12a
0181
(K12a
0181
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 12 10 4 8 1 7 11
Solving Sequence
3,9 4,5
2 6 1 8 10 11 7 12
c
3
c
2
c
5
c
1
c
8
c
9
c
10
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
19
+ 3u
18
+ ··· + 4b + 2u, −u
18
− 3u
17
+ ··· + 4a − 6, u
20
+ 5u
19
+ ··· + 12u + 4i
I
u
2
= h−82u
32
a + 53u
32
+ ··· + 116a + 32, 2u
32
a + u
32
+ ··· + 12a − 17, u
33
− 2u
32
+ ··· − u + 2i
I
v
1
= ha, b
2
+ b + 1, v + 1i
I
v
2
= ha, b − v + 1, v
2
− v + 1i
* 4 irreducible components of dim
C
= 0, with total 90 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
=
hu
19
+3u
18
+· · ·+4b+2u, −u
18
−3u
17
+· · ·+4a−6, u
20
+5u
19
+· · ·+12u+4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
1
4
u
18
+
3
4
u
17
+ ··· + u +
3
2
−
1
4
u
19
−
3
4
u
18
+ ··· −
9
4
u
3
−
1
2
u
a
2
=
−
7
4
u
19
− 8u
18
+ ··· − 15u −
9
2
−
3
4
u
19
−
15
4
u
18
+ ··· −
19
2
u − 4
a
6
=
−
7
4
u
19
− 8u
18
+ ··· − 15u −
9
2
9
4
u
19
+
31
4
u
18
+ ··· +
15
2
u + 1
a
1
=
−
5
2
u
19
−
47
4
u
18
+ ··· −
49
2
u −
17
2
−
3
4
u
19
−
15
4
u
18
+ ··· −
19
2
u − 4
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−
1
4
u
19
− u
18
+ ··· −
3
2
u −
1
2
−
1
4
u
19
−
5
4
u
18
+ ··· −
3
2
u − 1
a
7
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
−
7
4
u
19
− 7u
18
+ ··· −
21
2
u −
7
2
−
7
4
u
19
−
37
4
u
18
+ ··· −
37
2
u − 8
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −13u
19
− 66u
18
− 180u
17
− 337u
16
− 477u
15
− 527u
14
− 374u
13
− 30u
12
+ 397u
11
+
641u
10
+ 698u
9
+ 494u
8
+ 210u
7
− 106u
6
− 168u
5
− 196u
4
− 209u
3
− 259u
2
− 158u − 62
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
c
12
u
20
+ 7u
19
+ ··· + 6u + 1
c
2
, c
5
, c
6
c
11
u
20
+ u
19
+ ··· − 2u + 1
c
3
, c
8
u
20
+ 5u
19
+ ··· + 12u + 4
c
7
, c
9
u
20
− 5u
19
+ ··· − 48u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
c
12
y
20
+ 15y
19
+ ··· + 42y + 1
c
2
, c
5
, c
6
c
11
y
20
+ 7y
19
+ ··· + 6y + 1
c
3
, c
8
y
20
+ 5y
19
+ ··· + 48y + 16
c
7
, c
9
y
20
+ 13y
19
+ ··· + 2560y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956413 + 0.106188I
a = 0.666389 − 0.362681I
b = −0.690206 − 0.870989I
3.29641 + 5.31416I 3.14759 − 6.32881I
u = 0.956413 − 0.106188I
a = 0.666389 + 0.362681I
b = −0.690206 + 0.870989I
3.29641 − 5.31416I 3.14759 + 6.32881I
u = −0.859253 + 0.598044I
a = 0.726799 − 0.250535I
b = −0.710902 − 0.608435I
0.831191 + 0.623147I 2.59573 − 2.24523I
u = −0.859253 − 0.598044I
a = 0.726799 + 0.250535I
b = −0.710902 + 0.608435I
0.831191 − 0.623147I 2.59573 + 2.24523I
u = 0.511571 + 0.639622I
a = 1.075070 + 0.676318I
b = −0.102085 + 0.859228I
−2.97361 − 1.87280I −8.34696 + 4.79097I
u = 0.511571 − 0.639622I
