12n
0667
(K12n
0667
)
A knot diagram
1
Linearized knot diagam
4 5 6 8 9 12 11 2 3 6 7 8
Solving Sequence
6,12 4,7
3 11 8 1 10 9 5 2
c
6
c
3
c
11
c
7
c
12
c
10
c
9
c
5
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
20
− 26u
19
+ ··· + 7b + 97, −83u
20
− 325u
19
+ ··· + 63a + 558, u
21
+ 5u
20
+ ··· − 72u − 9i
I
u
2
= h−3u
14
a + 5u
14
+ ··· + a + 24, −u
14
a + 2u
13
a + ··· + 3a + 4, u
15
− 2u
14
+ ··· − 4u + 1i
I
u
3
= h−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
+ b − 4u − 1, u
8
+ 2u
7
+ 7u
6
+ 10u
5
+ 15u
4
+ 14u
3
+ 9u
2
+ a + 5u − 1,
u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1i
I
u
4
= hb + 1, 2u
2
a + a
2
− 2au + 3a + u − 1, u
3
− u
2
+ 2u − 1i
I
v
1
= ha, b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 67 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−3u
20
− 26u
19
+ · · · + 7b + 97, −83u
20
− 325u
19
+ · · · + 63a +
558, u
21
+ 5u
20
+ · · · − 72u − 9i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
83
63
u
20
+
325
63
u
19
+ ··· − 66u −
62
7
3
7
u
20
+
26
7
u
19
+ ··· − 95u −
97
7
a
7
=
1
u
2
a
3
=
110
63
u
20
+
559
63
u
19
+ ··· − 161u −
159
7
3
7
u
20
+
26
7
u
19
+ ··· − 95u −
97
7
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
83
63
u
20
+
325
63
u
19
+ ··· − 86u −
90
7
5
7
u
20
+
20
7
u
19
+ ··· − 52u −
52
7
a
5
=
−
97
63
u
20
−
458
63
u
19
+ ··· + 111u +
111
7
1
7
u
20
−
10
7
u
19
+ ··· + 103u +
110
7
a
2
=
−
52
63
u
20
−
215
63
u
19
+ ··· + 39u +
38
7
2
7
u
20
+
1
7
u
19
+ ··· + 36u +
38
7
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4
7
u
20
+
51
7
u
19
+ ··· − 324u −
456
7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
21
+ 2u
20
+ ··· + 8u + 1
c
2
u
21
+ 15u
20
+ ··· + 63u + 9
c
4
, c
9
u
21
− 2u
20
+ ··· − 11u
2
+ 1
c
5
, c
8
u
21
− u
20
+ ··· − u − 1
c
6
, c
7
, c
11
u
21
+ 5u
20
+ ··· − 72u − 9
c
10
, c
12
u
21
− 5u
20
+ ··· − 2988u − 1413
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
21
+ 30y
20
+ ··· + 6y −1
c
2
y
21
− 13y
20
+ ··· − 1377y −81
c
4
, c
9
y
21
− 22y
20
+ ··· + 22y −1
c
5
, c
8
y
21
− 11y
20
+ ··· + 21y −1
c
6
, c
7
, c
11
y
21
+ 23y
20
+ ··· + 324y −81
c
10
, c
12
y
21
+ 19y
20
+ ··· − 3839724y −1996569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.834623 + 0.573705I
a = 1.005930 + 0.264258I
b = 0.62121 − 1.82385I
6.40877 + 10.26430I −4.52348 − 6.93928I
u = −0.834623 − 0.573705I
a = 1.005930 − 0.264258I
b = 0.62121 + 1.82385I
6.40877 − 10.26430I −4.52348 + 6.93928I
u = −0.847213 + 0.586710I
a = −0.922945 + 0.173773I
b = 0.16137 + 1.79856I
6.42391 − 4.68256I −3.99466 + 2.17560I
u = −0.847213 − 0.586710I
a = −0.922945 − 0.173773I
b = 0.16137 − 1.79856I
6.42391 + 4.68256I −3.99466 − 2.17560I
u = 0.825151
a = −0.722716
b = −0.926404
−5.68389 −17.0230
