12n
0158
(K12n
0158
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 12 4 5 6 9 7 11
Solving Sequence
5,10 3,6
2 1 4 9 11 8 7 12
c
5
c
2
c
1
c
4
c
9
c
10
c
8
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h37u
25
+ 5u
24
+ ··· + 32b + 3, 11u
25
− u
24
+ ··· + 64a + 73, u
26
+ 5u
24
+ ··· + 7u
2
+ 1i
I
u
2
= h1.64036 × 10
19
u
35
− 6.55779 × 10
19
u
34
+ ··· + 1.64861 × 10
20
b − 8.76883 × 10
20
,
− 2.73439 × 10
20
u
35
+ 9.88504 × 10
20
u
34
+ ··· + 2.80263 × 10
21
a + 2.34140 × 10
22
,
u
36
− 2u
35
+ ··· − 16u + 17i
I
u
3
= hb + 1, −u
3
+ u
2
+ 2a + 1, u
4
+ u
2
+ u + 1i
I
u
4
= hb + 1, u
5
− u
4
+ u
3
− u
2
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
u
5
= h−a
2
+ 2au + b + 2a − 2u − 1, a
3
− 3a
2
u − 3a
2
+ 6au + a − 2u + 1, u
2
+ 1i
* 5 irreducible components of dim
C
= 0, with total 78 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
=
h37u
25
+5u
24
+· · ·+32b+3, 11u
25
−u
24
+· · ·+64a+73, u
26
+5u
24
+· · ·+7u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−0.171875u
25
+ 0.0156250u
24
+ ··· + 4.29688u − 1.14063
−1.15625u
25
− 0.156250u
24
+ ··· − 1.59375u − 0.0937500
a
6
=
1
−u
2
a
2
=
−1.32813u
25
− 0.140625u
24
+ ··· + 2.70313u − 1.23438
−1.15625u
25
− 0.156250u
24
+ ··· − 1.59375u − 0.0937500
a
1
=
1
8
u
24
+
1
2
u
22
+ ··· + u +
1
8
1
8
u
24
+
1
2
u
22
+ ··· + u +
1
8
a
4
=
1.39063u
25
+ 0.203125u
24
+ ··· + 4.48438u − 2.07813
0.593750u
25
+ 0.343750u
24
+ ··· − 0.0937500u − 0.593750
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
1
8
u
25
+
1
2
u
23
+ ··· +
1
8
u − 1
1
8
u
25
+
1
2
u
23
+ ··· + 2u
2
+
1
8
u
a
12
=
1
8
u
24
+
1
2
u
22
+ ··· + u +
1
8
1
8
u
24
+
1
2
u
22
+ ··· + u +
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
563
128
u
25
−
159
128
u
24
+ ··· −
1045
128
u −
521
128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 7u
25
+ ··· − 47u + 16
c
2
, c
4
u
26
− 5u
25
+ ··· − 17u + 4
c
3
, c
7
u
26
− 3u
25
+ ··· − 304u + 64
c
5
, c
6
, c
9
c
11
u
26
+ 5u
24
+ ··· + 7u
2
+ 1
c
8
u
26
+ 6u
25
+ ··· + 1024u + 256
c
10
, c
12
u
26
+ 10u
25
+ ··· + 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 29y
25
+ ··· − 4769y + 256
c
2
, c
4
y
26
− 7y
25
+ ··· + 47y + 16
c
3
, c
7
y
26
− 27y
25
+ ··· − 28928y + 4096
c
5
, c
6
, c
9
c
11
y
26
+ 10y
25
+ ··· + 14y + 1
c
8
y
26
+ 10y
25
+ ··· + 1540096y + 65536
c
10
, c
12
y
26
+ 22y
25
+ ··· + 22y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686718 + 0.790237I
a = 0.862776 + 0.752523I
b = −0.112686 − 0.757455I
1.98398 + 2.27305I 3.49441 − 2.95209I
u = 0.686718 − 0.790237I
a = 0.862776 − 0.752523I
b = −0.112686 + 0.757455I
1.98398 − 2.27305I 3.49441 + 2.95209I
u = 0.332646 + 0.885585I
a = 0.859182 + 0.253751I
b = 0.966203 + 0.651765I
0.374508 − 1.260680I 0.03372 − 2.82297I
u = 0.332646 − 0.885585I
a = 0.859182 − 0.253751I
