12n
0487
(K12n
0487
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 10 12 3 1 4 7 8
Solving Sequence
3,8
4
1,9
10 12 7 6 2 5 11
c
3
c
8
c
9
c
12
c
7
c
6
c
2
c
5
c
11
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h465502349422u
14
− 79727868434u
13
+ ··· + 599549983265b + 123387962359,
851737214407u
14
− 547553851564u
13
+ ··· + 599549983265a − 2100202102861,
u
15
− 14u
13
− 4u
12
+ 107u
11
+ 26u
10
− 207u
9
− 86u
8
+ 119u
7
− 16u
6
+ 74u
5
+ 44u
4
+ 3u
3
+ 7u
2
− 1i
I
u
2
= h−8u
9
+ 12u
8
− 14u
7
+ 7u
6
+ 8u
5
− 36u
4
+ 17u
3
− 29u
2
+ 25b − 13u + 34,
− 63u
9
+ 32u
8
− 54u
7
− 23u
6
+ 163u
5
− 171u
4
+ 112u
3
− 19u
2
+ 25a − 293u + 149,
u
10
− u
9
+ u
8
− 3u
6
+ 4u
5
− 3u
4
+ u
3
+ 5u
2
− 5u + 1i
* 2 irreducible components of dim
C
= 0, with total 25 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
=
h4.66×10
11
u
14
−7.97×10
10
u
13
+· · ·+6.00×10
11
b+1.23×10
11
, 8.52×10
11
u
14
−
5.48 × 10
11
u
13
+ · · · + 6.00 × 10
11
a − 2.10 × 10
12
, u
15
− 14u
13
+ · · · + 7u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
1
=
−1.42063u
14
+ 0.913275u
13
+ ··· + 1.01409u + 3.50296
−0.776420u
14
+ 0.132980u
13
+ ··· − 1.17993u − 0.205801
a
9
=
u
u
a
10
=
−1.49471u
14
− 0.580434u
13
+ ··· − 14.9172u + 0.00184502
0.320071u
14
− 0.134431u
13
+ ··· + 2.49471u + 0.580434
a
12
=
−1.42063u
14
+ 0.913275u
13
+ ··· + 1.01409u + 3.50296
−0.792950u
14
+ 0.229300u
13
+ ··· + 0.240700u − 1.11908
a
7
=
0.718288u
14
+ 0.713414u
13
+ ··· + 13.7373u − 0.207646
−0.977277u
14
+ 0.474429u
13
+ ··· − 1.89822u − 0.919215
a
6
=
−0.468813u
14
− 0.416564u
13
+ ··· − 3.44802u − 5.40828
−0.702958u
14
+ 0.430796u
13
+ ··· − 1.35532u + 0.991058
a
2
=
−0.644208u
14
+ 0.780295u
13
+ ··· + 2.19402u + 3.70877
−0.776420u
14
+ 0.132980u
13
+ ··· − 1.17993u − 0.205801
a
5
=
−0.580434u
14
− 0.320071u
13
+ ··· + 0.00184502u − 2.49471
−0.134431u
14
− 0.0198011u
13
+ ··· + 0.580434u + 0.320071
a
11
=
−1.49471u
14
− 0.580434u
13
+ ··· − 13.9172u + 0.00184502
0.320071u
14
− 0.134431u
13
+ ··· + 2.49471u + 0.580434
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2849816670076
599549983265
u
14
−
2328924086222
599549983265
u
13
+ ··· −
4273891768151
599549983265
u −
9195265038463
599549983265
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 3u
14
+ ··· + 9u + 1
c
2
, c
5
u
15
+ 3u
14
+ ··· + u + 1
c
3
, c
4
, c
8
c
10
u
15
− 14u
13
+ ··· + 7u
2
− 1
c
6
, c
9
u
15
+ u
14
+ ··· − 17u + 1
c
7
, c
11
, c
12
u
15
− 14u
14
+ ··· − 96u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 21y
14
+ ··· + 9y −1
c
2
, c
5
y
15
− 3y
14
+ ··· + 9y −1
c
3
, c
4
, c
8
c
10
y
15
− 28y
14
+ ··· + 14y −1
c
6
, c
9
y
15
+ 39y
14
+ ··· + 295y −1
c
7
, c
11
, c
12
y
15
− 10y
14
+ ··· + 4608y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.286970 + 0.003568I
a = 0.589686 − 0.744025I
b = 0.319963 − 1.267150I
4.37389 + 0.30095I −3.29649 − 1.17688I
u = 1.286970 − 0.003568I
a = 0.589686 + 0.744025I
b = 0.319963 + 1.267150I
4.37389 − 0.30095I −3.29649 + 1.17688I
u = −1.220550 + 0.546816I