u = −0.150569 + 1.281090I
a = 0.434742 − 0.402686I
b = 0.074569 + 0.138439I
3.22602 + 2.41816I −3.53897 − 1.93549I
u = −0.150569 − 1.281090I
a = 0.434742 + 0.402686I
b = 0.074569 − 0.138439I
3.22602 − 2.41816I −3.53897 + 1.93549I
u = −0.323088 + 0.617615I
a = 0.358624 − 0.512504I
b = −0.096498 + 0.850760I
0.52795 + 2.17494I −5.93194 − 4.33334I
u = −0.323088 − 0.617615I
a = 0.358624 + 0.512504I
b = −0.096498 − 0.850760I
0.52795 − 2.17494I −5.93194 + 4.33334I
u = 0.373837 + 1.314800I
a = 0.363936 + 0.564961I
b = −0.998750 + 0.204857I
−1.57111 − 4.30895I −11.00324 + 1.55396I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373837 − 1.314800I
a = 0.363936 − 0.564961I
b = −0.998750 − 0.204857I
−1.57111 + 4.30895I −11.00324 − 1.55396I
u = −0.027283 + 1.412760I
a = 0.78061 + 1.55576I
b = −1.109230 − 0.677694I
3.18953 + 0.20531I −5.89178 + 0.57061I
u = −0.027283 − 1.412760I
a = 0.78061 − 1.55576I
b = −1.109230 + 0.677694I
3.18953 − 0.20531I −5.89178 − 0.57061I
u = −0.437416 + 0.103332I
a = 0.929988 − 0.551312I
b = −0.189823 + 0.028334I
−0.974855 + 0.275619I −10.86571 − 2.54923I
u = −0.437416 − 0.103332I
a = 0.929988 + 0.551312I
b = −0.189823 − 0.028334I
−0.974855 − 0.275619I −10.86571 + 2.54923I
u = −0.09149 + 1.57120I
a = −0.26719 − 1.73552I
b = 0.33826 + 1.86261I
7.94844 + 3.68537I −6.18348 + 2.45338I
u = −0.09149 − 1.57120I
a = −0.26719 + 1.73552I
b = 0.33826 − 1.86261I
7.94844 − 3.68537I −6.18348 − 2.45338I
u = −0.28888 + 1.56597I
a = 0.45254 + 2.00394I
b = 1.01317 − 2.01561I
13.4087 + 14.4061I −2.12525 − 6.98840I
u = −0.28888 − 1.56597I
a = 0.45254 − 2.00394I
b = 1.01317 + 2.01561I
13.4087 − 14.4061I −2.12525 + 6.98840I
u = −0.28585 + 1.59217I
a = −0.77487 − 1.52631I
b = −0.35107 + 2.01142I
13.60260 − 0.45994I −1.43013 + 1.46856I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28585 − 1.59217I
a = −0.77487 + 1.52631I
b = −0.35107 − 2.01142I
13.60260 + 0.45994I −1.43013 − 1.46856I
7
II. I
u
2
= h−3u
14
a + 5u
14
+ · · · + a + 24, −u
14
a + 2u
13
a + · · · + 3a + 4, u
15
−
2u
14
+ · · · − 4u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
a
3
14
u
14
a −
5
14
u
14
+ ··· −
1
14
a −
12
7
a
7
=
1
u
2
a
3
=
0.214286au
14
− 0.357143u
14
+ ··· + 0.928571a − 1.71429
3
14
u
14
a −
5
14
u
14
+ ··· −
1
14
a −
12
7
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
10
7
u
14
a +
9
7
u
14
+ ··· −
8
7
a −
10
7
5
14
u
14
a +
1
14
u
14
+ ··· −
25
14
a −
6
7
a
5
=
−
1
14
u
14
a −
5
7
u
14
+ ··· +
6
7
a +
1
14
−0.142857au
14
− 0.928571u
14
+ ··· + 0.214286a − 0.357143
a
2
=
5
14
u
14
a −
3
7
u
14
+ ··· +
12
7
a +
9
14
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
14
− 16u
13
+ 97u
12
− 120u
11
+ 326u
10
− 337u
9
+ 511u
8
−
400u
7
+ 342u
6
− 95u
5
+ 10u
4
+ 150u
3
− 84u
2
+ 55u − 19