b = 0.966203 − 0.651765I
0.374508 + 1.260680I 0.03372 + 2.82297I
u = −0.943048 + 0.573575I
a = −0.572959 + 1.084400I
b = 1.06906 − 0.99419I
9.87605 + 3.35816I 3.98629 − 0.41980I
u = −0.943048 − 0.573575I
a = −0.572959 − 1.084400I
b = 1.06906 + 0.99419I
9.87605 − 3.35816I 3.98629 + 0.41980I
u = −0.597517 + 0.932496I
a = −0.074973 − 0.361234I
b = −1.085400 + 0.468804I
−1.78026 − 3.46737I −1.87106 + 4.78330I
u = −0.597517 − 0.932496I
a = −0.074973 + 0.361234I
b = −1.085400 − 0.468804I
−1.78026 + 3.46737I −1.87106 − 4.78330I
u = −0.925240 + 0.681323I
a = −0.07111 − 1.54316I
b = 0.94455 + 1.07986I
10.29890 − 4.17338I 4.09194 + 4.29853I
u = −0.925240 − 0.681323I
a = −0.07111 + 1.54316I
b = 0.94455 − 1.07986I
10.29890 + 4.17338I 4.09194 − 4.29853I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615881 + 1.015000I
a = −1.05911 − 1.42400I
b = −1.324650 + 0.202541I
−2.47670 + 6.15727I −1.31624 − 5.25780I
u = 0.615881 − 1.015000I
a = −1.05911 + 1.42400I
b = −1.324650 − 0.202541I
−2.47670 − 6.15727I −1.31624 + 5.25780I
u = 0.213984 + 0.755898I
a = 1.343350 + 0.180099I
b = 0.844053 − 0.643735I
0.79107 + 3.73974I 2.88234 − 8.52096I
u = 0.213984 − 0.755898I
a = 1.343350 − 0.180099I
b = 0.844053 + 0.643735I
0.79107 − 3.73974I 2.88234 + 8.52096I
u = −0.522459 + 1.135990I
a = 1.068060 − 0.495553I
b = 0.679614 + 0.169964I
−3.56752 − 8.00011I 1.95259 + 8.91191I
u = −0.522459 − 1.135990I
a = 1.068060 + 0.495553I
b = 0.679614 − 0.169964I
−3.56752 + 8.00011I 1.95259 − 8.91191I
u = −0.661950 + 1.073520I
a = −0.360539 + 1.342880I
b = −0.585613 − 0.805144I
0.06912 − 8.45528I −0.31615 + 7.82627I
u = −0.661950 − 1.073520I
a = −0.360539 − 1.342880I
b = −0.585613 + 0.805144I
0.06912 + 8.45528I −0.31615 − 7.82627I
u = 0.573105 + 0.355043I
a = 0.431069 − 0.470281I
b = 0.145218 + 0.443676I
1.181070 + 0.652752I 6.65549 − 2.84470I
u = 0.573105 − 0.355043I
a = 0.431069 + 0.470281I
b = 0.145218 − 0.443676I
1.181070 − 0.652752I 6.65549 + 2.84470I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715044 + 1.157990I
a = −0.890942 − 0.102027I
b = 0.750500 + 1.133340I
7.16363 + 8.23028I 1.13390 − 4.65943I
u = 0.715044 − 1.157990I
a = −0.890942 + 0.102027I
b = 0.750500 − 1.133340I
7.16363 − 8.23028I 1.13390 + 4.65943I
u = 0.674140 + 1.197450I
a = 1.10131 + 1.68297I
b = 1.16977 − 0.88449I
5.7894 + 15.5253I −0.62931 − 8.80838I
u = 0.674140 − 1.197450I
a = 1.10131 − 1.68297I
b = 1.16977 + 0.88449I
5.7894 − 15.5253I −0.62931 + 8.80838I
u = −0.161303 + 0.352465I
a = −0.88611 + 2.09278I
b = −0.960623 − 0.194500I
−1.73934 − 0.69423I −4.47291 + 0.47105I
u = −0.161303 − 0.352465I
a = −0.88611 − 2.09278I
b = −0.960623 + 0.194500I
−1.73934 + 0.69423I −4.47291 − 0.47105I
7
II. I
u
2
= h1.64 × 10
19
u
35
− 6.56 × 10
19
u
34
+ · · · + 1.65 × 10
20
b − 8.77 ×
10
20
, −2.73 × 10