a = −0.491530 − 0.908635I
b = −0.47712 − 1.50755I
3.32606 − 6.34337I −6.36496 + 6.14476I
u = −1.220550 − 0.546816I
a = −0.491530 + 0.908635I
b = −0.47712 + 1.50755I
3.32606 + 6.34337I −6.36496 − 6.14476I
u = 0.100194 + 0.555594I
a = 0.55980 − 2.69568I
b = −0.253685 − 0.984505I
−6.84743 − 2.37164I −5.86485 + 4.49258I
u = 0.100194 − 0.555594I
a = 0.55980 + 2.69568I
b = −0.253685 + 0.984505I
−6.84743 + 2.37164I −5.86485 − 4.49258I
u = 0.053551 + 0.530205I
a = 0.648734 + 0.711885I
b = −0.067055 + 0.375797I
−0.327240 + 1.083790I −4.63730 − 6.18366I
u = 0.053551 − 0.530205I
a = 0.648734 − 0.711885I
b = −0.067055 − 0.375797I
−0.327240 − 1.083790I −4.63730 + 6.18366I
u = −0.453145
a = −1.45303
b = −1.32667
−2.54518 9.96520
u = −0.384303
a = 1.94891
b = −0.219731
−1.51666 −4.64930
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.278558
a = 5.85314
b = −0.441847
−9.80649 −23.6470
u = 2.72441 + 1.12795I
a = 0.289084 − 0.671320I
b = 0.08254 − 1.84271I
16.0556 + 2.2374I −4.43024 + 0.I
u = 2.72441 − 1.12795I
a = 0.289084 + 0.671320I
b = 0.08254 + 1.84271I
16.0556 − 2.2374I −4.43024 + 0.I
u = −2.66513 + 1.31852I
a = −0.270282 − 0.679151I
b = −0.11052 − 1.88022I
15.8498 − 9.2839I −4.74065 + 4.04193I
u = −2.66513 − 1.31852I
a = −0.270282 + 0.679151I
b = −0.11052 + 1.88022I
15.8498 + 9.2839I −4.74065 − 4.04193I
6
II. I
u
2
= h−8u
9
+ 12u
8
+ · · · + 25b + 34, −63u
9
+ 32u
8
+ · · · + 25a +
149, u
10
− u
9
+ · · · − 5u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
1
=
2.52000u
9
− 1.28000u
8
+ ··· + 11.7200u − 5.96000
0.320000u
9
− 0.480000u
8
+ ··· + 0.520000u − 1.36000
a
9
=
u
u
a
10
=
−1.52000u
9
+ 0.280000u
8
+ ··· − 6.72000u + 0.960000
0.880000u
9
− 0.320000u
8
+ ··· + 3.68000u − 1.24000
a
12
=
2.52000u
9
− 1.28000u
8
+ ··· + 11.7200u − 5.96000
−0.560000u
9
− 0.160000u
8
+ ··· − 3.16000u − 0.120000
a
7
=
6
5
u
9
+
1
5
u
8
+ ··· +
31
5
u +
2
5
−1.12000u
9
+ 0.680000u
8
+ ··· − 6.32000u + 2.76000
a
6
=
−2.52000u
9
+ 1.28000u
8
+ ··· − 12.7200u + 5.96000
−0.240000u
9
+ 0.360000u
8
+ ··· − 1.64000u + 1.52000
a
2
=
11
5
u
9
−
4
5
u
8
+ ··· +
56
5
u −
23
5
0.320000u
9
− 0.480000u
8
+ ··· + 0.520000u − 1.36000
a
5
=
−1.24000u
9
+ 0.360000u
8
+ ··· − 6.64000u + 2.52000
0.560000u
9
+ 0.160000u
8
+ ··· + 3.16000u − 0.880000
a
11
=
−1.52000u
9
+ 0.280000u
8
+ ··· − 7.72000u + 0.960000
0.880000u
9
− 0.320000u
8
+ ··· + 3.68000u − 1.24000
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
303
25
u
9
−
167
25
u
8
+
249
25
u
7
+
88
25
u
6
−
878
25
u
5
+
826
25
u
4
−
622
25
u
3
+
114
25
u
2
+
1558
25
u −
944
25
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 2u
9
+ 9u
8
− 15u
7
+ 28u
6
− 38u
5
+ 35u
4
− 31u
3
+ 15u
2
− 6u + 1
c
2
u
10
+ 2u
9
+ u
8
− 3u
7
− 2u
6
+ 2u
5
+ 3u
4
− 3u
3
− 3u
2
+ 1
c
3
, c
10
u
10
− u
9
+ u
8
− 3u
6
+ 4u
5
− 3u
4
+ u
3
+ 5u
2
− 5u + 1
c
4
, c
8
u
10
+ u
9
+ u
8
− 3u
6
− 4u
5
− 3u
4
− u
3
+ 5u
2
+ 5u + 1
c
5
u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1
c
6
, c
9
u
10
+ 3u
7
− 5u
6
+ 2u
5
− 3u
4
− 2u
2
+ 8u − 3
c
7
u
10
− 5u
8
+ 3u
7
+ 10u
6
− 9u
