − 0.922349I
a = 1.041530 + 0.882518I
b = −1.74793 + 0.01501I
8.86503 − 5.36397I 3.49612 + 6.50559I
u = −1.059930 − 0.922349I
a = −1.22140 − 1.07135I
b = 2.05160 − 0.78425I
8.86503 − 5.36397I 3.49612 + 6.50559I
15
IV. I
u
4
= hb − 1, a
2
− a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
−1
0
a
9
=
a
1
a
8
=
a − 1
1
a
7
=
a − 1
−a + 2
a
11
=
a + 1
1
a
10
=
a
1
a
4
=
−a − 1
−a + 1
a
4
=
−a − 1
−a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
(u − 1)
2
c
2
, c
5
, c
8
(u + 1)
2
c
3
, c
4
, c
6
c
7
u
2
+ u − 1
c
9
u
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
10
, c
11
(y −1)
2
c
3
, c
4
, c
6
c
7
y
2
− 3y + 1
c
9
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 1.00000
0 5.00000
u = 1.00000
a = 1.61803
b = 1.00000
0 5.00000
19
V. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
1
0
a
2
=
1
0
a
3
=
1
0
a
6
=
1
0
a
9
=
0
1
a
8
=
−1
1
a
7
=
0
1
a
11
=
1
1
a
10
=
0
1
a
4
=
1
1
a
4
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
9
u
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
11
u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
9
y
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
11
y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
· (u
10
+ 2u
9
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
− u
3
− u
2
+ u + 1)
· (u
19
+ 5u
18
+ ··· − 10u
2
+ 3)
c
2
u(u + 1)
2
· (u
10
+ 2u
9
+ 9u
8
+ 15u
7
+ 28u
6
+ 36u
5
+ 35u
4
+ 22u
3
+ 15u
2
+ 6u + 1)
2
· (u
10
+ 4u
9
+ ··· + 3u + 1)(u
19
+ 5u
18
+ ··· + 60u + 9)
c
3
(u − 1)(u
2
+ u − 1)(u
10
+ u
9
+ ··· + u
2
+ 1)
· (u
19
+ 8u
17
+ ··· − u + 5)(u
20
+ 2u
19
+ ··· − 301u + 457)
c
4
, c
6
(u − 1)(u
2
+ u − 1)(u
10
+ u
8
+ ··· − u + 1)
· (u
19
+ u
18
+ ··· + 4u + 1)(u
20
+ 2u
19
+ ··· − 5u + 5)
c
5
u(u + 1)
2
(u
10
− 2u
9
+ 4u
7
− 2u
6
− 4u
5
+ 4u
4
+ u
3
− u
2
− u + 1)
· (u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 2u
3
− u
2
− 2u + 1)
2
· (u
19
+ 5u
18
+ ··· − 10u
2
+ 3)
c
7
(u − 1)(u
2
+ u − 1)(u
10
+ u
9
+ ··· + 4u + 1)
· (u
19
+ 20u
17
+ ··· + 3u + 1)(u
20
+ 12u
18
+ ··· − 989u + 1201)
c
8
(u − 1)(u + 1)
2
· (u
10
+ 5u
9
+ 11u
8
+ 18u
7
+ 23u
6
+ 21u
5
+ 19u
4
+ 11u
3
+ 7u
2
+ 2u + 1)
· (u
19
− 18u
17
+ ··· + 13u + 1)(u
20
− 3u
19
+ ··· + 410u + 55)
c
9
u
3
(u
10
+ 3u
9
+ 6u
8
+ 7u
7
+ 9u
6
+ 9u
5
+ 10u
4
+ 6u
3
+ 5u
2
+ 3u + 2)
2
· (u
10
+ 5u
9
+ 11u
8
+ 10u
7
− 5u
6
− 23u
5
− 21u
4
+ u
3
+ 18u
2
+ 15u + 5)
· (u
19
− 14u
18
+ ··· − 30u + 3)
c
10
(u − 1)
3
(u + 1)
20
· (u
10
+ 3u
9
− 11u
7
− 14u
6
+ 4u
5
+ 20u
4
+ 14u
3
+ 5u
2
+ 2u + 1)
· (u
19
− 21u
18
+ ··· − 1792u + 512)
c
11
(u − 1)
3
· (u
10
− 5u
9
+ 11u
8
− 18u
7
+ 23u
6
− 21u
5
+ 19u
4
− 11u
3
+ 7u
2
− 2u + 1)
· (u
19
− 18u
17
+ ··· + 13u + 1)(u
20
− 3u
19
+ ··· + 410u + 55)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y(y −1)
2
(y
10
− 4y
9
+ ··· − 3y + 1)
· (y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 36y
5
+ 35y
4
− 22y
3
+ 15y
2
− 6y + 1)
2
· (y
19
− 5y
18
+ ··· + 60y −9)
c
2
y(y −1)
2
(y
10
+ 8y
9
+ ··· + 13y + 1)(y
10
+ 14y
9
+ ··· − 6y + 1)
2
· (y
19
+ 23y
18
+ ··· − 1872y −81)
c
3
(y −1)(y
2
− 3y + 1)
· (y
10
+ 5y
9
+ 11y
8
+ 18y
7
+ 23y
6
+ 21y
5
+ 19y
4
+ 11y
3
+ 7y
2
+ 2y + 1)
· (y
19
+ 16y
18
+ ··· − 109y −25)
· (y
20
+ 12y
19
+ ··· − 305391y + 208849)
c
4
, c
6
(y −1)(y
2
− 3y + 1)
· (y
10
+ 2y
9
+ 7y
8
+ 11y
7
+ 19y
6
+ 21y
5
+ 23y
4
+ 18y
3
+ 11y
2
+ 5y + 1)
· (y
19
− 7y
18
+ ··· + 16y −1)(y
20
+ 28y
18
+ ··· − 275y + 25)
c
7
(y −1)(y
2
− 3y + 1)(y
10
+ 5y
9
+ ··· + 2y + 1)(y
19
+ 40y
18
+ ··· + 7y −1)
· (y
20
+ 24y
19
+ ··· − 10199399y + 1442401)
c
8
, c
11
((y −1)
3
)(y
10
− 3y
9
+ ··· + 10y + 1)(y
19
− 36y
18
+ ··· + 39y −1)
· (y
20
− 23y
19
+ ··· − 8050y + 3025)
c
9
y
3
(y
10
− 3y
9
+ ··· − 45y + 25)(y
10
+ 3y
9
+ ··· + 11y + 4)
2
· (y
19
+ 38y
17
+ ··· + 42y −9)
c
10
((y −1)
23
)(y
10
− 9y
9
+ ··· + 6y + 1)
· (y
19
− 9y
18
+ ··· + 2162688y −262144)
25