20
u
35
+ 9.89 × 10
20
u
34
+ · · · + 2.80 × 10
21
a + 2.34 ×
10
22
, u
36
− 2u
35
+ · · · − 16u + 17i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
0.0975652u
35
− 0.352706u
34
+ ··· + 2.60900u − 8.35431
−0.0994997u
35
+ 0.397778u
34
+ ··· − 0.756708u + 5.31894
a
6
=
1
−u
2
a
2
=
−0.00193454u
35
+ 0.0450723u
34
+ ··· + 1.85229u − 3.03538
−0.0994997u
35
+ 0.397778u
34
+ ··· − 0.756708u + 5.31894
a
1
=
0.167671u
35
− 0.201737u
34
+ ··· + 7.20414u − 0.801787
−0.203086u
35
+ 0.207511u
34
+ ··· − 4.38662u + 1.19177
a
4
=
−0.677695u
35
+ 1.09907u
34
+ ··· − 8.59244u + 5.59975
0.0381892u
35
− 0.396278u
34
+ ··· + 0.00858699u − 5.74660
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
−0.0123763u
35
+ 0.0202099u
34
+ ··· + 1.02313u + 3.72869
0.0511253u
35
− 0.134072u
34
+ ··· + 0.364967u − 2.38667
a
12
=
0.135850u
35
− 0.216397u
34
+ ··· + 6.63547u − 1.67092
−0.158595u
35
+ 0.210763u
34
+ ··· − 1.68145u + 1.66988
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
92294208925977637035
164860561334912795863
u
35
+
248194929627859910457
164860561334912795863
u
34
+ ··· −
1193076869772129210292
164860561334912795863
u +
1468116381237737523006
164860561334912795863
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
+ 4u
17
+ ··· + 11u + 1)
2
c
2
, c
4
(u
18
− 4u
17
+ ··· + 3u − 1)
2
c
3
, c
7
(u
18
+ u
17
+ ··· + 4u + 8)
2
c
5
, c
6
, c
9
c
11
u
36
− 2u
35
+ ··· − 16u + 17
c
8
(u
18
− 2u
17
+ ··· − 18u − 17)
2
c
10
, c
12
u
36
+ 18u
35
+ ··· + 1784u + 289
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 24y
17
+ ··· − 11y + 1)
2
c
2
, c
4
(y
18
− 4y
17
+ ··· − 11y + 1)
2
c
3
, c
7
(y
18
− 21y
17
+ ··· − 592y + 64)
2
c
5
, c
6
, c
9
c
11
y
36
+ 18y
35
+ ··· + 1784y + 289
c
8
(y
18
+ 10y
17
+ ··· − 1106y + 289)
2
c
10
, c
12
y
36
− 2y
35
+ ··· + 426376y + 83521
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591186 + 0.787704I
a = −1.56603 − 0.88745I
b = 0.889957 + 0.956699I
2.38234 − 1.09047I 0.174080 − 0.422577I
u = 0.591186 − 0.787704I
a = −1.56603 + 0.88745I
b = 0.889957 − 0.956699I
2.38234 + 1.09047I 0.174080 + 0.422577I
u = −0.794635 + 0.529818I
a = 0.753156 − 1.018670I
b = −0.405572 + 0.756937I
1.68246 + 2.95811I 2.86830 − 3.60082I
u = −0.794635 − 0.529818I
a = 0.753156 + 1.018670I
b = −0.405572 − 0.756937I
1.68246 − 2.95811I 2.86830 + 3.60082I
u = −0.575111 + 0.759119I
a = −0.73772 + 1.69762I
b = −1.189210 − 0.282581I
−1.21564 − 1.22055I 0.481280 − 0.071123I
u = −0.575111 − 0.759119I
a = −0.73772 − 1.69762I
b = −1.189210 + 0.282581I
−1.21564 + 1.22055I 0.481280 + 0.071123I
u = 0.167080 + 1.041030I
a = −2.61040 − 3.09914I
b = −1.10588
−5.41960 2.98163 + 0.I
u = 0.167080 − 1.041030I
a = −2.61040 + 3.09914I
b = −1.10588
−5.41960 2.98163 + 0.I
u = 0.997738 + 0.395002I
a = −0.292945 − 1.197000I
b = 1.13145 + 0.93287I