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
30
− 7u
29
+ ··· − 676u − 329
c
2
(u
15
− 7u
14
+ ··· + 28u − 8)
2
c
4
, c
9
u
30
− 14u
28
+ ··· − 641u + 151
c
5
, c
8
u
30
+ 9u
26
+ ··· − u − 1
c
6
, c
7
, c
11
(u
15
− 2u
14
+ ··· − 4u + 1)
2
c
10
, c
12
(u
15
+ 2u
14
+ ··· − 16u + 5)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
30
+ 33y
29
+ ··· + 1028130y + 108241
c
2
(y
15
− 7y
14
+ ··· + 528y − 64)
2
c
4
, c
9
y
30
− 28y
29
+ ··· + 125773y + 22801
c
5
, c
8
y
30
+ 18y
28
+ ··· − 35y + 1
c
6
, c
7
, c
11
(y
15
+ 16y
14
+ ··· − 4y − 1)
2
c
10
, c
12
(y
15
+ 16y
14
+ ··· − 344y − 25)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783022 + 0.548748I
a = −0.815000 − 0.070479I
b = 0.23196 − 1.72434I
7.57107 − 2.60312I −2.84235 + 2.92184I
u = 0.783022 + 0.548748I
a = 1.150630 − 0.405666I
b = 0.61243 + 1.61879I
7.57107 − 2.60312I −2.84235 + 2.92184I
u = 0.783022 − 0.548748I
a = −0.815000 + 0.070479I
b = 0.23196 + 1.72434I
7.57107 + 2.60312I −2.84235 − 2.92184I
u = 0.783022 − 0.548748I
a = 1.150630 + 0.405666I
b = 0.61243 − 1.61879I
7.57107 + 2.60312I −2.84235 − 2.92184I
u = −0.216855 + 1.221530I
a = 0.741221 − 0.405618I
b = −0.661072 + 0.460812I
1.58567 + 3.38986I −3.26125 − 8.75376I
u = −0.216855 + 1.221530I
a = 0.660981 + 1.010040I
b = 0.913612 + 0.021844I
1.58567 + 3.38986I −3.26125 − 8.75376I
u = −0.216855 − 1.221530I
a = 0.741221 + 0.405618I
b = −0.661072 − 0.460812I
1.58567 − 3.38986I −3.26125 + 8.75376I
u = −0.216855 − 1.221530I
a = 0.660981 − 1.010040I
b = 0.913612 − 0.021844I
1.58567 − 3.38986I −3.26125 + 8.75376I
u = −0.699136
a = 0.498930
b = −0.445090
−2.08475 −3.31340
u = −0.699136
a = 1.87307
b = 0.972659
−2.08475 −3.31340
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.061637 + 0.608365I
a = 0.934694 + 0.293027I
b = 0.986562 + 0.556921I
1.61379 + 2.57496I −1.10179 − 1.01110I
u = 0.061637 + 0.608365I
a = 0.94855 − 1.35297I
b = −0.329324 + 1.042070I
1.61379 + 2.57496I −1.10179 − 1.01110I
u = 0.061637 − 0.608365I
a = 0.934694 − 0.293027I
b = 0.986562 − 0.556921I
1.61379 − 2.57496I −1.10179 + 1.01110I
u = 0.061637 − 0.608365I
a = 0.94855 + 1.35297I
b = −0.329324 − 1.042070I
1.61379 − 2.57496I −1.10179 + 1.01110I
u = 0.09920 + 1.46553I
a = −0.395823 − 0.646191I
b = −0.609648 + 0.043969I
6.22877 − 5.97807I −2.99155 + 7.20850I
u = 0.09920 + 1.46553I
a = −0.26994 + 2.77190I
b = −0.31360 − 2.40695I
6.22877 − 5.97807I −2.99155 + 7.20850I
u = 0.09920 − 1.46553I
a = −0.395823 + 0.646191I
b = −0.609648 − 0.043969I
6.22877 + 5.97807I −2.99155 − 7.20850I
u = 0.09920 − 1.46553I
a = −0.26994 − 2.77190I
b = −0.31360 + 2.40695I
6.22877 + 5.97807I −2.99155 − 7.20850I
u = −0.01760 + 1.52899I
a = −1.250130 − 0.500701I
b = 2.00715 + 0.63605I
8.69622 + 2.65996I 1.50438 − 2.01476I
