12a
0683
(K12a
0683
)
A knot diagram
1
Linearized knot diagam
3 7 11 12 10 8 2 1 5 6 4 9
Solving Sequence
2,8
7
3,11
4 1 9 6 10 5 12
c
7
c
2
c
3
c
1
c
8
c
6
c
10
c
5
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
29
− 7u
28
+ ··· + b + 7, −7u
30
+ 21u
29
+ ··· + 2a + 16, u
31
− 3u
30
+ ··· + 2u + 2i
I
u
2
= h−u
18
− u
17
+ ··· + b − 1, −u
18
a − u
18
+ ··· − a − 1, u
19
+ u
18
+ ··· + 2u − 1i
I
u
3
= h−u
2
+ b − u − 1, u
3
+ 2a − u − 2, u
4
+ u
2
+ 2i
I
u
4
= hb + u, a + 1, u
2
+ 1i
I
u
5
= hu
3
+ u
2
+ b − 1, u
3
+ u
2
+ a + u, u
4
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 80 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
29
−7u
28
+· · ·+b+7, −7u
30
+21u
29
+· · ·+2a+16, u
31
−3u
30
+· · ·+2u+2i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
7
2
u
30
−
21
2
u
29
+ ··· − 13u − 8
−4u
29
+ 7u
28
+ ··· − 15u − 7
a
4
=
−
1
2
u
30
+
1
2
u
29
+ ··· + u
2
+ u
−u
30
+ 2u
29
+ ··· + 2u + 1
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
6
=
u
2
+ 1
u
2
a
10
=
5
2
u
30
−
15
2
u
29
+ ··· − 9u − 5
−3u
29
+ 5u
28
+ ··· − 11u − 5
a
5
=
3
2
u
30
−
5
2
u
29
+ ··· +
15
2
u
3
+ u
2
u
30
− 2u
29
+ ··· − u − 1
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
30
+ 8u
29
−18u
28
+ 42u
27
−66u
26
+ 130u
25
−152u
24
+ 264u
23
−238u
22
+ 400u
21
−
254u
20
+ 478u
19
− 184u
18
+ 486u
17
− 50u
16
+ 466u
15
+ 62u
14
+ 410u
13
+ 144u
12
+
350u
11
+ 186u
10
+ 252u
9
+ 162u
8
+ 174u
7
+ 138u
6
+ 104u
5
+ 80u
4
+ 36u
3
+ 40u
2
+ 34u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
31
+ 11u
30
+ ··· − 28u − 4
c
2
, c
7
u
31
+ 3u
30
+ ··· + 2u − 2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
31
+ u
30
+ ··· + 2u + 1
c
8
, c
12
u
31
− 15u
30
+ ··· + 3142u − 314
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
31
+ 19y
30
+ ··· − 336y −16
c
2
, c
7
y
31
+ 11y
30
+ ··· − 28y −4
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
31
− 41y
30
+ ··· + 6y −1
c
8
, c
12
y
31
+ 23y
30
+ ··· − 1185660y −98596
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834590 + 0.582027I
a = −1.21990 + 2.11129I
b = −2.24694 + 1.05205I
−12.7225 − 9.0086I −8.83881 + 3.40935I
u = 0.834590 − 0.582027I
a = −1.21990 − 2.11129I
b = −2.24694 − 1.05205I
−12.7225 + 9.0086I −8.83881 − 3.40935I
u = 0.722502 + 0.621547I
a = 1.250200 − 0.565257I
b = 1.254610 + 0.368661I
0.64783 − 2.08671I −2.33564 + 4.90914I
u = 0.722502 − 0.621547I
a = 1.250200 + 0.565257I
b = 1.254610 − 0.368661I
0.64783 + 2.08671I −2.33564 − 4.90914I
u = −0.011192 + 1.055950I
a = −0.403491 − 0.377694I
b = 0.403341 − 0.421839I
−4.70000 − 1.40560I −10.10684 + 4.97569I
u = −0.011192 − 1.055950I
a = −0.403491 + 0.377694I
b = 0.403341 + 0.421839I
−4.70000 + 1.40560I −10.10684 − 4.97569I
u = −0.660425 + 0.655957I
a = 0.095218 − 0.222295I
b = 0.082932 + 0.209267I
0.242168 − 0.690936I −4.10470 + 4.18335I
u = −0.660425 − 0.655957I