8.25713 − 9.46502I 2.19641 + 5.12935I
u = 0.997738 − 0.395002I
a = −0.292945 + 1.197000I
b = 1.13145 − 0.93287I
8.25713 + 9.46502I 2.19641 − 5.12935I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.274534 + 0.872882I
a = 0.93452 + 2.44113I
b = −0.509257 − 0.343539I
−3.86556 − 1.11682I −2.38496 + 6.15764I
u = −0.274534 − 0.872882I
a = 0.93452 − 2.44113I
b = −0.509257 + 0.343539I
−3.86556 + 1.11682I −2.38496 − 6.15764I
u = 0.588697 + 0.917985I
a = 0.52281 + 2.44549I
b = 1.023450 − 0.903197I
1.96168 + 5.76942I −0.89628 − 5.17142I
u = 0.588697 − 0.917985I
a = 0.52281 − 2.44549I
b = 1.023450 + 0.903197I
1.96168 − 5.76942I −0.89628 + 5.17142I
u = 0.985654 + 0.488151I
a = −0.268666 + 1.306090I
b = 0.841043 − 1.112380I
9.21890 − 2.04734I 3.38974 + 0.64724I
u = 0.985654 − 0.488151I
a = −0.268666 − 1.306090I
b = 0.841043 + 1.112380I
9.21890 + 2.04734I 3.38974 − 0.64724I
u = 0.670337 + 0.891635I
a = −0.058974 − 1.277660I
b = −0.405572 + 0.756937I
1.68246 + 2.95811I 2.86830 − 3.60082I
u = 0.670337 − 0.891635I
a = −0.058974 + 1.277660I
b = −0.405572 − 0.756937I
1.68246 − 2.95811I 2.86830 + 3.60082I
u = 0.626901 + 0.585336I
a = −0.339138 + 0.406991I
b = −1.189210 − 0.282581I
−1.21564 − 1.22055I 0.481280 − 0.071123I
u = 0.626901 − 0.585336I
a = −0.339138 − 0.406991I
b = −1.189210 + 0.282581I
−1.21564 + 1.22055I 0.481280 + 0.071123I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453358 + 1.062450I
a = 1.049730 + 0.489075I
b = 0.550076 − 0.259421I
−0.92819 + 3.34376I 3.77359 − 4.65236I
u = 0.453358 − 1.062450I
a = 1.049730 − 0.489075I
b = 0.550076 + 0.259421I
−0.92819 − 3.34376I 3.77359 + 4.65236I
u = −0.106316 + 1.174290I
a = 0.436208 − 0.085284I
b = −0.509257 + 0.343539I
−3.86556 + 1.11682I −2.38496 − 6.15764I
u = −0.106316 − 1.174290I
a = 0.436208 + 0.085284I
b = −0.509257 − 0.343539I
−3.86556 − 1.11682I −2.38496 + 6.15764I
u = −0.331026 + 1.152710I
a = 0.999190 − 0.535049I
b = 0.441998
−4.89262 −6 − 1.185937 + 0.10I
u = −0.331026 − 1.152710I
a = 0.999190 + 0.535049I
b = 0.441998
−4.89262 −6 − 1.185937 + 0.10I
u = −0.715398 + 0.207958I
a = 0.433150 − 0.002861I
b = 0.550076 − 0.259421I
−0.92819 + 3.34376I 3.77359 − 4.65236I
u = −0.715398 − 0.207958I
a = 0.433150 + 0.002861I
b = 0.550076 + 0.259421I
−0.92819 − 3.34376I 3.77359 + 4.65236I
u = −0.775491 + 1.032570I
a = −0.952803 + 0.345976I
b = 0.841043 − 1.112380I
9.21890 − 2.04734I 3.38974 + 0.64724I
u = −0.775491 − 1.032570I
a = −0.952803 − 0.345976I
b = 0.841043 + 1.112380I
9.21890 + 2.04734I 3.38974 − 0.64724I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726810 + 1.099240I
a = 0.83534 − 1.78440I
b = 1.13145 + 0.93287I
8.25713 − 9.46502I 2.19641 + 5.12935I
u = −0.726810 − 1.099240I
a = 0.83534 + 1.78440I
b = 1.13145 − 0.93287I
8.25713 + 9.46502I 2.19641 − 5.12935I
