12a
0332
(K12a
0332
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 9 2 4 7 1 12 5 10
Solving Sequence
5,12
11
4,8
3 7 10 1 9 6 2
c
11
c
4
c
3
c
7
c
10
c
12
c
9
c
5
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
36
+ 2u
35
+ ··· + b + 1, u
36
− 3u
35
+ ··· + 2a − 3, u
37
− 3u
36
+ ··· + u + 2i
I
u
2
= h−u
26
a − 2u
27
+ ··· − a + 2, 2u
27
a + 2u
26
a + ··· + a
2
+ 1, u
28
+ u
27
+ ··· − u
2
+ 1i
I
u
3
= hu
7
− u
6
− u
5
+ 3u
3
+ b − u, −u
7
+ 2u
6
+ u
5
− 2u
4
− 3u
3
+ 4u
2
+ a + 2u − 2, u
8
− u
6
+ 3u
4
− 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 101 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
= h−u
36
+2u
35
+· · ·+b+1, u
36
−3u
35
+· · ·+2a−3, u
37
−3u
36
+· · ·+u+2i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
8
=
−
1
2
u
36
+
3
2
u
35
+ ··· + u +
3
2
u
36
− 2u
35
+ ··· − u − 1
a
3
=
−
5
2
u
36
+
5
2
u
35
+ ··· − 5u −
1
2
−2u
36
+ 9u
35
+ ··· + 13u + 9
a
7
=
1
2
u
36
−
3
2
u
35
+ ··· − u −
1
2
−2u
36
+ 3u
35
+ ··· − u + 1
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
6
=
−u
13
+ 2u
11
− 5u
9
+ 6u
7
− 6u
5
+ 4u
3
− u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
a
2
=
3
2
u
36
−
3
2
u
35
+ ··· + 3u +
3
2
u
36
− 5u
35
+ ··· − 7u − 5
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
36
+ 12u
35
−2u
34
−54u
33
+ 30u
32
+ 204u
31
−162u
30
−520u
29
+ 510u
28
+ 1120u
27
−
1224u
26
− 1954u
25
+ 2294u
24
+ 2956u
23
− 3538u
22
− 3846u
21
+ 4422u
20
+ 4450u
19
−
4544u
18
− 4538u
17
+ 3660u
16
+ 4144u
15
− 2156u
14
− 3248u
13
+ 644u
12
+ 2146u
11
+
292u
10
− 1052u
9
− 570u
8
+ 292u
7
+ 378u
6
+ 46u
5
− 134u
4
− 70u
3
+ 4u
2
+ 26u + 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
37
+ 16u
36
+ ··· − 5u − 1
c
2
, c
3
, c
6
c
7
u
37
+ 8u
35
+ ··· + 3u − 1
c
4
, c
11
u
37
+ 3u
36
+ ··· + u − 2
c
5
u
37
− 21u
36
+ ··· + 11969u − 898
c
9
, c
10
, c
12
u
37
− 9u
36
+ ··· + 9u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
37
+ 20y
36
+ ··· + 83y −1
c
2
, c
3
, c
6
c
7
y
37
+ 16y
36
+ ··· − 5y −1
c
4
, c
11
y
37
− 9y
36
+ ··· + 9y −4
c
5
y
37
− 9y
36
+ ··· + 9968617y −806404
c
9
, c
10
, c
12
y
37
+ 39y
36
+ ··· + 257y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956735 + 0.301871I
a = 0.107211 + 0.253891I
b = −0.426927 − 0.834723I
4.07996 − 1.69437I 12.28632 + 1.79481I
u = −0.956735 − 0.301871I
a = 0.107211 − 0.253891I
b = −0.426927 + 0.834723I
4.07996 + 1.69437I 12.28632 − 1.79481I
u = 0.958389 + 0.235458I