a = 1.075070 − 0.676318I
b = −0.102085 − 0.859228I
−2.97361 + 1.87280I −8.34696 − 4.79097I
u = 0.193921 + 1.176600I
a = −1.33172 − 1.10006I
b = 0.775256 + 0.795478I
8.04637 + 1.61009I 7.70402 − 2.24180I
u = 0.193921 − 1.176600I
a = −1.33172 + 1.10006I
b = 0.775256 − 0.795478I
8.04637 − 1.61009I 7.70402 + 2.24180I
u = −0.962446 + 0.718212I
a = 0.613669 + 0.425585I
b = −0.666520 + 1.031640I
−1.66717 − 10.06630I −1.36976 + 7.52063I
u = −0.962446 − 0.718212I
a = 0.613669 − 0.425585I
b = −0.666520 − 1.031640I
−1.66717 + 10.06630I −1.36976 − 7.52063I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824880 + 0.894608I
a = 0.753015 − 1.021300I
b = −0.023434 − 1.120850I
−9.84057 + 3.07245I −9.39268 − 2.83211I
u = −0.824880 − 0.894608I
a = 0.753015 + 1.021300I
b = −0.023434 + 1.120850I
−9.84057 − 3.07245I −9.39268 + 2.83211I
u = 0.337755 + 1.176280I
a = −2.12989 + 0.17473I
b = 0.738480 − 0.944822I
7.12649 − 9.83704I 5.40465 + 9.06026I
u = 0.337755 − 1.176280I
a = −2.12989 − 0.17473I
b = 0.738480 + 0.944822I
7.12649 + 9.83704I 5.40465 − 9.06026I
u = −0.716852 + 1.049790I
a = −0.357717 + 0.974184I
b = 0.809192 − 0.602967I
2.16361 + 5.20834I 3.98742 − 2.19274I
u = −0.716852 − 1.049790I
a = −0.357717 − 0.974184I
b = 0.809192 + 0.602967I
2.16361 − 5.20834I 3.98742 + 2.19274I
u = −0.342141 + 0.579550I
a = 0.950288 − 0.152216I
b = −0.318780 − 0.354384I
0.155657 + 1.086730I 2.50050 − 5.83378I
u = −0.342141 − 0.579550I
a = 0.950288 + 0.152216I
b = −0.318780 + 0.354384I
0.155657 − 1.086730I 2.50050 + 5.83378I
u = −0.794089 + 1.065150I
a = −1.96591 + 0.82985I
b = 0.688998 + 1.054600I
−0.5586 + 16.5027I −0.23050 − 11.16239I
u = −0.794089 − 1.065150I
a = −1.96591 − 0.82985I
b = 0.688998 − 1.054600I
−0.5586 − 16.5027I −0.23050 + 11.16239I
6
II. I
u
2
= h−82u
32
a + 53u
32
+ · · · + 116a + 32, 2u
32
a + u
32
+ · · · + 12a −
17, u
33
− 2u
32
+ · · · − u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
1.20588au
32
− 0.779412u
32
+ ··· − 1.70588a − 0.470588
a
2
=
1.27941au
32
− 0.147059u
32
+ ··· + 0.470588a − 1.60294
0.514706au
32
+ 0.426471u
32
+ ··· − 1.26471a − 0.176471
a
6
=
1.27941au
32
− 0.147059u
32
+ ··· + 0.470588a − 1.60294
−0.647059au
32
− 1.26471u
32
+ ··· − 1.35294a + 2.26471
a
1
=
1.79412au
32
+ 0.279412u
32
+ ··· − 0.794118a − 1.77941
0.514706au
32
+ 0.426471u
32
+ ··· − 1.26471a − 0.176471
a
8
=
u
u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
11
=
−0.911765au
32
+ 1.05882u
32
+ ··· + 2.91176a − 1.30882
−u
32
+ 2u
31
+ ··· −
1
2
u + 2
a
7
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
12
=
−0.911765au
32
+ 1.55882u
32
+ ··· + 2.91176a − 0.308824
1.35294au
32
− 1.01471u
32
