12n
0717
(K12n
0717
)
A knot diagram
1
Linearized knot diagam
4 10 11 10 12 3 4 11 1 7 9 5
Solving Sequence
5,10 1,4
2 3 9 12 6 7 8 11
c
4
c
1
c
2
c
9
c
12
c
5
c
6
c
7
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h25879u
15
− 46049u
14
+ ··· + 675712b − 1063104,
463377u
15
− 1801209u
14
+ ··· + 9459968a − 26845656, u
16
− 3u
15
+ ··· − 32u − 16i
I
u
2
= h56993u
13
a + 77423u
13
+ ··· + 148181a + 443926,
− 5240829u
13
a − 8288009u
13
+ ··· − 52771818a + 2325177,
u
14
+ u
13
+ 10u
12
+ 8u
11
+ 36u
10
+ 22u
9
+ 61u
8
+ 34u
7
+ 73u
6
+ 54u
5
+ 82u
4
+ 53u
3
+ 43u
2
+ 20u + 11i
I
u
3
= h31u
15
− 15u
14
+ ··· + 92b − 472, −577u
15
+ 3333u
14
+ ··· + 9292a + 191294,
u
16
+ 11u
14
+ 54u
12
+ 160u
10
+ 329u
8
+ 496u
6
+ 526u
4
+ 343u
2
+ 101i
I
v
1
= ha, −v
2
+ b − 3v −1, v
3
+ 3v
2
+ 2v + 1i
* 4 irreducible components of dim
C
= 0, with total 63 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
= h2.59 × 10
4
u
15
− 4.60 × 10
4
u
14
+ · · · + 6.76 × 10
5
b − 1.06 × 10
6
, 4.63 ×
10
5
u
15
−1.80×10
6
u
14
+· · ·+9.46×10
6
a−2.68×10
7
, u
16
−3u
15
+· · ·−32u−16i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
−0.0489829u
15
+ 0.190403u
14
+ ··· − 2.28630u + 2.83782
−0.0382989u
15
+ 0.0681489u
14
+ ··· + 1.61772u + 1.57331
a
4
=
1
u
2
a
2
=
−0.0363658u
15
+ 0.193159u
14
+ ··· − 3.29721u + 1.95978
−0.0226024u
15
− 0.0410566u
14
+ ··· + 3.11903u + 2.22303
a
3
=
−0.0363658u
15
+ 0.193159u
14
+ ··· − 3.29721u + 1.95978
−0.0126172u
15
− 0.00275582u
14
+ ··· + 1.01091u + 0.878038
a
9
=
−0.0877234u
15
+ 0.254037u
14
+ ··· − 1.23991u + 4.49819
−0.0395677u
15
+ 0.170191u
14
+ ··· − 1.04092u + 0.176944
a
12
=
−0.0106841u
15
+ 0.122254u
14
+ ··· − 3.90403u + 1.26451
−0.0382989u
15
+ 0.0681489u
14
+ ··· + 1.61772u + 1.57331
a
6
=
−0.0800201u
15
+ 0.250091u
14
+ ··· + 1.11319u − 1.40403
0.0910791u
15
− 0.322836u
14
+ ··· + 0.378447u + 0.00921990
a
7
=
−0.0489829u
15
+ 0.190403u
14
+ ··· − 2.28630u + 2.83782
0.0126172u
15
+ 0.00275582u
14
+ ··· − 1.01091u − 0.878038
a
8
=
−0.0106841u
15
+ 0.122254u
14
+ ··· − 3.90403u + 1.26451
−0.00563321u
15
− 0.00282644u
14
+ ··· + 1.09780u − 0.130074
a
11
=
0.0877234u
15
− 0.254037u
14
+ ··· + 1.23991u − 4.49819
−0.0179562u
15
+ 0.0609672u
14
+ ··· + 0.654917u + 0.323076
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3140595
4729984
u
15
+
9339149
4729984
u
14
+ ··· +
1984439
1182496
u +
1721569
73906
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− u