5
− 7u
4
+ 9u
3
+ u
2
− u − 1
c
11
, c
12
u
10
− 5u
8
− 3u
7
+ 10u
6
+ 9u
5
− 7u
4
− 9u
3
+ u
2
+ u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 14y
9
+ ··· − 6y + 1
c
2
, c
5
y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 38y
5
+ 35y
4
− 31y
3
+ 15y
2
− 6y + 1
c
3
, c
4
, c
8
c
10
y
10
+ y
9
− 5y
8
− 4y
7
+ 15y
6
+ 4y
5
− 27y
4
+ 3y
3
+ 29y
2
− 15y + 1
c
6
, c
9
y
10
− 10y
8
− 15y
7
+ 9y
6
+ 20y
5
− 19y
4
+ 10y
3
+ 22y
2
− 52y + 9
c
7
, c
11
, c
12
y
10
− 10y
9
+ ··· − 3y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.047150 + 0.419466I
a = −0.745457 + 0.844492I
b = −0.28578 + 1.89933I
5.01632 + 5.84673I −1.85887 − 5.25090I
u = 1.047150 − 0.419466I
a = −0.745457 − 0.844492I
b = −0.28578 − 1.89933I
5.01632 − 5.84673I −1.85887 + 5.25090I
u = −1.154050 + 0.132803I
a = 0.775839 + 0.664119I
b = 0.24316 + 1.73359I
5.60821 + 1.13028I −1.128175 − 0.572443I
u = −1.154050 − 0.132803I
a = 0.775839 − 0.664119I
b = 0.24316 − 1.73359I
5.60821 − 1.13028I −1.128175 + 0.572443I
u = 0.734349
a = 2.32032
b = −0.271586
−9.51751 4.60600
u = 0.328497 + 1.235550I
a = 0.448610 − 0.982537I
b = −0.188603 − 0.504750I
−7.98285 − 1.51634I −9.37010 + 3.27052I
u = 0.328497 − 1.235550I
a = 0.448610 + 0.982537I
b = −0.188603 + 0.504750I
−7.98285 + 1.51634I −9.37010 − 3.27052I
u = −0.228999 + 1.295180I
a = 0.201014 − 0.252463I
b = −0.068161 − 0.994177I
−3.05365 − 2.41009I −4.28312 + 3.73455I
u = −0.228999 − 1.295180I
a = 0.201014 + 0.252463I
b = −0.068161 + 0.994177I
−3.05365 + 2.41009I −4.28312 − 3.73455I
u = 0.280460
a = −2.68033
b = −1.12964
−2.81801 −20.3250
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
− 2u
9
+ 9u
8
− 15u
7
+ 28u
6
− 38u
5
+ 35u
4
− 31u
3
+ 15u
2
− 6u + 1)
· (u
15
+ 3u
14
+ ··· + 9u + 1)
c
2
(u
10
+ 2u
9
+ u
8
− 3u
7
− 2u
6
+ 2u
5
+ 3u
4
− 3u
3
− 3u
2
+ 1)
· (u
15
+ 3u
14
+ ··· + u + 1)
c
3
, c
10
(u
10
− u
9
+ u
8
− 3u
6
+ 4u
5
− 3u
4
+ u
3
+ 5u
2
− 5u + 1)
· (u
15
− 14u
13
+ ··· + 7u
2
− 1)
c
4
, c
8
(u
10
+ u
9
+ u
8
− 3u
6
− 4u
5
− 3u
4
− u
3
+ 5u
2
+ 5u + 1)
· (u
15
− 14u
13
+ ··· + 7u
2
− 1)
c
5
(u
10
− 2u
9
+ u
8
+ 3u
7
− 2u
6
− 2u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
· (u
15
+ 3u
14
+ ··· + u + 1)
c
6
, c
9
(u
10
+ 3u
7
+ ··· + 8u − 3)(u
15
+ u
14
+ ··· − 17u + 1)
c
7
(u
10
− 5u
8
+ 3u
7
+ 10u
6
− 9u
5
− 7u
4
+ 9u
3
+ u
2
− u − 1)
· (u
15
− 14u
14
+ ··· − 96u + 32)
c
11
, c
12
(u
10
− 5u
8
− 3u
7
+ 10u
6
+ 9u
5
− 7u
4
− 9u
3
+ u
2
+ u − 1)
· (u
15
− 14u
14
+ ··· − 96u + 32)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 14y
9
+ ··· − 6y + 1)(y
15
+ 21y
14
+ ··· + 9y −1)
c
2
, c
5
(y
10
− 2y
9
+ 9y
8
− 15y
7
+ 28y
6
− 38y
5
+ 35y
4
− 31y
3
+ 15y
2
− 6y + 1)
· (y
15
− 3y
14
+ ··· + 9y −1)
c
3
, c
4
, c
8
c
10
(y
10
+ y
9
− 5y
8
− 4y
7
+ 15y
6
+ 4y
5
− 27y
4
+ 3y
3
+ 29y
2
− 15y + 1)
· (y
15
− 28y
14
+ ··· + 14y −1)
c
6
, c
9
(y
10
− 10y
8
− 15y
7
+ 9y
6
+ 20y
5
− 19y
4
+ 10y
3
+ 22y
2
− 52y + 9)
· (y
15
+ 39y
14
+ ··· + 295y −1)
c
7
, c
11
, c
12
(y
10
− 10y
9
+ ··· − 3y + 1)(y
15
− 10y
14
+ ··· + 4608y −1024)
12