a = −0.753757 + 0.244529I
b = 0.864634 + 0.110338I
4.44965 + 3.84432I 12.5649 − 6.9040I
u = 0.958389 − 0.235458I
a = −0.753757 − 0.244529I
b = 0.864634 − 0.110338I
4.44965 − 3.84432I 12.5649 + 6.9040I
u = 0.974044 + 0.110846I
a = 0.438179 + 0.800925I
b = −0.697177 + 1.212880I
1.78420 − 6.55614I 9.22168 + 4.71128I
u = 0.974044 − 0.110846I
a = 0.438179 − 0.800925I
b = −0.697177 − 1.212880I
1.78420 + 6.55614I 9.22168 − 4.71128I
u = −0.869494 + 0.549252I
a = 1.04527 + 1.02873I
b = 0.332238 − 0.481286I
−2.07404 + 1.88888I 3.74513 − 1.47237I
u = −0.869494 − 0.549252I
a = 1.04527 − 1.02873I
b = 0.332238 + 0.481286I
−2.07404 − 1.88888I 3.74513 + 1.47237I
u = −0.985335 + 0.388773I
a = −1.78941 − 1.15884I
b = 0.368742 + 0.784022I
0.19576 − 12.29670I 5.96416 + 10.82953I
u = −0.985335 − 0.388773I
a = −1.78941 + 1.15884I
b = 0.368742 − 0.784022I
0.19576 + 12.29670I 5.96416 − 10.82953I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806001 + 0.770895I
a = 0.69552 + 1.27487I
b = 0.833243 − 1.116330I
−1.90734 + 2.28917I 4.88020 − 3.21889I
u = −0.806001 − 0.770895I
a = 0.69552 − 1.27487I
b = 0.833243 + 1.116330I
−1.90734 − 2.28917I 4.88020 + 3.21889I
u = 0.695248 + 0.472483I
a = 0.444025 − 1.024300I
b = −0.122253 + 0.573991I
−1.19445 + 1.82713I 4.12966 − 6.04101I
u = 0.695248 − 0.472483I
a = 0.444025 + 1.024300I
b = −0.122253 − 0.573991I
−1.19445 − 1.82713I 4.12966 + 6.04101I
u = 0.826193 + 0.842773I
a = −0.567500 − 0.335315I
b = 0.360895 − 0.189373I
−3.16743 + 0.36820I 6.31788 − 2.12826I
u = 0.826193 − 0.842773I
a = −0.567500 + 0.335315I
b = 0.360895 + 0.189373I
−3.16743 − 0.36820I 6.31788 + 2.12826I
u = −0.492238 + 0.655396I
a = 0.068505 + 1.209380I
b = −0.723783 − 1.213940I
−3.23955 − 6.28444I 0.23042 + 7.24447I
u = −0.492238 − 0.655396I
a = 0.068505 − 1.209380I
b = −0.723783 + 1.213940I
−3.23955 + 6.28444I 0.23042 − 7.24447I
u = −0.942981 + 0.761048I
a = 1.151510 + 0.744837I
b = −0.60571 − 2.01178I
−1.50596 − 8.08923I 6.07656 + 8.51523I
u = −0.942981 − 0.761048I
a = 1.151510 − 0.744837I
b = −0.60571 + 2.01178I
−1.50596 + 8.08923I 6.07656 − 8.51523I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827155 + 0.889743I
a = 1.41124 − 2.73920I
b = 2.08237 + 4.08970I
−8.12556 − 10.18450I 0.37161 + 5.66795I
u = 0.827155 − 0.889743I
a = 1.41124 + 2.73920I
b = 2.08237 − 4.08970I
−8.12556 + 10.18450I 0.37161 − 5.66795I
u = 0.960937 + 0.799626I
a = 0.367828 + 0.480609I