15
+ ··· − 11u + 1
c
2
u
16
− 2u
15
+ ··· + 194u − 121
c
3
u
16
− u
15
+ ··· − 19u + 7
c
4
u
16
− 3u
15
+ ··· − 32u − 16
c
5
, c
7
, c
12
u
16
+ u
15
+ ··· − 4u + 4
c
6
u
16
+ 7u
15
+ ··· − 65u + 28
c
8
, c
11
u
16
+ 3u
15
+ ··· + 13u − 28
c
9
, c
10
u
16
− 2u
14
+ ··· + 4u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 21y
15
+ ··· − 131y + 1
c
2
y
16
+ 26y
15
+ ··· − 15614y + 14641
c
3
y
16
− 19y
15
+ ··· − 501y + 49
c
4
y
16
+ 23y
15
+ ··· − 2304y + 256
c
5
, c
7
, c
12
y
16
+ 19y
15
+ ··· − 80y + 16
c
6
y
16
− 25y
15
+ ··· − 33289y + 784
c
8
, c
11
y
16
+ y
15
+ ··· − 7169y + 784
c
9
, c
10
y
16
− 4y
15
+ ··· − 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119335 + 1.038870I
a = −0.494008 − 1.094850I
b = 0.17992 + 1.59062I
−3.83744 − 3.93600I 2.87663 + 4.26125I
u = 0.119335 − 1.038870I
a = −0.494008 + 1.094850I
b = 0.17992 − 1.59062I
−3.83744 + 3.93600I 2.87663 − 4.26125I
u = −0.034961 + 1.296400I
a = −0.608719 + 0.180864I
b = −0.891539 − 0.005634I
−3.72865 + 1.11794I 3.47362 − 6.30090I
u = −0.034961 − 1.296400I
a = −0.608719 − 0.180864I
b = −0.891539 + 0.005634I
−3.72865 − 1.11794I 3.47362 + 6.30090I
u = −0.622483 + 0.254551I
a = 0.390738 + 0.662414I
b = −0.030479 + 1.183440I
−1.46484 + 2.93564I 5.07482 − 1.11353I
u = −0.622483 − 0.254551I
a = 0.390738 − 0.662414I
b = −0.030479 − 1.183440I
−1.46484 − 2.93564I 5.07482 + 1.11353I
u = 0.28607 + 1.44355I
a = 0.138612 − 0.552258I
b = −0.181437 + 0.590003I
1.87947 − 1.24485I 11.40323 + 4.68247I
u = 0.28607 − 1.44355I
a = 0.138612 + 0.552258I
b = −0.181437 − 0.590003I
1.87947 + 1.24485I 11.40323 − 4.68247I
u = 0.503828
a = 0.941502
b = 0.334619
0.729058 13.6990
u = −0.382038
a = 3.33621
b = 0.692814
6.53070 22.8110
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03599 + 1.87656I
a = 0.554024 + 0.651219I
b = −0.12246 − 1.50429I
−15.1090 − 2.7222I 2.22525 + 1.87237I
u = 0.03599 − 1.87656I
a = 0.554024 − 0.651219I
b = −0.12246 + 1.50429I
−15.1090 + 2.7222I 2.22525 − 1.87237I
u = 1.25896 + 1.40167I
a = −0.587811 + 0.033755I
b = −0.566111 − 1.293200I
−5.72547 + 7.15671I 3.37598 − 8.21855I
u = 1.25896 − 1.40167I
a = −0.587811 − 0.033755I
b = −0.566111 + 1.293200I
−5.72547 − 7.15671I 3.37598 + 8.21855I
u = 0.39619 + 1.87970I
a = 0.718306 − 0.433411I
b = 0.59839 + 1.77105I
−15.9449 + 14.1335I 2.81526 − 6.31158I
u = 0.39619 − 1.87970I
a = 0.718306 + 0.433411I
b = 0.59839 − 1.77105I
−15.9449 − 14.1335I 2.81526 + 6.31158I
6
II.
