12n
0471
(K12n
0471
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 12 11 5 4 6 7 10
Solving Sequence
6,12 3,7
2 1 5 11 8 9 10 4
c
6
c
2
c
1
c
5
c
11
c
7
c
8
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−147633099219u
43
+ 379863908626u
42
+ ··· + 592898388701b − 1077740574717,
1873032055350u
43
− 3613432711737u
42
+ ··· + 1185796777402a − 16189929128661,
u
44
− 2u
43
+ ··· − 12u − 1i
I
u
2
= hb − 1, 2u
2
a + a
2
− 2au + 4a + u − 1, u
3
− u
2
+ 2u − 1i
I
u
3
= hb + 1, −u
2
+ a − u − 2, u
3
+ u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 53 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−1.48 × 10
11
u
43
+ 3.80 × 10
11
u
42
+ · · · + 5.93 × 10
11
b − 1.08 ×
10
12
, 1.87 × 10
12
u
43
− 3.61 × 10
12
u
42
+ · · · + 1.19 × 10
12
a − 1.62 ×
10
13
, u
44
− 2u
43
+ · · · − 12u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−1.57956u
43
+ 3.04726u
42
+ ··· + 15.8478u + 13.6532
0.249002u
43
− 0.640690u
42
+ ··· + 7.19437u + 1.81775
a
7
=
1
−u
2
a
2
=
−1.33055u
43
+ 2.40657u
42
+ ··· + 23.0422u + 15.4710
0.249002u
43
− 0.640690u
42
+ ··· + 7.19437u + 1.81775
a
1
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
1.94605u
43
− 3.56049u
42
+ ··· − 33.9928u − 16.2437
−0.106829u
43
+ 0.292551u
42
+ ··· − 3.38360u − 1.39701
a
11
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−1.90349u
43
+ 4.58255u
42
+ ··· + 32.9049u + 21.3530
−0.231468u
43
+ 0.479188u
42
+ ··· + 1.51379u + 1.68525
a
10
=
−u
3
− 2u
u
3
+ u
a
4
=
1.63753u
43
− 3.01547u
42
+ ··· − 38.8903u − 16.9586
0.0851016u
43
− 0.122356u
42
+ ··· − 0.258282u − 0.988042
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
248546356620
592898388701
u
43
+
1117851140785
592898388701
u
42
+ ··· −
3366360188518
592898388701
u −
8799598819910
592898388701
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 14u
43
+ ··· + 687u + 49
c
2
, c
5
u
44
+ 4u
43
+ ··· + 13u − 7
c
3
, c
4
, c
9
u
44
− u
43
+ ··· − 8u − 8
c
6
, c
7
, c
11
u
44
− 2u
43
+ ··· − 12u − 1
c
8
u
44
+ 3u
43
+ ··· + 8u + 8
c
10
u
44
+ 2u
43
+ ··· − 216u − 13
c
12
u
44
+ 20u
43
+ ··· − 582288u + 12161
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 42y
43
+ ··· − 11859y + 2401
c
2
, c
5
y
44
− 14y
43
+ ··· − 687y + 49
c
3
, c
4
, c
9
y
44
− 37y
43
+ ··· − 64y + 64
c
6
, c
7
, c
11
y
44
+ 36y
43
+ ··· − 120y + 1
c
8
y
44
+ 47y
43
+ ··· − 960y + 64
c
10
y
44
− 44y
43
+ ··· − 21852y + 169
c
12
y
44
− 68y
43
+ ··· − 423863999800y + 147889921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177625 + 1.046220I
a = 0.142421 − 1.282600I
b = −0.111509 + 0.704372I
−1.13792 + 1.81248I −1.86603 − 4.45266I
u = 0.177625 − 1.046220I
a = 0.142421 + 1.282600I