+ ··· − 1.35294a + 1.26471
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −u
32
−2u
31
−3u
30
−8u
29
−11u
28
−28u
27
−26u
26
−60u
25
−55u
24
−114u
23
−106u
22
−
160u
21
− 162u
20
− 198u
19
− 234u
18
− 196u
17
− 257u
16
− 162u
15
− 244u
14
− 124u
13
−
166u
12
−72u
11
−64u
10
−54u
9
+ 4u
8
−28u
7
+ 34u
6
−16u
5
+ 22u
4
−6u
3
+ 4u
2
−2u + 1
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
c
12
u
66
+ 24u
65
+ ··· + 17u + 1
c
2
, c
5
, c
6
c
11
u
66
+ 2u
65
+ ··· + u + 1
c
3
, c
8
(u
33
− 2u
32
+ ··· − u + 2)
2
c
7
, c
9
(u
33
− 10u
32
+ ··· − 23u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
c
12
y
66
+ 36y
65
+ ··· + 97y + 1
c
2
, c
5
, c
6
c
11
y
66
+ 24y
65
+ ··· + 17y + 1
c
3
, c
8
(y
33
+ 10y
32
+ ··· − 23y −4)
2
c
7
, c
9
(y
33
+ 26y
32
+ ··· − 335y −16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.049702 + 0.985538I
a = 0.804899 − 0.013377I
b = −0.628084 − 0.033140I
4.01597 + 2.68651I 7.73425 − 3.44417I
u = −0.049702 + 0.985538I
a = −2.27679 − 1.25073I
b = 0.701064 + 0.855945I
4.01597 + 2.68651I 7.73425 − 3.44417I
u = −0.049702 − 0.985538I
a = 0.804899 + 0.013377I
b = −0.628084 + 0.033140I
4.01597 − 2.68651I 7.73425 + 3.44417I
u = −0.049702 − 0.985538I
a = −2.27679 + 1.25073I
b = 0.701064 − 0.855945I
4.01597 − 2.68651I 7.73425 + 3.44417I
u = 0.665379 + 0.776145I
a = 0.635938 − 0.460788I
b = −0.589255 − 1.034860I
−0.77598 + 2.47863I 0.24297 − 1.77615I
u = 0.665379 + 0.776145I
a = 0.110839 − 1.231880I
b = 0.688258 + 0.559125I
−0.77598 + 2.47863I 0.24297 − 1.77615I
u = 0.665379 − 0.776145I
a = 0.635938 + 0.460788I
b = −0.589255 + 1.034860I
−0.77598 − 2.47863I 0.24297 + 1.77615I
u = 0.665379 − 0.776145I
a = 0.110839 + 1.231880I
b = 0.688258 − 0.559125I
−0.77598 − 2.47863I 0.24297 + 1.77615I
u = −0.949159
a = 0.675796 + 0.350096I
b = −0.692476 + 0.839598I
3.39234 3.61540
u = −0.949159
a = 0.675796 − 0.350096I
b = −0.692476 − 0.839598I
3.39234 3.61540
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613502 + 0.901064I
a = 0.759830 − 0.160326I
b = −0.702709 − 0.395207I
0.98851 + 2.36009I 3.77869 − 2.94560I
u = −0.613502 + 0.901064I
a = −0.213518 + 1.274820I
b = 0.731665 − 0.610211I
0.98851 + 2.36009I 3.77869 − 2.94560I
u = −0.613502 − 0.901064I
a = 0.759830 + 0.160326I
b = −0.702709 + 0.395207I
0.98851 − 2.36009I 3.77869 + 2.94560I
u = −0.613502 − 0.901064I
a = −0.213518 − 1.274820I
b = 0.731665 + 0.610211I
0.98851 − 2.36009I 3.77869 + 2.94560I
u = 0.234138 + 0.867139I
a = 0.767729 + 0.625996I
b = −0.302796 + 1.009580I
0.87226 − 5.71730I 1.14087 + 8.70218I
u = 0.234138 + 0.867139I
a = −3.20869 + 0.72540I
b = 0.660835 − 0.903263I
0.87226 − 5.71730I 1.14087 + 8.70218I
u = 0.234138 − 0.867139I