I
u
2
= h5.70 × 10
4
au
13
+ 7.74 × 10
4
u
13
+ · · · + 1.48 × 10
5
a + 4.44 × 10
5
, −5.24 ×
10
6
au
13
−8.29×10
6
u
13
+· · ·−5.28×10
7
a+2.33×10
6
, u
14
+u
13
+· · ·+20u+11i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
a
−0.0750130au
13
− 0.101903u
13
+ ··· − 0.195033a − 0.584286
a
4
=
1
u
2
a
2
=
0.0750130au
13
+ 0.101903u
13
+ ··· + 1.19503a + 0.584286
−0.224463au
13
− 0.244106u
13
+ ··· + 0.0452147a − 0.589078
a
3
=
0.0750130au
13
+ 0.101903u
13
+ ··· + 1.19503a + 0.584286
−0.0750130au
13
− 0.101903u
13
+ ··· − 0.195033a − 0.584286
a
9
=
0.0975842au
13
+ 0.0595029u
13
+ ··· + 0.627079a + 0.991682
−0.163468au
13
− 0.151136u
13
+ ··· − 0.199622a − 1.64704
a
12
=
0.0750130au
13
+ 0.101903u
13
+ ··· + 1.19503a + 0.584286
−0.0750130au
13
− 0.101903u
13
+ ··· − 0.195033a − 0.584286
a
6
=
−0.00230200au
13
+ 0.190411u
13
+ ··· − 1.39365a + 0.990069
0.0204495au
13
− 0.0406805u
13
+ ··· − 0.334311a − 1.07057
a
7
=
0.0570072u
13
− 0.0405770u
12
+ ··· − a + 0.574026
−0.0750130au
13
+ 0.0927235u
13
+ ··· − 0.195033a − 0.654532
a
8
=
−0.0750130au
13
+ 0.0751547u
13
+ ··· − 1.19503a − 1.15393
0.0744365au
13
+ 0.246160u
13
+ ··· − 0.435280a + 1.14362
a
11
=
0.0975842au
13
+ 0.0187794u
13
+ ··· + 0.627079a + 0.0745087
0.0535514au
13
− 0.0354421u
13
+ ··· + 1.01996a + 0.618570
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4926
30391
u
13
−
83536
151955
u
12
+ ··· −
1805974
151955
u −
701964
151955
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 5u
27
+ ··· + 1150u + 5663
c
2
u
28
+ u
27
+ ··· + 20378u + 5689
c
3
u
28
− 14u
26
+ ··· + 40u + 13
c
4
(u
14
+ u
13
+ ··· + 20u + 11)
2
c
5
, c
7
, c
12
u
28
− 4u
27
+ ··· + 52u + 4
c
6
(u
14
− 3u
13
+ ··· + 9u + 1)
2
c
8
, c
11
(u
14
− 2u
13
+ ··· + 10u + 19)
2
c
9
, c
10
u
28
− u
27
+ ··· − 2u + 7
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 65y
27
+ ··· + 1024529950y + 32069569
c
2
y
28
+ 95y
27
+ ··· + 1623868142y + 32364721
c
3
y
28
− 28y
27
+ ··· + 5316y + 169
c
4
(y
14
+ 19y
13
+ ··· + 546y + 121)
2
c
5
, c
7
, c
12
y
28
+ 22y
27
+ ··· − 192y + 16
c
6
(y
14
− 25y
13
+ ··· + 213y + 1)
2
c
8
, c
11
(y
14
+ 6y
13
+ ··· + 1572y + 361)
2
c
9
, c
10
y
28
+ 5y
27
+ ··· + 808y + 49
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.608535 + 0.818694I
a = −0.411980 + 0.907499I
b = 0.06835 − 1.89797I
−6.55425 − 2.13545I −1.029851 + 0.927255I
u = −0.608535 + 0.818694I
a = −1.176640 + 0.343109I
b = −0.361633 + 1.267890I
−6.55425 − 2.13545I −1.029851 + 0.927255I
u = −0.608535 − 0.818694I
a = −0.411980 − 0.907499I
b = 0.06835 + 1.89797I
−6.55425 + 2.13545I −1.029851 − 0.927255I
u = −0.608535 − 0.818694I
a = −1.176640 − 0.343109I
b = −0.361633 − 1.267890I
−6.55425 + 2.13545I −1.029851 − 0.927255I