u = −0.01760 + 1.52899I
a = 0.23286 − 2.06811I
b = −0.18397 + 1.61289I
8.69622 + 2.65996I 1.50438 − 2.01476I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01760 − 1.52899I
a = −1.250130 + 0.500701I
b = 2.00715 − 0.63605I
8.69622 − 2.65996I 1.50438 + 2.01476I
u = −0.01760 − 1.52899I
a = 0.23286 + 2.06811I
b = −0.18397 − 1.61289I
8.69622 − 2.65996I 1.50438 + 2.01476I
u = 0.367791 + 0.287869I
a = −1.078570 + 0.747772I
b = −0.34613 − 1.55473I
0.39798 − 4.38767I −9.5578 + 11.0682I
u = 0.367791 + 0.287869I
a = −1.52156 − 2.49296I
b = −0.006820 − 0.312135I
0.39798 − 4.38767I −9.5578 + 11.0682I
u = 0.367791 − 0.287869I
a = −1.078570 − 0.747772I
b = −0.34613 + 1.55473I
0.39798 + 4.38767I −9.5578 − 11.0682I
u = 0.367791 − 0.287869I
a = −1.52156 + 2.49296I
b = −0.006820 + 0.312135I
0.39798 + 4.38767I −9.5578 − 11.0682I
u = 0.27238 + 1.54795I
a = −0.97464 + 1.65279I
b = −0.05742 − 2.01595I
14.4273 − 6.4879I −0.59296 + 3.62205I
u = 0.27238 + 1.54795I
a = 0.45074 − 1.92343I
b = 0.99248 + 1.70658I
14.4273 − 6.4879I −0.59296 + 3.62205I
u = 0.27238 − 1.54795I
a = −0.97464 − 1.65279I
b = −0.05742 + 2.01595I
14.4273 + 6.4879I −0.59296 − 3.62205I
u = 0.27238 − 1.54795I
a = 0.45074 + 1.92343I
b = 0.99248 − 1.70658I
14.4273 + 6.4879I −0.59296 − 3.62205I
13
III. I
u
3
= h−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
+ b − 4u − 1, u
8
+ 2u
7
+ · · · + a −
1, u
9
+ 2u
8
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
−u
8
− 2u
7
− 7u
6
− 10u
5
− 15u
4
− 14u
3
− 9u
2
− 5u + 1
u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 6u
2
+ 4u + 1
a
7
=
1
u
2
a
3
=
−u
8
− 2u
7
− 6u
6
− 8u
5
− 10u
4
− 8u
3
− 3u
2
− u + 2
u
6
+ 2u
5
+ 5u
4
+ 6u
3
+ 6u
2
+ 4u + 1
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
−u
7
− 2u
6
− 6u
5
− 8u
4
− 10u
3
− 9u
2
− 4u − 3
−u
8
− 2u
7
− 6u
6
− 8u
5
− 11u
4
− 9u
3
− 6u
2
− 3u
a
5
=
−u
8
− 2u
7
− 7u
6
− 9u
5
− 14u
4
− 11u
3
− 7u
2
− 3u + 2
u
7
+ 2u
6
+ 6u
5
+ 8u
4
+ 10u
3
+ 8u
2
+ 4u + 1
a
2
=
−u
8
− 2u
7
− 6u
6
− 10u
5
− 13u
4
− 16u
3
− 11u
2
− 9u − 3
−u
7
− u
6
− 4u
5
− 3u
4
− 4u
3
− 2u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
− 4u
6
− 13u
5
− 32u
4
− 38u
3
− 40u
2
− 24u − 8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
9
+ 3u
8
+ 9u
7
+ 14u
6
+ 18u
5
+ 18u
4
+ 13u
3
+ 8u
2
+ 4u + 1
c
2
u
9
+ 12u
8
+ ··· + 401u + 89
c
4
, c
9
u
9
− u
8
− u
7
+ 2u
6
+ 2u
5
− 2u
4
− u
3
+ 2u
2
− 1
c
5
, c
8
u
9
− 2u
7
− u
6
+ 2u
5
+ 2u
4
− 2u
3
− u
2
+ u + 1
c
6
, c
7
u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1
c
10
, c
12
u
9
+ 2u
8
+ 3u
7
+ u
6
− 18u
5
− 20u
4
− 4u
3
− 11u
2
− 1
c
11
u
9
− 2u
8
+ 7u
7
− 10u
6
+ 16u
5
− 16u
4
+ 13u
3
− 9u
2
+ 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
9
+ 9y
8
+ 33y
7
+ 46y
6
+ 14y
5
− 14y
4