a = 0.767729 − 0.625996I
b = −0.302796 − 1.009580I
0.87226 + 5.71730I 1.14087 − 8.70218I
u = 0.234138 − 0.867139I
a = −3.20869 − 0.72540I
b = 0.660835 + 0.903263I
0.87226 + 5.71730I 1.14087 − 8.70218I
u = −0.702940 + 0.870739I
a = 0.621937 + 0.465792I
b = −0.595356 + 1.060450I
−2.09778 + 2.69718I −1.77480 − 3.09544I
u = −0.702940 + 0.870739I
a = −2.43936 + 1.09343I
b = 0.644093 + 1.024190I
−2.09778 + 2.69718I −1.77480 − 3.09544I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.702940 − 0.870739I
a = 0.621937 − 0.465792I
b = −0.595356 − 1.060450I
−2.09778 − 2.69718I −1.77480 + 3.09544I
u = −0.702940 − 0.870739I
a = −2.43936 − 1.09343I
b = 0.644093 − 1.024190I
−2.09778 − 2.69718I −1.77480 + 3.09544I
u = 0.788902 + 0.806240I
a = 0.733919 + 0.201231I
b = −0.735371 + 0.501044I
−4.43280 − 1.52216I −3.69925 + 2.61889I
u = 0.788902 + 0.806240I
a = 0.842836 + 1.040260I
b = −0.006541 + 1.075980I
−4.43280 − 1.52216I −3.69925 + 2.61889I
u = 0.788902 − 0.806240I
a = 0.733919 − 0.201231I
b = −0.735371 − 0.501044I
−4.43280 + 1.52216I −3.69925 − 2.61889I
u = 0.788902 − 0.806240I
a = 0.842836 − 1.040260I
b = −0.006541 − 1.075980I
−4.43280 + 1.52216I −3.69925 − 2.61889I
u = 0.920485 + 0.670333I
a = 0.621962 − 0.425064I
b = −0.657901 − 1.017940I
−0.37164 + 4.66065I 0.61587 − 2.80152I
u = 0.920485 + 0.670333I
a = 0.712997 + 0.235993I
b = −0.751562 + 0.591432I
−0.37164 + 4.66065I 0.61587 − 2.80152I
u = 0.920485 − 0.670333I
a = 0.621962 + 0.425064I
b = −0.657901 + 1.017940I
−0.37164 − 4.66065I 0.61587 + 2.80152I
u = 0.920485 − 0.670333I
a = 0.712997 − 0.235993I
b = −0.751562 − 0.591432I
−0.37164 − 4.66065I 0.61587 + 2.80152I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845575 + 0.795122I
a = 0.616836 + 0.443798I
b = −0.634247 + 1.046440I
−5.99253 − 3.68906I −6.07547 + 2.52126I
u = −0.845575 + 0.795122I
a = 0.816085 − 1.096950I
b = 0.018187 − 1.093160I
−5.99253 − 3.68906I −6.07547 + 2.52126I
u = −0.845575 − 0.795122I
a = 0.616836 − 0.443798I
b = −0.634247 − 1.046440I
−5.99253 + 3.68906I −6.07547 − 2.52126I
u = −0.845575 − 0.795122I
a = 0.816085 + 1.096950I
b = 0.018187 + 1.093160I
−5.99253 + 3.68906I −6.07547 − 2.52126I
u = 0.679751 + 0.948328I
a = 0.740250 + 0.160964I
b = −0.746944 + 0.406974I
−0.22436 − 7.71485I 1.58056 + 7.57230I
u = 0.679751 + 0.948328I
a = −2.35312 − 0.86592I
b = 0.664524 − 1.021430I
−0.22436 − 7.71485I 1.58056 + 7.57230I
u = 0.679751 − 0.948328I
a = 0.740250 − 0.160964I
b = −0.746944 − 0.406974I
−0.22436 + 7.71485I 1.58056 − 7.57230I
u = 0.679751 − 0.948328I
a = −2.35312 + 0.86592I
b = 0.664524 + 1.021430I
−0.22436 + 7.71485I 1.58056 − 7.57230I
u = −0.105432 + 0.816987I