b = −0.706212 − 0.437969I
−2.75006 + 5.76064I 7.04693 − 2.89668I
u = 0.960937 − 0.799626I
a = 0.367828 − 0.480609I
b = −0.706212 + 0.437969I
−2.75006 − 5.76064I 7.04693 + 2.89668I
u = 0.888234 + 0.886878I
a = −1.24637 + 2.29159I
b = −1.53871 − 3.88705I
−10.85650 + 5.89802I −1.00813 − 7.72734I
u = 0.888234 − 0.886878I
a = −1.24637 − 2.29159I
b = −1.53871 + 3.88705I
−10.85650 − 5.89802I −1.00813 + 7.72734I
u = −0.916359 + 0.865710I
a = −1.40408 − 1.51780I
b = −0.73441 + 3.20038I
−8.85573 − 3.20735I 5.22275 + 2.78415I
u = −0.916359 − 0.865710I
a = −1.40408 + 1.51780I
b = −0.73441 − 3.20038I
−8.85573 + 3.20735I 5.22275 − 2.78415I
u = 0.947451 + 0.860827I
a = −2.19419 + 1.40646I
b = −0.12980 − 3.94938I
−10.66820 + 0.56453I −0.58196 + 3.04417I
u = 0.947451 − 0.860827I
a = −2.19419 − 1.40646I
b = −0.12980 + 3.94938I
−10.66820 − 0.56453I −0.58196 − 3.04417I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983458 + 0.824484I
a = 2.65593 − 1.57243I
b = −0.29611 + 5.01537I
−7.6317 + 16.5331I 1.29247 − 10.38801I
u = 0.983458 − 0.824484I
a = 2.65593 + 1.57243I
b = −0.29611 − 5.01537I
−7.6317 − 16.5331I 1.29247 + 10.38801I
u = −0.240182 + 0.666603I
a = −0.12252 − 1.87056I
b = 0.79192 + 1.32245I
−2.16954 + 8.48653I 0.54078 − 6.28516I
u = −0.240182 − 0.666603I
a = −0.12252 + 1.87056I
b = 0.79192 − 1.32245I
−2.16954 − 8.48653I 0.54078 + 6.28516I
u = −0.595207
a = 0.354844
b = 0.343586
0.761151 13.8790
u = −0.054179 + 0.561331I
a = 0.765177 + 0.865041I
b = 0.175261 − 0.166101I
1.44057 − 1.28380I 5.75923 + 3.39663I
u = −0.054179 − 0.561331I
a = 0.765177 − 0.865041I
b = 0.175261 + 0.166101I
1.44057 + 1.28380I 5.75923 − 3.39663I
8
II. I
u
2
=
h−u
26
a−2u
27
+· · ·−a+2, 2u
27
a+2u
26
a+· · ·+a
2
+1, u
28
+u
27
+· · ·−u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
8
=
a
u
26
a + 2u
27
+ ··· + a − 2
a
3
=
−2u
27
− 3u
26
+ ··· − 2a + 1
2u
25
a + 2u
24
a + ··· + 2au − 1
a
7
=
−2u
27
a − 4u
26
a + ··· + 2a + 2u
2u
27
a + 4u
27
+ ··· + 2a − 4
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
6
=
−u
13
+ 2u
11
− 5u
9
+ 6u
7
− 6u
5
+ 4u
3
− u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
a
2
=
−2u
27
− 2u
26
+ ··· − 2a + 2
−2u
27
a − 4u
26
a + ··· + 2a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
26
− 4u
25
+ 12u
24
+ 16u
23
− 44u
22
− 52u
21
+ 88u
20
+
116u
19
− 168u
18
− 204u
17
+ 236u
16
+ 284u
15
− 288u
14
− 312u
13
+ 280u
12
+ 256u
11
−
224u
10
− 152u
9
+ 136u
8