a = 0.095218 + 0.222295I
b = 0.082932 − 0.209267I
0.242168 + 0.690936I −4.10470 − 4.18335I
u = −0.317662 + 1.028560I
a = −0.763693 + 0.390412I
b = −0.158967 − 0.909525I
−12.44600 − 3.27738I −13.9945 + 3.6592I
u = −0.317662 − 1.028560I
a = −0.763693 − 0.390412I
b = −0.158967 + 0.909525I
−12.44600 + 3.27738I −13.9945 − 3.6592I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688487 + 0.854024I
a = −1.32554 + 1.02312I
b = −1.78639 − 0.42763I
3.47574 + 2.64776I 2.40040 − 3.76300I
u = 0.688487 − 0.854024I
a = −1.32554 − 1.02312I
b = −1.78639 + 0.42763I
3.47574 − 2.64776I 2.40040 + 3.76300I
u = 0.806865 + 0.777962I
a = −0.57745 − 2.39117I
b = 1.39431 − 2.37858I
−5.26559 − 1.70254I −7.93225 + 0.49720I
u = 0.806865 − 0.777962I
a = −0.57745 + 2.39117I
b = 1.39431 + 2.37858I
−5.26559 + 1.70254I −7.93225 − 0.49720I
u = −0.772524 + 0.407584I
a = 0.357260 + 0.680444I
b = −0.553330 − 0.380046I
−13.7371 − 5.6675I −9.37862 + 3.30798I
u = −0.772524 − 0.407584I
a = 0.357260 − 0.680444I
b = −0.553330 + 0.380046I
−13.7371 + 5.6675I −9.37862 − 3.30798I
u = −0.062033 + 1.149980I
a = 1.032410 + 0.353539I
b = −0.470604 + 1.165310I
−19.0694 − 7.7866I −15.0141 + 3.7811I
u = −0.062033 − 1.149980I
a = 1.032410 − 0.353539I
b = −0.470604 − 1.165310I
−19.0694 + 7.7866I −15.0141 − 3.7811I
u = −0.655738 + 0.995207I
a = −0.016249 + 0.192084I
b = −0.180508 − 0.142129I
−0.76854 − 4.47807I −5.49078 + 0.99191I
u = −0.655738 − 0.995207I
a = −0.016249 − 0.192084I
b = −0.180508 + 0.142129I
−0.76854 + 4.47807I −5.49078 − 0.99191I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663735 + 1.013080I
a = 0.869119 − 1.080960I
b = 1.67196 + 0.16301I
−0.50643 + 7.41412I −4.69631 − 9.68387I
u = 0.663735 − 1.013080I
a = 0.869119 + 1.080960I
b = 1.67196 − 0.16301I
−0.50643 − 7.41412I −4.69631 + 9.68387I
u = 0.755579 + 0.953754I
a = 2.25812 + 0.93449I
b = 0.81492 + 2.85977I
−5.80221 + 7.55915I −8.80311 − 5.88769I
u = 0.755579 − 0.953754I
a = 2.25812 − 0.93449I
b = 0.81492 − 2.85977I
−5.80221 − 7.55915I −8.80311 + 5.88769I
u = −0.598928 + 1.072520I
a = 0.297943 − 0.455847I
b = 0.310457 + 0.592568I
−15.6742 + 0.5629I −12.28287 + 1.51453I
u = −0.598928 − 1.072520I
a = 0.297943 + 0.455847I
b = 0.310457 − 0.592568I
−15.6742 − 0.5629I −12.28287 − 1.51453I
u = 0.689812 + 1.062820I
a = −2.28466 + 0.81265I
b = −2.43969 − 1.86761I
−14.1718 + 14.7070I −10.75887 − 7.88304I
u = 0.689812 − 1.062820I
a = −2.28466 − 0.81265I
b = −2.43969 + 1.86761I
−14.1718 − 14.7070I −10.75887 + 7.88304I
u = −0.671467
a = −1.07798
b = 0.723830
−9.27702 −8.24970
u = −0.247335 + 0.431598I
a = 0.469701 − 0.366440I
b = 0.041981 + 0.293355I
−0.139351 − 0.826891I −3.53813 + 8.27499I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247335 − 0.431598I
a = 0.469701 + 0.366440I
b = 0.041981 − 0.293355I
−0.139351 + 0.826891I −3.53813 − 8.27499I
8
II.