a = 0.746933 − 0.576307I
b = −0.361341 − 0.997749I
1.188190 + 0.603355I 3.29363 − 1.93093I
u = −0.105432 + 0.816987I
a = −1.96741 + 2.42976I
b = 0.654202 − 0.802439I
1.188190 + 0.603355I 3.29363 − 1.93093I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.105432 − 0.816987I
a = 0.746933 + 0.576307I
b = −0.361341 + 0.997749I
1.188190 − 0.603355I 3.29363 + 1.93093I
u = −0.105432 − 0.816987I
a = −1.96741 − 2.42976I
b = 0.654202 + 0.802439I
1.188190 − 0.603355I 3.29363 + 1.93093I
u = 0.750104 + 0.942029I
a = −0.186018 − 1.000410I
b = 0.778688 + 0.566100I
−4.01232 − 4.27816I −2.78151 + 3.10265I
u = 0.750104 + 0.942029I
a = 0.751867 + 0.949236I
b = −0.065283 + 1.116190I
−4.01232 − 4.27816I −2.78151 + 3.10265I
u = 0.750104 − 0.942029I
a = −0.186018 + 1.000410I
b = 0.778688 − 0.566100I
−4.01232 + 4.27816I −2.78151 − 3.10265I
u = 0.750104 − 0.942029I
a = 0.751867 − 0.949236I
b = −0.065283 − 1.116190I
−4.01232 + 4.27816I −2.78151 − 3.10265I
u = −0.267647 + 1.175100I
a = −1.17158 + 1.12572I
b = 0.782054 − 0.772553I
7.64872 + 4.10928I 6.76207 − 3.53487I
u = −0.267647 + 1.175100I
a = −2.10317 − 0.34278I
b = 0.742093 + 0.926355I
7.64872 + 4.10928I 6.76207 − 3.53487I
u = −0.267647 − 1.175100I
a = −1.17158 − 1.12572I
b = 0.782054 + 0.772553I
7.64872 − 4.10928I 6.76207 + 3.53487I
u = −0.267647 − 1.175100I
a = −2.10317 + 0.34278I
b = 0.742093 − 0.926355I
7.64872 − 4.10928I 6.76207 + 3.53487I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.777774 + 0.973678I
a = 0.721347 − 0.956074I
b = −0.063549 − 1.135640I
−5.43107 + 9.74498I −4.76319 − 7.62687I
u = −0.777774 + 0.973678I
a = −2.11190 + 0.96967I
b = 0.666975 + 1.046950I
−5.43107 + 9.74498I −4.76319 − 7.62687I
u = −0.777774 − 0.973678I
a = 0.721347 + 0.956074I
b = −0.063549 + 1.135640I
−5.43107 − 9.74498I −4.76319 + 7.62687I
u = −0.777774 − 0.973678I
a = −2.11190 − 0.96967I
b = 0.666975 − 1.046950I
−5.43107 − 9.74498I −4.76319 + 7.62687I
u = 0.759296 + 1.058880I
a = −0.337168 − 0.916661I
b = 0.821726 + 0.590691I
0.83529 − 10.84000I 1.88810 + 6.73875I
u = 0.759296 + 1.058880I
a = −2.02862 − 0.79380I
b = 0.688861 − 1.045760I
0.83529 − 10.84000I 1.88810 + 6.73875I
u = 0.759296 − 1.058880I
a = −0.337168 + 0.916661I
b = 0.821726 − 0.590691I
0.83529 + 10.84000I 1.88810 − 6.73875I
u = 0.759296 − 1.058880I
a = −2.02862 + 0.79380I
b = 0.688861 + 1.045760I
0.83529 + 10.84000I 1.88810 − 6.73875I
u = 0.525723 + 0.430540I
a = 0.685556 − 0.437340I
b = −0.568437 − 0.942925I
−0.58470 + 2.92924I −3.69112 − 1.50327I
u = 0.525723 + 0.430540I
a = 1.65240 + 0.02104I
b = 0.192277 + 0.600483I
−0.58470 + 2.92924I −3.69112 − 1.50327I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.525723 − 0.430540I