+ 40u
7
− 64u
6
+ 16u
5
+ 16u
4
− 16u
3
+ 4u + 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
56
+ 31u
55
+ ··· + 27u + 4
c
2
, c
3
, c
6
c
7
u
56
− u
55
+ ··· + u + 2
c
4
, c
11
(u
28
− u
27
+ ··· − u
2
+ 1)
2
c
5
(u
28
+ 7u
27
+ ··· + 8u + 1)
2
c
9
, c
10
, c
12
(u
28
− 7u
27
+ ··· − 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
56
− 13y
55
+ ··· + 927y + 16
c
2
, c
3
, c
6
c
7
y
56
+ 31y
55
+ ··· + 27y + 4
c
4
, c
11
(y
28
− 7y
27
+ ··· − 2y + 1)
2
c
5
(y
28
+ y
27
+ ··· + 62y + 1)
2
c
9
, c
10
, c
12
(y
28
+ 29y
27
+ ··· + 14y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.899770 + 0.359295I
a = 1.02424 + 1.44935I
b = 0.317596 + 0.143962I
−2.76021 − 3.76187I 4.54869 + 7.99757I
u = −0.899770 + 0.359295I
a = −2.28758 − 0.15491I
b = 1.40296 + 0.75227I
−2.76021 − 3.76187I 4.54869 + 7.99757I
u = −0.899770 − 0.359295I
a = 1.02424 − 1.44935I
b = 0.317596 − 0.143962I
−2.76021 + 3.76187I 4.54869 − 7.99757I
u = −0.899770 − 0.359295I
a = −2.28758 + 0.15491I
b = 1.40296 − 0.75227I
−2.76021 + 3.76187I 4.54869 − 7.99757I
u = −0.954301 + 0.165131I
a = 0.453330 − 0.469903I
b = −0.670608 − 1.151640I
3.64668 + 1.29573I 12.16340 + 0.19021I
u = −0.954301 + 0.165131I
a = −0.381153 − 0.148423I
b = 0.877426 − 0.189403I
3.64668 + 1.29573I 12.16340 + 0.19021I
u = −0.954301 − 0.165131I
a = 0.453330 + 0.469903I
b = −0.670608 + 1.151640I
3.64668 − 1.29573I 12.16340 − 0.19021I
u = −0.954301 − 0.165131I
a = −0.381153 + 0.148423I
b = 0.877426 + 0.189403I
3.64668 − 1.29573I 12.16340 − 0.19021I
u = 0.971170 + 0.356128I
a = −0.056263 − 0.455331I
b = −0.331645 + 0.653502I
2.55576 + 6.87695I 9.38448 − 7.29150I
u = 0.971170 + 0.356128I
a = −1.66109 + 0.82974I
b = 0.635990 − 0.561304I
2.55576 + 6.87695I 9.38448 − 7.29150I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971170 − 0.356128I
a = −0.056263 + 0.455331I
b = −0.331645 − 0.653502I
2.55576 − 6.87695I 9.38448 + 7.29150I
u = 0.971170 − 0.356128I
a = −1.66109 − 0.82974I
b = 0.635990 + 0.561304I
2.55576 − 6.87695I 9.38448 + 7.29150I
u = 0.816311 + 0.219669I
a = 1.44748 − 0.37350I
b = −0.48686 + 1.64839I
−1.87609 + 0.68499I 8.66956 − 0.56233I
u = 0.816311 + 0.219669I
a = 0.89236 − 1.56400I
b = −0.222133 − 0.418971I
−1.87609 + 0.68499I 8.66956 − 0.56233I
u = 0.816311 − 0.219669I
a = 1.44748 + 0.37350I
b = −0.48686 − 1.64839I
−1.87609 − 0.68499I 8.66956 + 0.56233I
u = 0.816311 − 0.219669I
a = 0.89236 + 1.56400I