u = 0.867236 + 0.768486I
a = 0.660917 − 0.753698I
b = 0.417481 + 0.355557I
1.07339 − 1.32380I 7.73703 − 5.74981I
u = 0.867236 + 0.768486I
a = 0.437028 + 0.279301I
b = −0.241912 + 0.857846I
1.07339 − 1.32380I 7.73703 − 5.74981I
u = 0.867236 − 0.768486I
a = 0.660917 + 0.753698I
b = 0.417481 − 0.355557I
1.07339 + 1.32380I 7.73703 + 5.74981I
u = 0.867236 − 0.768486I
a = 0.437028 − 0.279301I
b = −0.241912 − 0.857846I
1.07339 + 1.32380I 7.73703 + 5.74981I
u = 0.166845 + 0.745853I
a = 1.198390 − 0.576968I
b = 0.58958 + 1.51898I
0.78349 + 4.75239I 9.02300 − 5.96017I
u = 0.166845 + 0.745853I
a = −0.90241 + 1.32619I
b = −0.128235 + 0.168215I
0.78349 + 4.75239I 9.02300 − 5.96017I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.166845 − 0.745853I
a = 1.198390 + 0.576968I
b = 0.58958 − 1.51898I
0.78349 − 4.75239I 9.02300 + 5.96017I
u = 0.166845 − 0.745853I
a = −0.90241 − 1.32619I
b = −0.128235 − 0.168215I
0.78349 − 4.75239I 9.02300 + 5.96017I
u = −0.564009 + 0.438487I
a = −0.755998 + 0.580538I
b = −0.825125 − 0.177451I
−2.32511 − 1.81694I 2.43913 + 3.97393I
u = −0.564009 + 0.438487I
a = 1.174370 − 0.329537I
b = 0.126698 − 1.153290I
−2.32511 − 1.81694I 2.43913 + 3.97393I
u = −0.564009 − 0.438487I
a = −0.755998 − 0.580538I
b = −0.825125 + 0.177451I
−2.32511 + 1.81694I 2.43913 − 3.97393I
u = −0.564009 − 0.438487I
a = 1.174370 + 0.329537I
b = 0.126698 + 1.153290I
−2.32511 + 1.81694I 2.43913 − 3.97393I
u = −0.22941 + 1.46771I
a = −1.023950 − 0.634998I
b = −0.25347 + 1.40401I
−8.50378 − 4.79575I −8.7502 + 11.1583I
u = −0.22941 + 1.46771I
a = 0.405862 + 0.057348I
b = 2.70787 − 0.47109I
−8.50378 − 4.79575I −8.7502 + 11.1583I
u = −0.22941 − 1.46771I
a = −1.023950 + 0.634998I
b = −0.25347 − 1.40401I
−8.50378 + 4.79575I −8.7502 − 11.1583I
u = −0.22941 − 1.46771I
a = 0.405862 − 0.057348I
b = 2.70787 + 0.47109I
−8.50378 + 4.79575I −8.7502 − 11.1583I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20751 + 1.75492I
a = 0.579759 − 0.748808I
b = −0.11875 + 1.53558I
−15.7247 − 5.5362I 2.24093 + 2.42211I
u = −0.20751 + 1.75492I
a = 0.732938 + 0.492983I
b = 0.60418 − 1.81331I
−15.7247 − 5.5362I 2.24093 + 2.42211I
u = −0.20751 − 1.75492I
a = 0.579759 + 0.748808I
b = −0.11875 − 1.53558I
−15.7247 + 5.5362I 2.24093 − 2.42211I
u = −0.20751 − 1.75492I
a = 0.732938 − 0.492983I
b = 0.60418 + 1.81331I
−15.7247 + 5.5362I 2.24093 − 2.42211I
u = 0.07539 + 1.95612I
a = −0.602812 + 0.538409I
b = −0.34660 − 1.66417I
−9.87238 + 4.14557I −1.66007 − 2.24011I
u = 0.07539 + 1.95612I
a = 0.457249 + 0.003148I
b = −0.238434 − 0.063577I
−9.87238 + 4.14557I −1.66007 − 2.24011I
u = 0.07539 − 1.95612I
a = −0.602812 − 0.538409I
b = −0.34660 + 1.66417I
−9.87238 − 4.14557I −1.66007 + 2.24011I