I
u
2
= h−u
18
−u
17
+· · ·+b−1, −u
18
a−u
18
+· · ·−a−1, u
19
+u
18
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
a
u
18
+ u
17
+ ··· − u + 1
a
4
=
u
18
+ u
17
+ ··· − a + 2u
u
18
a + u
17
a + ··· + u + 1
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
6
=
u
2
+ 1
u
2
a
10
=
−u
18
− u
17
+ ··· + a + 1
u
14
+ u
13
+ ··· − u + 1
a
5
=
−u
18
− u
17
+ ··· + a − u
2u
16
+ 2u
15
+ ··· − u − 1
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
17
+ 4u
16
+ 12u
15
+ 12u
14
+ 28u
13
+ 24u
12
+ 36u
11
+ 32u
10
+
36u
9
+ 28u
8
+ 28u
7
+ 28u
6
+ 12u
5
+ 16u
4
+ 12u
3
+ 12u
2
− 4u − 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
19
+ 7u
18
+ ··· + 2u − 1)
2
c
2
, c
7
(u
19
− u
18
+ ··· + 2u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
38
+ u
37
+ ··· + 11u − 16
c
8
, c
12
(u
19
+ 5u
18
+ ··· + 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
19
+ 11y
18
+ ··· + 42y −1)
2
c
2
, c
7
(y
19
+ 7y
18
+ ··· + 2y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
38
− 33y
37
+ ··· − 153y + 256
c
8
, c
12
(y
19
+ 19y
18
+ ··· + 10y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787239 + 0.559366I
a = −1.59518 − 1.01906I
b = −1.96110 − 0.37239I
−5.72757 + 4.39903I −7.06652 − 2.80289I
u = −0.787239 + 0.559366I
a = 1.43202 + 1.49055I
b = 1.82582 − 0.09005I
−5.72757 + 4.39903I −7.06652 − 2.80289I
u = −0.787239 − 0.559366I
a = −1.59518 + 1.01906I
b = −1.96110 + 0.37239I
−5.72757 − 4.39903I −7.06652 + 2.80289I
u = −0.787239 − 0.559366I
a = 1.43202 − 1.49055I
b = 1.82582 + 0.09005I
−5.72757 − 4.39903I −7.06652 + 2.80289I
u = −0.709462 + 0.766103I
a = 0.29719 + 1.53619I
b = 1.57544 + 1.21787I
0.332249 + 0.168160I −1.83171 − 0.91431I
u = −0.709462 + 0.766103I
a = −0.16941 − 1.89955I
b = −1.38773 − 0.86219I
0.332249 + 0.168160I −1.83171 − 0.91431I
u = −0.709462 − 0.766103I
a = 0.29719 − 1.53619I
b = 1.57544 − 1.21787I
0.332249 − 0.168160I −1.83171 + 0.91431I
u = −0.709462 − 0.766103I
a = −0.16941 + 1.89955I
b = −1.38773 + 0.86219I
0.332249 − 0.168160I −1.83171 + 0.91431I
u = 0.588600 + 0.865037I
a = 1.55445 − 0.80251I
b = 2.17659 + 0.04078I
−2.82151 + 2.32534I −9.72826 − 3.09456I
u = 0.588600 + 0.865037I
a = 1.20249 − 1.69796I
b = 1.60915 + 0.87230I
−2.82151 + 2.32534I −9.72826 − 3.09456I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.588600 − 0.865037I
a = 1.55445 + 0.80251I
b = 2.17659 − 0.04078I
−2.82151 − 2.32534I −9.72826 + 3.09456I
u = 0.588600 − 0.865037I
a = 1.20249 + 1.69796I
b = 1.60915 − 0.87230I
−2.82151 − 2.32534I −9.72826 + 3.09456I
u = 0.745489 + 0.500016I
a = −0.996497 − 0.309724I
b = −1.167150 + 0.064986I
−6.12368 + 1.53005I −7.79395 − 2.54963I
u = 0.745489 + 0.500016I
a = −1.039500 + 0.784391I
b = −0.588010 − 0.729160I
−6.12368 + 1.53005I −7.79395 − 2.54963I
u = 0.745489 − 0.500016I
a = −0.996497 + 0.309724I
b = −1.167150 − 0.064986I
−6.12368 − 1.53005I −7.79395 + 2.54963I
u = 0.745489 − 0.500016I
a = −1.039500 − 0.784391I
b = −0.588010 + 0.729160I
−6.12368 − 1.53005I −7.79395 + 2.54963I
u = 0.021471 + 1.128170I
a = 0.965139 − 0.110361I
b = −1.080140 − 0.504142I
−11.59750 + 3.11880I −13.58624 − 2.69239I
u = 0.021471 + 1.128170I
a = −0.464921 + 0.948575I
b = 0.145228 + 1.086470I
−11.59750 + 3.11880I −13.58624 − 2.69239I
u = 0.021471 − 1.128170I