b = −0.222133 + 0.418971I
−1.87609 − 0.68499I 8.66956 + 0.56233I
u = 0.894569 + 0.739690I
a = 0.546052 − 0.607895I
b = −0.438838 + 1.131330I
−1.35470 + 2.81005I 6.61718 − 2.93426I
u = 0.894569 + 0.739690I
a = 0.522067 − 0.615995I
b = 0.467816 + 0.278002I
−1.35470 + 2.81005I 6.61718 − 2.93426I
u = 0.894569 − 0.739690I
a = 0.546052 + 0.607895I
b = −0.438838 − 1.131330I
−1.35470 − 2.81005I 6.61718 + 2.93426I
u = 0.894569 − 0.739690I
a = 0.522067 + 0.615995I
b = 0.467816 − 0.278002I
−1.35470 − 2.81005I 6.61718 + 2.93426I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594944 + 0.540484I
a = 0.796189 − 0.763146I
b = −0.123628 + 0.489316I
−1.33499 + 1.97473I 3.44037 − 3.90307I
u = 0.594944 + 0.540484I
a = 0.187055 − 1.218540I
b = −0.446420 + 0.779097I
−1.33499 + 1.97473I 3.44037 − 3.90307I
u = 0.594944 − 0.540484I
a = 0.796189 + 0.763146I
b = −0.123628 − 0.489316I
−1.33499 − 1.97473I 3.44037 + 3.90307I
u = 0.594944 − 0.540484I
a = 0.187055 + 1.218540I
b = −0.446420 − 0.779097I
−1.33499 − 1.97473I 3.44037 + 3.90307I
u = −0.824272 + 0.873080I
a = −0.868359 + 0.410750I
b = 0.860810 + 0.419716I
−5.36393 + 4.77850I 3.36601 − 2.38985I
u = −0.824272 + 0.873080I
a = 1.10511 + 2.56923I
b = 2.16209 − 3.37931I
−5.36393 + 4.77850I 3.36601 − 2.38985I
u = −0.824272 − 0.873080I
a = −0.868359 − 0.410750I
b = 0.860810 − 0.419716I
−5.36393 − 4.77850I 3.36601 + 2.38985I
u = −0.824272 − 0.873080I
a = 1.10511 − 2.56923I
b = 2.16209 + 3.37931I
−5.36393 − 4.77850I 3.36601 + 2.38985I
u = 0.848977 + 0.862822I
a = −1.61944 + 2.47231I
b = −1.04855 − 4.31824I
−10.42220 − 0.98573I −1.20004 + 1.21736I
u = 0.848977 + 0.862822I
a = 0.52453 − 2.98229I
b = 3.47400 + 2.91986I
−10.42220 − 0.98573I −1.20004 + 1.21736I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848977 − 0.862822I
a = −1.61944 − 2.47231I
b = −1.04855 + 4.31824I
−10.42220 + 0.98573I −1.20004 − 1.21736I
u = 0.848977 − 0.862822I
a = 0.52453 + 2.98229I
b = 3.47400 − 2.91986I
−10.42220 + 0.98573I −1.20004 − 1.21736I
u = −0.883885 + 0.841772I
a = −0.579421 − 0.504600I
b = −0.614694 + 1.257450I
−8.24265 − 2.93440I 1.90343 + 3.53352I
u = −0.883885 + 0.841772I
a = −1.73296 − 2.18260I
b = −0.90166 + 3.97609I
−8.24265 − 2.93440I 1.90343 + 3.53352I
u = −0.883885 − 0.841772I
a = −0.579421 + 0.504600I
b = −0.614694 − 1.257450I
−8.24265 + 2.93440I 1.90343 − 3.53352I
u = −0.883885 − 0.841772I
a = −1.73296 + 2.18260I
b = −0.90166 − 3.97609I