u = 0.066926 + 1.357280I
a = 0.785883 + 0.110703I
b = 0.889957 − 0.956699I
2.38234 + 1.09047I 0.174080 + 0.422577I
u = 0.066926 − 1.357280I
a = 0.785883 − 0.110703I
b = 0.889957 + 0.956699I
2.38234 − 1.09047I 0.174080 − 0.422577I
u = 0.151444 + 1.368190I
a = 0.753153 − 0.013270I
b = 1.023450 + 0.903197I
1.96168 − 5.76942I −0.89628 + 5.17142I
u = 0.151444 − 1.368190I
a = 0.753153 + 0.013270I
b = 1.023450 − 0.903197I
1.96168 + 5.76942I −0.89628 − 5.17142I
14
III. I
u
3
= hb + 1, −u
3
+ u
2
+ 2a + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1
2
u
3
−
1
2
u
2
−
1
2
−1
a
6
=
1
−u
2
a
2
=
1
2
u
3
−
1
2
u
2
−
3
2
−1
a
1
=
−1
0
a
4
=
1
2
u
3
−
1
2
u
2
−
1
2
−1
a
9
=
−u
u
3
+ u
a
11
=
−u
3
−u
2
a
8
=
u
3
u
3
+ u
a
7
=
u
3
u
3
+ u
a
12
=
−u
3
− u
2
− u − 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
21
4
u
3
−
11
4
u
2
+
1
2
u −
1
4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
2
+ u + 1
c
8
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
9
, c
11
u
4
+ u
2
− u + 1
c
10
, c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −0.278726 + 0.483420I
b = −1.00000
−0.66484 − 1.39709I 1.69137 + 3.76574I
u = −0.547424 − 0.585652I
a = −0.278726 − 0.483420I
b = −1.00000
−0.66484 + 1.39709I 1.69137 − 3.76574I
u = 0.547424 + 1.120870I
a = −0.971274 − 0.813859I
b = −1.00000
−4.26996 + 7.64338I −7.31637 − 4.91712I
u = 0.547424 − 1.120870I
a = −0.971274 + 0.813859I
b = −1.00000
−4.26996 − 7.64338I −7.31637 + 4.91712I
18
IV.
I
u
4
= hb + 1, u
5
− u
4
+ u
3
− u
2
+ a + u, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−u
5
+ u
4
− u
3
+ u
2
− u
−1
a
6
=
1
−u
2
a
2
=
−u
5
+ u
4
− u
3
+ u
2
− u − 1
−1
a
1
=
−1
0
a
4
=
−u
5
+ u
4
− u
3
+ u
2
− u
−1
a
9
=
−u
u
3
+ u
a
11
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
3
u
3
+ u
a
7
=
u
3
u
3
+ u
a
12
=
−u
4
− u
2
+ u − 1
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
5
+ 3u
3
+ u
2
+ 3u − 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
(u
3
+ u
2
− 1)
2
c
9
, c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
10
, c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
y
6
c
5
, c
6
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
(y
3
− y
2
+ 2y − 1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.767394 + 0.943705I
b = −1.00000
−1.91067 − 2.82812I −2.82789 + 2.41717I
u = −0.498832 − 1.001300I
a = −0.767394 − 0.943705I
b = −1.00000
−1.91067 + 2.82812I −2.82789 − 2.41717I
u = 0.284920 + 1.115140I
a = −1.37744 − 1.47725I
b = −1.00000
−6.04826 −11.34423 + 0.I
u = 0.284920 − 1.115140I
a = −1.37744 + 1.47725I
b = −1.00000
−6.04826 −11.34423 + 0.I
u = 0.713912 + 0.305839I
a = −0.355167 − 0.198843I
b = −1.00000
−1.91067 − 2.82812I −2.82789 + 2.41717I
u = 0.713912 − 0.305839I
a = −0.355167 + 0.198843I
b = −1.00000
−1.91067 + 2.82812I −2.82789 − 2.41717I
22
V.