− 3y
3
+ 4y
2
− 1
c
2
y
9
− 6y
8
+ ··· + 8789y − 7921
c
4
, c
9
y
9
− 3y
8
+ 9y
7
− 14y
6
+ 18y
5
− 18y
4
+ 13y
3
− 8y
2
+ 4y − 1
c
5
, c
8
y
9
− 4y
8
+ 8y
7
− 13y
6
+ 18y
5
− 18y
4
+ 14y
3
− 9y
2
+ 3y − 1
c
6
, c
7
, c
11
y
9
+ 10y
8
+ 41y
7
+ 86y
6
+ 86y
5
+ 4y
4
− 75y
3
− 61y
2
− 14y − 1
c
10
, c
12
y
9
+ 2y
8
− 31y
7
− 37y
6
+ 384y
5
− 230y
4
− 422y
3
− 161y
2
− 22y − 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942156
a = 0.835924
b = 0.693833
−4.78668 −6.85480
u = 0.025437 + 1.219490I
a = −0.848257 + 0.499627I
b = −0.174357 − 0.757557I
3.87432 − 3.77454I −1.17699 + 5.61151I
u = 0.025437 − 1.219490I
a = −0.848257 − 0.499627I
b = −0.174357 + 0.757557I
3.87432 + 3.77454I −1.17699 − 5.61151I
u = −0.465053 + 1.257920I
a = 0.128314 + 0.500319I
b = 0.628101 + 0.278164I
−0.89563 + 5.00672I −5.11040 − 6.89072I
u = −0.465053 − 1.257920I
a = 0.128314 − 0.500319I
b = 0.628101 − 0.278164I
−0.89563 − 5.00672I −5.11040 + 6.89072I
u = −0.05596 + 1.56008I
a = −0.27494 − 1.81410I
b = 0.58625 + 1.89814I
8.14041 + 4.21823I −1.16365 − 10.14642I
u = −0.05596 − 1.56008I
a = −0.27494 + 1.81410I
b = 0.58625 − 1.89814I
8.14041 − 4.21823I −1.16365 + 10.14642I
u = −0.033345 + 0.402052I
a = 2.07693 − 1.08799I
b = 0.113094 + 1.126000I
1.14384 + 3.68908I −2.12153 − 6.55211I
u = −0.033345 − 0.402052I
a = 2.07693 + 1.08799I
b = 0.113094 − 1.126000I
1.14384 − 3.68908I −2.12153 + 6.55211I
17
IV. I
u
4
= hb + 1, 2u
2
a + a
2
− 2au + 3a + u − 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
4
=
a
−1
a
7
=
1
u
2
a
3
=
a − 1
−1
a
11
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
1
=
−1
0
a
10
=
u
2
+ 1
u
2
− u + 1
a
9
=
2u
2
a − au + 2a + u + 1
u
2
a − au + u
2
+ a + 1
a
5
=
−u
2
+ u − 2
−au − 2
a
2
=
a − 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
− 16
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
6
c
2
u
6
c
4
, c
5
, c
8
c
9
u
6
+ u
5
− 3u
4
− 3u
3
+ 3u
2
+ u − 1
c
6
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
10
, c
12
(u
3
− u
2
+ 1)
2
c
11
(u
3
+ u
2
+ 2u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y − 1)
6
c
2
y
6
c
4
, c
5
, c
8
c
9
y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1
c
6
, c
7
, c
11
(y
3
+ 3y
2
+ 2y − 1)
2
c
10
, c
12
(y
3
− y
2
+ 2y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 1.153780 + 0.265134I
b = −1.00000
1.37919 − 2.82812I −7.68821 − 2.81140I
u = 0.215080 + 1.307140I
a = −0.398899 + 1.224590I
b = −1.00000
1.37919 − 2.82812I −7.68821 − 2.81140I
u = 0.215080 − 1.307140I
a = 1.153780 − 0.265134I
b = −1.00000
1.37919 + 2.82812I −7.68821 + 2.81140I
u = 0.215080 − 1.307140I
a = −0.398899 − 1.224590I
b = −1.00000
1.37919 + 2.82812I −7.68821 + 2.81140I
u = 0.569840
a = 0.161059
b = −1.00000
−2.75839 −17.6240
u = 0.569840