a = 0.965139 + 0.110361I
b = −1.080140 + 0.504142I
−11.59750 − 3.11880I −13.58624 + 2.69239I
u = 0.021471 − 1.128170I
a = −0.464921 − 0.948575I
b = 0.145228 − 1.086470I
−11.59750 − 3.11880I −13.58624 + 2.69239I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167515 + 0.839557I
a = −1.53925 − 0.74620I
b = 0.085530 + 0.151965I
−4.70093 + 1.72326I −11.81965 − 5.18112I
u = 0.167515 + 0.839557I
a = 0.193624 − 0.063242I
b = 0.36863 − 1.41729I
−4.70093 + 1.72326I −11.81965 − 5.18112I
u = 0.167515 − 0.839557I
a = −1.53925 + 0.74620I
b = 0.085530 − 0.151965I
−4.70093 − 1.72326I −11.81965 + 5.18112I
u = 0.167515 − 0.839557I
a = 0.193624 + 0.063242I
b = 0.36863 + 1.41729I
−4.70093 − 1.72326I −11.81965 + 5.18112I
u = −0.687512 + 0.928828I
a = 1.83316 + 0.24348I
b = 1.18697 − 1.80258I
−0.16029 − 5.52702I −3.57206 + 7.00248I
u = −0.687512 + 0.928828I
a = −1.86487 + 0.10244I
b = −1.48646 + 1.53530I
−0.16029 − 5.52702I −3.57206 + 7.00248I
u = −0.687512 − 0.928828I
a = 1.83316 − 0.24348I
b = 1.18697 + 1.80258I
−0.16029 + 5.52702I −3.57206 − 7.00248I
u = −0.687512 − 0.928828I
a = −1.86487 − 0.10244I
b = −1.48646 − 1.53530I
−0.16029 + 5.52702I −3.57206 − 7.00248I
u = 0.636878 + 1.050560I
a = −0.563849 + 0.610645I
b = −1.65719 + 0.48350I
−7.70394 + 3.71612I −10.19900 − 2.45937I
u = 0.636878 + 1.050560I
a = −0.362743 + 1.357530I
b = −1.000620 − 0.203449I
−7.70394 + 3.71612I −10.19900 − 2.45937I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636878 − 1.050560I
a = −0.563849 − 0.610645I
b = −1.65719 − 0.48350I
−7.70394 − 3.71612I −10.19900 + 2.45937I
u = 0.636878 − 1.050560I
a = −0.362743 − 1.357530I
b = −1.000620 + 0.203449I
−7.70394 − 3.71612I −10.19900 + 2.45937I
u = −0.666721 + 1.052350I
a = 1.51291 + 1.05726I
b = 2.53933 − 0.66065I
−7.18622 − 9.88550I −9.13872 + 7.31129I
u = −0.666721 + 1.052350I
a = −1.53887 − 1.43806I
b = −2.12129 + 0.88721I
−7.18622 − 9.88550I −9.13872 + 7.31129I
u = −0.666721 − 1.052350I
a = 1.51291 − 1.05726I
b = 2.53933 + 0.66065I
−7.18622 + 9.88550I −9.13872 − 7.31129I
u = −0.666721 − 1.052350I
a = −1.53887 + 1.43806I
b = −2.12129 − 0.88721I
−7.18622 + 9.88550I −9.13872 − 7.31129I
u = 0.381963
a = −0.253895
b = 0.971005
−2.38250 −0.527780
u = 0.381963
a = 2.54214
b = −0.0969785
−2.38250 −0.527780
15
III. I
u
3
= h−u
2
+ b − u − 1, u
3
+ 2a − u − 2, u
4
+ u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−
1
2
u
3
+
1
2
u + 1
u
2
+ u + 1
a
4
=
−
1
2
u
3
+
3
2
u + 1
u
3
+ u
2
+ 2u + 1
a
1
=
u
3
−u
a
9
=
−u
2
− 1
−u
2
a
6
=
u
2
+ 1
u
2
a
10
=
−
1
2
u
3
− u
2
+
1
2
u
u + 1
a
5
=
−
1
2
u
3
+
1
2
u + 1
u
2
+ u + 1
a
12
=
−u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 12
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 2)
2
c
2
, c
7
, c
8
c
12
u
4
+ u
2
+ 2
c
3
, c
4
, c
9
c
10
(u − 1)
4
c
5
, c
11
(u + 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
2
+ 3y + 4)
2
c
2
, c
7
, c
8
c
12
(y
2
+ y + 2)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y −1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = 2.15417 + 0.28654I
b = 1.17610 + 2.30119I
−2.46740 + 5.33349I −10.00000 − 5.29150I
u = 0.676097 − 0.978318I
a = 2.15417 − 0.28654I
b = 1.17610 − 2.30119I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 + 0.978318I
a = −0.154169 + 0.286543I