I
u
5
= h−a
2
+ 2au + b + 2a − 2u − 1, a
3
− 3a
2
u − 3a
2
+ 6au + a − 2u + 1, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
a
a
2
− 2au − 2a + 2u + 1
a
6
=
1
1
a
2
=
a
2
− 2au − a + 2u + 1
a
2
− 2au − 2a + 2u + 1
a
1
=
au + 2
au − u + 2
a
4
=
−a
2
u − 2a
2
+ 7au + 2a − 5u + 2
−a
2
+ 3au + 2a − 3u
a
9
=
−u
0
a
11
=
u
u
a
8
=
−u
0
a
7
=
−a + 2u
−a + 2u + 1
a
12
=
au + u + 2
au + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
− 8au − 8a + 8u − 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
7
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
11
(u
2
+ 1)
3
c
8
u
6
c
10
, c
12
(u + 1)
6
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
3
, c
7
(y
3
− 3y
2
+ 2y + 1)
2
c
5
, c
6
, c
9
c
11
(y + 1)
6
c
8
y
6
c
10
, c
12
(y − 1)
6
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.437720 + 0.337641I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 1.000000I
a = 1.56228 + 0.33764I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 1.000000I
a = 1.00000 + 2.32472I
b = −0.754878
−4.40332 −11.01951 + 0.I
u = − 1.000000I
a = 0.437720 − 0.337641I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = − 1.000000I
a = 1.56228 − 0.33764I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = − 1.000000I
a = 1.00000 − 2.32472I
b = −0.754878
−4.40332 −11.01951 + 0.I
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
18
+ 4u
17
+ ··· + 11u + 1)
2
· (u
26
+ 7u
25
+ ··· − 47u + 16)
c
2
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
18
− 4u
17
+ ··· + 3u − 1)
2
· (u
26
− 5u
25
+ ··· − 17u + 4)
c
3
, c
7
u
10
(u
6
− 3u
4
+ 2u
2
+ 1)(u
18
+ u
17
+ ··· + 4u + 8)
2
· (u
26
− 3u
25
+ ··· − 304u + 64)
c
4
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
18
− 4u
17
+ ··· + 3u − 1)
2
· (u
26
− 5u
25
+ ··· − 17u + 4)
c
5
, c
6
(u
2
+ 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
26
+ 5u
24
+ ··· + 7u
2
+ 1)(u
36
− 2u
35
+ ··· − 16u + 17)
c
8
u
6
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· ((u
18
− 2u
17
+ ··· − 18u − 17)
2
)(u
26
+ 6u
25
+ ··· + 1024u + 256)
c
9
, c
11
(u
2
+ 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
26
+ 5u
24
+ ··· + 7u
2
+ 1)(u
36
− 2u
35
+ ··· − 16u + 17)
c
10
, c
12
(u + 1)
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
26
+ 10u
25
+ ··· + 14u + 1)(u
36
+ 18u
35
+ ··· + 1784u + 289)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
18
+ 24y
17
+ ··· − 11y + 1)
2
· (y
26
+ 29y
25
+ ··· − 4769y + 256)
c
2
, c
4
((y − 1)
10
)(y
3
− y
2
+ 2y − 1)
2
(y
18
− 4y
17
+ ··· − 11y + 1)
2
· (y
26
− 7y
25
+ ··· + 47y + 16)
c
3
, c
7
y
10
(y
3
− 3y
2
+ 2y + 1)
2
(y
18
− 21y
17
+ ··· − 592y + 64)
2
· (y
26
− 27y
25
+ ··· − 28928y + 4096)
c
5
, c
6
, c
9
c
11
(y + 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
26
+ 10y
25
+ ··· + 14y + 1)(y
36
+ 18y
35
+ ··· + 1784y + 289)
c
8
y
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
18
+ 10y
17
+ ··· − 1106y + 289)
2
· (y
26
+ 10y
25
+ ··· + 1540096y + 65536)
c
10
, c
12
(y − 1)
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
26
+ 22y
25
+ ··· + 22y + 1)(y
36
− 2y
35
+ ··· + 426376y + 83521)
28