a = 0.685556 + 0.437340I
b = −0.568437 + 0.942925I
−0.58470 − 2.92924I −3.69112 + 1.50327I
u = 0.525723 − 0.430540I
a = 1.65240 − 0.02104I
b = 0.192277 − 0.600483I
−0.58470 − 2.92924I −3.69112 + 1.50327I
u = −0.486625 + 0.301249I
a = 1.095810 + 0.119505I
b = 0.185860 − 0.292702I
0.09834 + 1.49688I −1.55937 − 4.19988I
u = −0.486625 + 0.301249I
a = 0.781578 − 0.368136I
b = −0.519509 − 0.755598I
0.09834 + 1.49688I −1.55937 − 4.19988I
u = −0.486625 − 0.301249I
a = 1.095810 − 0.119505I
b = 0.185860 + 0.292702I
0.09834 − 1.49688I −1.55937 + 4.19988I
u = −0.486625 − 0.301249I
a = 0.781578 + 0.368136I
b = −0.519509 + 0.755598I
0.09834 − 1.49688I −1.55937 + 4.19988I
16
III. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
5
=
0
b
a
2
=
1
−b − 1
a
6
=
b
b + 1
a
1
=
−b
−b − 1
a
8
=
−1
0
a
10
=
−1
0
a
11
=
0
−b
a
7
=
−1
0
a
12
=
−b
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b + 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
, c
11
u
2
− u + 1
c
2
, c
6
, c
12
u
2
+ u + 1
c
3
, c
7
, c
8
c
9
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
7
, c
8
c
9
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
20
IV. I
v
2
= ha, b − v + 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
v − 1
a
2
=
1
−v
a
6
=
v − 1
v
a
1
=
−v + 1
−v
a
8
=
v
0
a
10
=
v
0
a
11
=
0
−1
a
7
=
v
0
a
12
=
−v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
, c
11
u
2
− u + 1
c
2
, c
6
, c
12
u
2
+ u + 1
c
3
, c
7
, c
8
c
9
u
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
10
c
11
, c
12
y
2
+ y + 1
c
3
, c
7
, c
8
c
9
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
0 −3.00000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
0 −3.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
((u
2
− u + 1)
2
)(u
20
+ 7u
19
+ ··· + 6u + 1)(u
66
+ 24u
65
+ ··· + 17u + 1)
c
2
, c
6
((u
2
+ u + 1)
2
)(u
20
+ u
19
+ ··· − 2u + 1)(u
66
+ 2u
65
+ ··· + u + 1)
c
3
, c
8
u
4
(u
20
+ 5u
19
+ ··· + 12u + 4)(u
33
− 2u
32
+ ··· − u + 2)
2
c
5
, c
11
((u
2
− u + 1)
2
)(u
20
+ u
19
+ ··· − 2u + 1)(u
66
+ 2u
65
+ ··· + u + 1)
c
7
, c
9
u
4
(u
20
− 5u
19
+ ··· − 48u + 16)(u
33
− 10u
32
+ ··· − 23u + 4)
2
c
12
((u
2
+ u + 1)
2
)(u
20
+ 7u
19
+ ··· + 6u + 1)(u
66
+ 24u
65
+ ··· + 17u + 1)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
10
c
12
((y
2
+ y + 1)
2
)(y
20
+ 15y
19
+ ··· + 42y + 1)
· (y
66
+ 36y
65
+ ··· + 97y + 1)
c
2
, c
5
, c
6
c
11
((y
2
+ y + 1)
2
)(y
20
+ 7y
19
+ ··· + 6y + 1)(y
66
+ 24y
65
+ ··· + 17y + 1)
c
3
, c
8
y
4
(y
20
+ 5y
19
+ ··· + 48y + 16)(y
33
+ 10y
32
+ ··· − 23y − 4)
2
c
7
, c
9
y
4
(y
20
+ 13y
19
+ ··· + 2560y + 256)
· (y
33
+ 26y
32
+ ··· − 335y − 16)
2
26