−8.24265 + 2.93440I 1.90343 − 3.53352I
u = −0.921489 + 0.824235I
a = −0.547487 − 0.474537I
b = −0.21718 + 1.66408I
−8.12146 − 3.27187I 2.26749 + 1.59380I
u = −0.921489 + 0.824235I
a = −2.04938 − 1.94889I
b = −0.66887 + 3.95674I
−8.12146 − 3.27187I 2.26749 + 1.59380I
u = −0.921489 − 0.824235I
a = −0.547487 + 0.474537I
b = −0.21718 − 1.66408I
−8.12146 + 3.27187I 2.26749 − 1.59380I
u = −0.921489 − 0.824235I
a = −2.04938 + 1.94889I
b = −0.66887 − 3.95674I
−8.12146 + 3.27187I 2.26749 − 1.59380I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956709 + 0.821698I
a = 2.87664 − 0.62418I
b = −2.04478 + 4.61109I
−10.08390 + 7.24627I −0.35343 − 6.30493I
u = 0.956709 + 0.821698I
a = −2.34992 + 1.84192I
b = −0.59666 − 4.17927I
−10.08390 + 7.24627I −0.35343 − 6.30493I
u = 0.956709 − 0.821698I
a = 2.87664 + 0.62418I
b = −2.04478 − 4.61109I
−10.08390 − 7.24627I −0.35343 + 6.30493I
u = 0.956709 − 0.821698I
a = −2.34992 − 1.84192I
b = −0.59666 + 4.17927I
−10.08390 − 7.24627I −0.35343 + 6.30493I
u = −0.975960 + 0.814541I
a = 0.461489 − 0.788364I
b = −1.176520 + 0.452581I
−4.88826 − 11.04430I 4.28365 + 7.20583I
u = −0.975960 + 0.814541I
a = 2.47158 + 1.26067I
b = −0.68026 − 4.45661I
−4.88826 − 11.04430I 4.28365 + 7.20583I
u = −0.975960 − 0.814541I
a = 0.461489 + 0.788364I
b = −1.176520 − 0.452581I
−4.88826 + 11.04430I 4.28365 − 7.20583I
u = −0.975960 − 0.814541I
a = 2.47158 − 1.26067I
b = −0.68026 + 4.45661I
−4.88826 + 11.04430I 4.28365 − 7.20583I
u = 0.190095 + 0.611771I
a = 0.740553 − 0.573961I
b = 0.0110804 − 0.0583490I
0.14328 − 3.38176I 3.65042 + 2.75424I
u = 0.190095 + 0.611771I
a = 0.25617 + 1.77312I
b = 0.491611 − 1.016080I
0.14328 − 3.38176I 3.65042 + 2.75424I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.190095 − 0.611771I
a = 0.740553 + 0.573961I
b = 0.0110804 + 0.0583490I
0.14328 + 3.38176I 3.65042 − 2.75424I
u = 0.190095 − 0.611771I
a = 0.25617 − 1.77312I
b = 0.491611 + 1.016080I
0.14328 + 3.38176I 3.65042 − 2.75424I
u = −0.313097 + 0.488114I
a = −0.290579 + 1.243310I
b = −1.211500 − 0.586102I
−4.53523 + 0.50746I −2.74123 − 1.23953I
u = −0.313097 + 0.488114I
a = 0.61878 − 2.72822I
b = −0.32060 + 1.46145I
−4.53523 + 0.50746I −2.74123 − 1.23953I
u = −0.313097 − 0.488114I
a = −0.290579 − 1.243310I
b = −1.211500 + 0.586102I
−4.53523 − 0.50746I −2.74123 + 1.23953I
u = −0.313097 − 0.488114I
a = 0.61878 + 2.72822I
b = −0.32060 − 1.46145I
−4.53523 − 0.50746I −2.74123 + 1.23953I
17
III.