u = 0.07539 − 1.95612I
a = 0.457249 − 0.003148I
b = −0.238434 + 0.063577I
−9.87238 − 4.14557I −1.66007 + 2.24011I
12
III. I
u
3
= h31u
15
− 15u
14
+ · · · + 92b − 472, −577u
15
+ 3333u
14
+ · · · +
9292a + 191294, u
16
+ 11u
14
+ · · · + 343u
2
+ 101i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
1
=
0.0620964u
15
− 0.358696u
14
+ ··· + 1.99473u − 20.5870
−0.336957u
15
+ 0.163043u
14
+ ··· − 28.1196u + 5.13043
a
4
=
1
u
2
a
2
=
0.246879u
15
+ 0.0760870u
14
+ ··· + 23.8426u + 10.5109
−0.478261u
15
− 0.478261u
14
+ ··· − 46.7826u − 38.7826
a
3
=
0.246879u
15
+ 0.0760870u
14
+ ··· + 23.8426u + 10.5109
−0.184783u
15
− 0.434783u
14
+ ··· − 21.8478u − 31.0978
a
9
=
−0.627206u
15
− 0.391304u
14
+ ··· − 41.2622u − 21.9130
0.239130u
15
+ 0.336957u
14
+ ··· + 15.6413u + 28.1196
a
12
=
0.399053u
15
− 0.521739u
14
+ ··· + 30.1143u − 25.7174
−0.336957u
15
+ 0.163043u
14
+ ··· − 28.1196u + 5.13043
a
6
=
0.243328u
15
− 0.130435u
14
+ ··· + 25.1461u + 4.44565
−0.521739u
15
+ 0.369565u
14
+ ··· − 49.2174u + 11.1957
a
7
=
−0.0620964u
15
− 0.358696u
14
+ ··· − 1.99473u − 20.5870
−0.184783u
15
+ 0.434783u
14
+ ··· − 21.8478u + 31.0978
a
8
=
−0.399053u
15
− 0.521739u
14
+ ··· − 30.1143u − 25.7174
0.293478u
15
+ 0.706522u
14
+ ··· + 12.1848u + 47.5652
a
11
=
0.627206u
15
− 0.391304u
14
+ ··· + 41.2622u − 21.9130
−0.695652u
15
+ 0.315217u
14
+ ··· − 47.7065u + 11.4022
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
2
23
u
14
−
34
23
u
12
−
220
23
u
10
−
766
23
u
8
−
1666
23
u
6
−
2524
23
u
4
−
2672
23
u
2
−
1354
23
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 602u + 79
c
2
u
16
− 2u
15
+ ··· + 2u + 1
c
3
u
16
+ u
15
+ ··· + 4u + 1
c
4
u
16
+ 11u
14
+ ··· + 343u
2
+ 101
c
5
, c
7
u
16
− u
15
+ ··· − 8u + 4
c
6
(u
8
− 4u
7
+ 4u
6
+ u
5
− 4u
4
+ 4u
3
+ 4u
2
− u − 1)
2
c
8
(u
8
+ 2u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
+ u
2
+ 5u + 1)
2
c
9
u
16
− 2u
14
+ ··· + 7u
2
+ 1
c
10
u
16
− 2u
14
+ ··· + 7u
2
+ 1
c
11
(u
8
− 2u
7
− u
6
+ 3u
5
− 2u
4
+ 3u
3
+ u
2
− 5u + 1)
2
c
12
u
16
+ u
15
+ ··· + 8u + 4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 28y
15
+ ··· + 11898y + 6241
c
2
y
16
+ 32y
15
+ ··· + 50y + 1
c
3
y
16
− 9y
15
+ ··· − 6y + 1
c
4
(y
8
+ 11y
7
+ 54y
6
+ 160y
5
+ 329y
4
+ 496y
3
+ 526y
2
+ 343y + 101)
2
c
5
, c
7
, c
12
y
16
+ 7y
15
+ ··· + 224y + 16
c
6
(y
8
− 8y
7
+ 16y
6
+ 7y
5
+ 30y
4
− 54y
3
+ 32y
2
− 9y + 1)
2
c
8
, c
11
(y
8
− 6y
7
+ 9y
6
+ 9y
5
− 34y
4
+ 15y
3
+ 27y
2
− 23y + 1)
2
c
9
, c
10
y
16
− 4y
15
+ ··· + 14y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090290I
a = −0.961088 + 0.180402I
b = −0.664122 − 0.999638I
−5.13962 −1.84340
u = − 1.090290I
a = −0.961088 − 0.180402I