a = −2.67081
b = −1.00000
−2.75839 −17.6240
21
V. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
−1
0
a
4
=
0
−1
a
7
=
1
0
a
3
=
−1
−1
a
11
=
−1
0
a
8
=
1
0
a
1
=
−1
0
a
10
=
−1
0
a
9
=
−2
−1
a
5
=
−1
−1
a
2
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
u + 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
u
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
8
, c
9
y − 1
c
2
, c
6
, c
7
c
10
, c
11
, c
12
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
25
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
6
(u + 1)
· (u
9
+ 3u
8
+ 9u
7
+ 14u
6
+ 18u
5
+ 18u
4
+ 13u
3
+ 8u
2
+ 4u + 1)
· (u
21
+ 2u
20
+ ··· + 8u + 1)(u
30
− 7u
29
+ ··· − 676u − 329)
c
2
u
7
(u
9
+ 12u
8
+ ··· + 401u + 89)(u
15
− 7u
14
+ ··· + 28u − 8)
2
· (u
21
+ 15u
20
+ ··· + 63u + 9)
c
4
, c
9
(u + 1)(u
6
+ u
5
− 3u
4
− 3u
3
+ 3u
2
+ u − 1)
· (u
9
− u
8
− u
7
+ 2u
6
+ 2u
5
− 2u
4
− u
3
+ 2u
2
− 1)
· (u
21
− 2u
20
+ ··· − 11u
2
+ 1)(u
30
− 14u
28
+ ··· − 641u + 151)
c
5
, c
8
(u + 1)(u
6
+ u
5
− 3u
4
− 3u
3
+ 3u
2
+ u − 1)
· (u
9
− 2u
7
+ ··· + u + 1)(u
21
− u
20
+ ··· − u − 1)
· (u
30
+ 9u
26
+ ··· − u − 1)
c
6
, c
7
u(u
3
− u
2
+ 2u − 1)
2
· (u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1)
· ((u
15
− 2u
14
+ ··· − 4u + 1)
2
)(u
21
+ 5u
20
+ ··· − 72u − 9)
c
10
, c
12
u(u
3
− u
2
+ 1)
2
(u
9
+ 2u
8
+ 3u
7
+ u
6
− 18u
5
− 20u
4
− 4u
3
− 11u
2
− 1)
· ((u
15
+ 2u
14
+ ··· − 16u + 5)
2
)(u
21
− 5u
20
+ ··· − 2988u − 1413)
c
11
u(u
3
+ u
2
+ 2u + 1)
2
· (u
9
− 2u
8
+ 7u
7
− 10u
6
+ 16u
5
− 16u
4
+ 13u
3
− 9u
2
+ 2u − 1)
· ((u
15
− 2u
14
+ ··· − 4u + 1)
2
)(u
21
+ 5u
20
+ ··· − 72u − 9)
26
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y − 1)
7
(y
9
+ 9y
8
+ 33y
7
+ 46y
6
+ 14y
5
− 14y
4
− 3y
3
+ 4y
2
− 1)
· (y
21
+ 30y
20
+ ··· + 6y − 1)(y
30
+ 33y
29
+ ··· + 1028130y + 108241)
c
2
y
7
(y
9
− 6y
8
+ ··· + 8789y − 7921)(y
15
− 7y
14
+ ··· + 528y − 64)
2
· (y
21
− 13y
20
+ ··· − 1377y − 81)
c
4
, c
9
(y − 1)(y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1)
· (y
9
− 3y
8
+ 9y
7
− 14y
6
+ 18y
5
− 18y
4
+ 13y
3
− 8y
2
+ 4y − 1)
· (y
21
− 22y
20
+ ··· + 22y − 1)(y
30
− 28y
29
+ ··· + 125773y + 22801)
c
5
, c
8
(y − 1)(y
6
− 7y
5
+ 21y
4
− 31y
3
+ 21y
2
− 7y + 1)
· (y
9
− 4y
8
+ 8y
7
− 13y
6
+ 18y
5
− 18y
4
+ 14y
3
− 9y
2
+ 3y − 1)
· (y
21
− 11y
20
+ ··· + 21y − 1)(y
30
+ 18y
28
+ ··· − 35y + 1)
c
6
, c
7
, c
11
y(y
3
+ 3y
2
+ 2y − 1)
2
· (y
9
+ 10y
8
+ 41y
7
+ 86y
6
+ 86y
5
+ 4y
4
− 75y
3
− 61y
2
− 14y − 1)
· ((y
15
+ 16y
14
+ ··· − 4y − 1)
2
)(y
21
+ 23y
20
+ ··· + 324y − 81)
c
10
, c
12
y(y
3
− y
2
+ 2y − 1)
2
· (y
9
+ 2y
8
− 31y
7
− 37y
6
+ 384y
5
− 230y
4
− 422y
3
− 161y
2
− 22y − 1)
· (y
15
+ 16y
14
+ ··· − 344y − 25)
2
· (y
21
+ 19y
20
+ ··· − 3839724y − 1996569)
27