b = −0.176097 − 0.344557I
−2.46740 − 5.33349I −10.00000 + 5.29150I
u = −0.676097 − 0.978318I
a = −0.154169 − 0.286543I
b = −0.176097 + 0.344557I
−2.46740 + 5.33349I −10.00000 − 5.29150I
19
IV. I
u
4
= hb + u, a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
−1
a
3
=
u
0
a
11
=
−1
−u
a
4
=
u − 1
−u
a
1
=
−u
u
a
9
=
0
1
a
6
=
0
−1
a
10
=
−1
−u + 1
a
5
=
−1
−u
a
12
=
−u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
9
, c
10
(u − 1)
2
c
2
, c
7
, c
8
c
12
u
2
+ 1
c
5
, c
11
(u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
9
c
10
, c
11
(y −1)
2
c
2
, c
7
, c
8
c
12
(y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = − 1.000000I
−6.57974 −16.0000
u = − 1.000000I
a = −1.00000
b = 1.000000I
−6.57974 −16.0000
23
V. I
u
5
= hu
3
+ u
2
+ b − 1, u
3
+ u
2
+ a + u, u
4
+ 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
11
=
−u
3
− u
2
− u
−u
3
− u
2
+ 1
a
4
=
u
3
+ u
2
+ 2u
2u
3
+ u
2
+ u − 1
a
1
=
u
3
u
3
a
9
=
u
2
+ 1
u
2
a
6
=
u
2
+ 1
u
2
a
10
=
−u
3
− u + 1
−u
3
+ 1
a
5
=
u
3
+ u
2
+ u
u
3
+ u
2
− 1
a
12
=
u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
+ 1)
2
c
2
, c
7
, c
8
c
12
u
4
+ 1
c
3
, c
4
, c
9
c
10
(u + 1)
4
c
5
, c
11
(u − 1)
4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y + 1)
4
c
2
, c
7
, c
8
c
12
(y
2
+ 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y −1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = − 2.41421I
b = 1.70711 − 1.70711I
−1.64493 −8.00000
u = 0.707107 − 0.707107I
a = 2.41421I
b = 1.70711 + 1.70711I
−1.64493 −8.00000
u = −0.707107 + 0.707107I
a = − 0.414214I
b = 0.292893 + 0.292893I
−1.64493 −8.00000
u = −0.707107 − 0.707107I
a = 0.414214I
b = 0.292893 − 0.292893I
−1.64493 −8.00000
27
VI. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
8
=
1
0
a
7
=
1
0
a
3
=
−1
0
a
11
=
0
1
a
4
=
−1
−1
a
1
=
−1
0
a
9
=
1
0
a
6
=
1
0
a
10
=
1
1
a
5
=
0
−1
a
12
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
u
c
3
, c
4
, c
9
c
10
u + 1
c
5
, c
11
u − 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y −1
30
(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
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u − 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
19
+ 7u
18
+ ··· + 2u − 1)
2
· (u
31
+ 11u
30
+ ··· − 28u − 4)
c
2
, c
7
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
19
− u
18
+ ··· + 2u + 1)
2
· (u
31
+ 3u
30
+ ··· + 2u − 2)
c
3
, c
4
, c
9
c
10
((u − 1)
6
)(u + 1)
5
(u
31
+ u
30
+ ··· + 2u + 1)(u
38
+ u
37
+ ··· + 11u − 16)
c
5
, c
11
((u − 1)
5
)(u + 1)
6
(u
31
+ u
30
+ ··· + 2u + 1)(u
38
+ u
37
+ ··· + 11u − 16)
c
8
, c
12
u(u
2
+ 1)(u
4
+ 1)(u
4
+ u
2
+ 2)(u
19
+ 5u
18
+ ··· + 2u + 1)
2
· (u
31
− 15u
30
+ ··· + 3142u − 314)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y(y −1)
2
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
19
+ 11y
18
+ ··· + 42y −1)
2
· (y
31
+ 19y
30
+ ··· − 336y −16)
c
2
, c
7
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
19
+ 7y
18
+ ··· + 2y −1)
2
· (y
31
+ 11y
30
+ ··· − 28y −4)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
((y −1)
11
)(y
31
− 41y
30
+ ··· + 6y −1)(y
38
− 33y
37
+ ··· − 153y + 256)
c
8
, c
12
y(y + 1)
2
(y
2
+ 1)
2
(y
2
+ y + 2)
2
(y
19
+ 19y
18
+ ··· + 10y −1)
2
· (y
31
+ 23y
30
+ ··· − 1185660y −98596)
33