b = −0.664122 + 0.999638I
−5.13962 −1.84340
u = 0.258427 + 1.166580I
a = −0.565702 + 1.110660I
b = −0.139231 − 0.937062I
−0.44142 + 5.36486I 3.50284 − 6.38935I
u = 0.258427 − 1.166580I
a = −0.565702 − 1.110660I
b = −0.139231 + 0.937062I
−0.44142 − 5.36486I 3.50284 + 6.38935I
u = −0.258427 + 1.166580I
a = −0.870065 − 0.439798I
b = −0.83736 + 1.51086I
−0.44142 − 5.36486I 3.50284 + 6.38935I
u = −0.258427 − 1.166580I
a = −0.870065 + 0.439798I
b = −0.83736 − 1.51086I
−0.44142 + 5.36486I 3.50284 − 6.38935I
u = 0.892618 + 0.961745I
a = 0.611276 − 0.635790I
b = 0.197106 + 0.382187I
0.89291 − 1.78628I 1.46883 + 8.62602I
u = 0.892618 − 0.961745I
a = 0.611276 + 0.635790I
b = 0.197106 − 0.382187I
0.89291 + 1.78628I 1.46883 − 8.62602I
u = −0.892618 + 0.961745I
a = −0.259050 + 0.347570I
b = 0.227991 + 0.862739I
0.89291 + 1.78628I 1.46883 − 8.62602I
u = −0.892618 − 0.961745I
a = −0.259050 − 0.347570I
b = 0.227991 − 0.862739I
0.89291 − 1.78628I 1.46883 + 8.62602I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50959I
a = −0.312012 − 0.703036I
b = 0.167596 + 0.929211I
0.871886 3.60060
u = − 1.50959I
a = −0.312012 + 0.703036I
b = 0.167596 − 0.929211I
0.871886 3.60060
u = −0.26473 + 1.55369I
a = 0.266058 + 0.030684I
b = 1.84403 − 0.56362I
−8.18722 − 4.50719I 6.14971 − 1.09337I
u = −0.26473 − 1.55369I
a = 0.266058 − 0.030684I
b = 1.84403 + 0.56362I
−8.18722 + 4.50719I 6.14971 + 1.09337I
u = 0.26473 + 1.55369I
a = −0.909417 + 0.550848I
b = −0.29601 − 1.42725I
−8.18722 + 4.50719I 6.14971 + 1.09337I
u = 0.26473 − 1.55369I
a = −0.909417 − 0.550848I
b = −0.29601 + 1.42725I
−8.18722 − 4.50719I 6.14971 − 1.09337I
17
IV. I
v
1
= ha, −v
2
+ b − 3v − 1, v
3
+ 3v
2
+ 2v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
1
=
0
v
2
+ 3v + 1
a
4
=
1
0
a
2
=
−v
2
− 3v − 1
v
2
+ 3v + 1
a
3
=
−2v
2
− 4v − 1
v
2
+ 3v + 1
a
9
=
v
−v
2
− 2v
a
12
=
−v
2
− 3v − 1
v
2
+ 3v + 1
a
6
=
−v − 1
v + 2
a
7
=
3v
2
+ 6v + 3
−v
2
− 3v − 1
a
8
=
2v
2
+ 3v + 2
−v
2
− 3v − 1
a
11
=
−2v
v
2
+ 2v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9v
2
− 22v − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
3
− u
2
+ 2u − 1
c
2
, c
10
u
3
− u + 1
c
3
u
3
+ u
2
− 1
c
4
u
3
c
5
, c
7
u
3
+ u
2
+ 2u + 1
c
6
u
3
+ 4u
2
+ 7u + 5
c
8
u
3
− 2u
2
+ u − 1
c
9
u
3
− u − 1
c
11
u
3
+ 2u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
9
, c
10
y
3
− 2y
2
+ y − 1
c
3
y
3
− y
2
+ 2y − 1
c
4
y
3
c
6
y
3
− 2y
2
+ 9y − 25
c
8
, c
11
y
3
− 2y
2
− 3y − 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.337641 + 0.562280I
a = 0
b = −0.215080 + 1.307140I
−1.45094 + 3.77083I 5.24751 − 8.95287I
v = −0.337641 − 0.562280I
a = 0
b = −0.215080 − 1.307140I
−1.45094 − 3.77083I 5.24751 + 8.95287I
v = −2.32472