I
u
3
= hu
7
−u
6
−u
5
+3u
3
+b−u, −u
7
+2u
6
+· · ·+a−2, u
8
−u
6
+3u
4
−2u
2
+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
8
=
u
7
− 2u
6
− u
5
+ 2u
4
+ 3u
3
− 4u
2
− 2u + 2
−u
7
+ u
6
+ u
5
− 3u
3
+ u
a
3
=
−u
6
− 2u
2
+ u
−u
7
+ u
5
+ u
4
− 2u
3
+ u + 1
a
7
=
u
7
− u
6
− u
5
+ u
4
+ 3u
3
− 2u
2
− 2u + 1
−u
7
+ u
5
− 3u
3
− u
2
+ u
a
10
=
−u
2
+ 1
u
2
a
1
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
6
=
u
3
u
5
− u
3
+ u
a
2
=
−u
6
+ u
4
− 3u
2
+ u + 1
−u
7
+ u
5
− 2u
3
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
6
+ 4u
4
− 12u
2
+ 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
c
2
, c
3
, c
6
c
7
(u
2
+ 1)
4
c
4
, c
11
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
c
5
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
8
(u + 1)
8
c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y −1)
8
c
2
, c
3
, c
6
c
7
(y + 1)
8
c
4
, c
11
(y
4
− y
3
+ 3y
2
− 2y + 1)
2
c
5
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
9
, c
10
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.720342 + 0.351808I
a = −0.417258 − 0.893260I
b = 0.157709 − 0.792046I
−3.07886 + 1.41510I −0.17326 − 4.90874I
u = 0.720342 − 0.351808I
a = −0.417258 + 0.893260I
b = 0.157709 + 0.792046I
−3.07886 − 1.41510I −0.17326 + 4.90874I
u = −0.720342 + 0.351808I
a = 1.82449 + 1.98811I
b = −0.643355 − 1.006420I
−3.07886 − 1.41510I −0.17326 + 4.90874I
u = −0.720342 − 0.351808I
a = 1.82449 − 1.98811I
b = −0.643355 + 1.006420I
−3.07886 + 1.41510I −0.17326 − 4.90874I
u = 0.911292 + 0.851808I
a = −2.28927 + 2.37001I
b = −1.08282 − 5.08987I
−10.08060 + 3.16396I −3.82674 − 2.56480I
u = 0.911292 − 0.851808I
a = −2.28927 − 2.37001I
b = −1.08282 + 5.08987I
−10.08060 − 3.16396I −3.82674 + 2.56480I
u = −0.911292 + 0.851808I
a = −1.11796 − 1.27516I
b = −0.43154 + 2.29140I
−10.08060 − 3.16396I −3.82674 + 2.56480I
u = −0.911292 − 0.851808I
a = −1.11796 + 1.27516I
b = −0.43154 − 2.29140I
−10.08060 + 3.16396I −3.82674 − 2.56480I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
37
+ 16u
36
+ ··· − 5u − 1)(u
56
+ 31u
55
+ ··· + 27u + 4)
c
2
, c
3
, c
6
c
7
((u
2
+ 1)
4
)(u
37
+ 8u
35
+ ··· + 3u − 1)(u
56
− u
55
+ ··· + u + 2)
c
4
, c
11
(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)(u
28
− u
27
+ ··· − u
2
+ 1)
2
· (u
37
+ 3u
36
+ ··· + u − 2)
c
5
(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
28
+ 7u
27
+ ··· + 8u + 1)
2
· (u
37
− 21u
36
+ ··· + 11969u − 898)
c
8
((u + 1)
8
)(u
37
+ 16u
36
+ ··· − 5u − 1)(u
56
+ 31u
55
+ ··· + 27u + 4)
c
9
, c
10
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
28
− 7u
27
+ ··· − 2u + 1)
2
· (u
37
− 9u
36
+ ··· + 9u − 4)
c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
28
− 7u
27
+ ··· − 2u + 1)
2
· (u
37
− 9u
36
+ ··· + 9u − 4)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
8
)(y
37
+ 20y
36
+ ··· + 83y −1)(y
56
− 13y
55
+ ··· + 927y + 16)
c
2
, c
3
, c
6
c
7
((y + 1)
8
)(y
37
+ 16y
36
+ ··· − 5y −1)(y
56
+ 31y
55
+ ··· + 27y + 4)
c
4
, c
11
((y
4
− y
3
+ 3y
2
− 2y + 1)
2
)(y
28
− 7y
27
+ ··· − 2y + 1)
2
· (y
37
− 9y
36
+ ··· + 9y −4)
c
5
((y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
)(y
28
+ y
27
+ ··· + 62y + 1)
2
· (y
37
− 9y
36
+ ··· + 9968617y −806404)
c
9
, c
10
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
28
+ 29y
27
+ ··· + 14y + 1)
2
· (y
37
+ 39y
36
+ ··· + 257y −16)
23