a = 0
b = −0.569840
6.19175 −1.49500
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)(u
16
− 10u
15
+ ··· − 602u + 79)
· (u
16
− u
15
+ ··· − 11u + 1)(u
28
− 5u
27
+ ··· + 1150u + 5663)
c
2
(u
3
− u + 1)(u
16
− 2u
15
+ ··· + 194u − 121)(u
16
− 2u
15
+ ··· + 2u + 1)
· (u
28
+ u
27
+ ··· + 20378u + 5689)
c
3
(u
3
+ u
2
− 1)(u
16
− u
15
+ ··· − 19u + 7)(u
16
+ u
15
+ ··· + 4u + 1)
· (u
28
− 14u
26
+ ··· + 40u + 13)
c
4
u
3
(u
14
+ u
13
+ ··· + 20u + 11)
2
(u
16
+ 11u
14
+ ··· + 343u
2
+ 101)
· (u
16
− 3u
15
+ ··· − 32u − 16)
c
5
, c
7
(u
3
+ u
2
+ 2u + 1)(u
16
− u
15
+ ··· − 8u + 4)(u
16
+ u
15
+ ··· − 4u + 4)
· (u
28
− 4u
27
+ ··· + 52u + 4)
c
6
(u
3
+ 4u
2
+ 7u + 5)(u
8
− 4u
7
+ 4u
6
+ u
5
− 4u
4
+ 4u
3
+ 4u
2
− u − 1)
2
· ((u
14
− 3u
13
+ ··· + 9u + 1)
2
)(u
16
+ 7u
15
+ ··· − 65u + 28)
c
8
(u
3
− 2u
2
+ u − 1)(u
8
+ 2u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
+ u
2
+ 5u + 1)
2
· ((u
14
− 2u
13
+ ··· + 10u + 19)
2
)(u
16
+ 3u
15
+ ··· + 13u − 28)
c
9
(u
3
− u − 1)(u
16
− 2u
14
+ ··· + 4u
2
− 1)(u
16
− 2u
14
+ ··· + 7u
2
+ 1)
· (u
28
− u
27
+ ··· − 2u + 7)
c
10
(u
3
− u + 1)(u
16
− 2u
14
+ ··· + 4u
2
− 1)(u
16
− 2u
14
+ ··· + 7u
2
+ 1)
· (u
28
− u
27
+ ··· − 2u + 7)
c
11
(u
3
+ 2u
2
+ u + 1)(u
8
− 2u
7
− u
6
+ 3u
5
− 2u
4
+ 3u
3
+ u
2
− 5u + 1)
2
· ((u
14
− 2u
13
+ ··· + 10u + 19)
2
)(u
16
+ 3u
15
+ ··· + 13u − 28)
c
12
(u
3
− u
2
+ 2u − 1)(u
16
+ u
15
+ ··· + 8u + 4)(u
16
+ u
15
+ ··· − 4u + 4)
· (u
28
− 4u
27
+ ··· + 52u + 4)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y − 1)(y
16
− 28y
15
+ ··· + 11898y + 6241)
· (y
16
− 21y
15
+ ··· − 131y + 1)
· (y
28
− 65y
27
+ ··· + 1024529950y + 32069569)
c
2
(y
3
− 2y
2
+ y − 1)(y
16
+ 26y
15
+ ··· − 15614y + 14641)
· (y
16
+ 32y
15
+ ··· + 50y + 1)
· (y
28
+ 95y
27
+ ··· + 1623868142y + 32364721)
c
3
(y
3
− y
2
+ 2y − 1)(y
16
− 19y
15
+ ··· − 501y + 49)
· (y
16
− 9y
15
+ ··· − 6y + 1)(y
28
− 28y
27
+ ··· + 5316y + 169)
c
4
y
3
· (y
8
+ 11y
7
+ 54y
6
+ 160y
5
+ 329y
4
+ 496y
3
+ 526y
2
+ 343y + 101)
2
· ((y
14
+ 19y
13
+ ··· + 546y + 121)
2
)(y
16
+ 23y
15
+ ··· − 2304y + 256)
c
5
, c
7
, c
12
(y
3
+ 3y
2
+ 2y − 1)(y
16
+ 7y
15
+ ··· + 224y + 16)
· (y
16
+ 19y
15
+ ··· − 80y + 16)(y
28
+ 22y
27
+ ··· − 192y + 16)
c
6
(y
3
− 2y
2
+ 9y − 25)
· (y
8
− 8y
7
+ 16y
6
+ 7y
5
+ 30y
4
− 54y
3
+ 32y
2
− 9y + 1)
2
· ((y
14
− 25y
13
+ ··· + 213y + 1)
2
)(y
16
− 25y
15
+ ··· − 33289y + 784)
c
8
, c
11
(y
3
− 2y
2
− 3y − 1)
· (y
8
− 6y
7
+ 9y
6
+ 9y
5
− 34y
4
+ 15y
3
+ 27y
2
− 23y + 1)
2
· ((y
14
+ 6y
13
+ ··· + 1572y + 361)
2
)(y
16
+ y
15
+ ··· − 7169y + 784)
c
9
, c
10
(y
3
− 2y
2
+ y − 1)(y
16
− 4y
15
+ ··· + 14y + 1)(y
16
− 4y
15
+ ··· − 8y + 1)
· (y
28
+ 5y
27
+ ··· + 808y + 49)
23