b = −0.111509 − 0.704372I
−1.13792 − 1.81248I −1.86603 + 4.45266I
u = −0.905481 + 0.047868I
a = −1.61810 − 2.71471I
b = 0.969501 + 0.973014I
8.90320 − 3.55413I 1.57190 + 2.73369I
u = −0.905481 − 0.047868I
a = −1.61810 + 2.71471I
b = 0.969501 − 0.973014I
8.90320 + 3.55413I 1.57190 − 2.73369I
u = 0.888633 + 0.113112I
a = 1.63253 − 2.72104I
b = −1.13181 + 0.84989I
4.21307 + 8.73460I −2.10151 − 5.42806I
u = 0.888633 − 0.113112I
a = 1.63253 + 2.72104I
b = −1.13181 − 0.84989I
4.21307 − 8.73460I −2.10151 + 5.42806I
u = 0.895146 + 0.030335I
a = 1.50372 + 2.63941I
b = −0.725758 − 1.037770I
5.49591 + 1.83935I −0.526060 − 1.054264I
u = 0.895146 − 0.030335I
a = 1.50372 − 2.63941I
b = −0.725758 + 1.037770I
5.49591 − 1.83935I −0.526060 + 1.054264I
u = −0.124146 + 1.195890I
a = 0.103513 + 1.322400I
b = −1.136390 − 0.239685I
−4.44373 − 1.62575I −5.71135 − 1.58189I
u = −0.124146 − 1.195890I
a = 0.103513 − 1.322400I
b = −1.136390 + 0.239685I
−4.44373 + 1.62575I −5.71135 + 1.58189I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028993 + 1.237360I
a = 0.27041 + 1.84256I
b = 1.116190 − 0.284540I
−10.24070 − 0.43963I −11.19118 − 0.81443I
u = −0.028993 − 1.237360I
a = 0.27041 − 1.84256I
b = 1.116190 + 0.284540I
−10.24070 + 0.43963I −11.19118 + 0.81443I
u = 0.755269
a = −2.04829
b = 1.32092
−2.54326 −3.28070
u = 0.453023 + 1.165750I
a = 1.46711 + 1.23873I
b = −1.053650 − 0.886079I
0.98373 − 3.94476I −4.68762 + 2.02851I
u = 0.453023 − 1.165750I
a = 1.46711 − 1.23873I
b = −1.053650 + 0.886079I
0.98373 + 3.94476I −4.68762 − 2.02851I
u = −0.254381 + 1.244050I
a = −1.35227 − 1.46538I
b = 0.461470 + 0.356687I
−7.86357 − 3.29517I −5.01423 + 4.50472I
u = −0.254381 − 1.244050I
a = −1.35227 + 1.46538I
b = 0.461470 − 0.356687I
−7.86357 + 3.29517I −5.01423 − 4.50472I
u = −0.530116 + 0.484400I
a = 0.22811 + 1.92477I
b = −0.793793 − 0.687491I
−1.89298 − 4.16205I −4.34545 + 6.93236I
u = −0.530116 − 0.484400I
a = 0.22811 − 1.92477I
b = −0.793793 + 0.687491I
−1.89298 + 4.16205I −4.34545 − 6.93236I
u = 0.319810 + 1.254700I
a = −0.613086 + 0.914327I
b = 1.341730 + 0.022586I
−6.42106 + 3.87791I −7.73542 − 3.96367I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.319810 − 1.254700I
a = −0.613086 − 0.914327I
b = 1.341730 − 0.022586I
−6.42106 − 3.87791I −7.73542 + 3.96367I
u = −0.447807 + 1.241790I
a = −1.49241 + 1.30249I
b = 0.865876 − 1.008920I
5.21565 − 1.27455I 0
u = −0.447807 − 1.241790I
a = −1.49241 − 1.30249I
b = 0.865876 + 1.008920I
5.21565 + 1.27455I 0
u = 0.431847 + 1.254620I
a = 0.25969 − 2.31831I
b = −0.822510 + 0.981509I
1.70650 + 2.90262I 0
u = 0.431847 − 1.254620I
a = 0.25969 + 2.31831I
b = −0.822510 − 0.981509I
1.70650 − 2.90262I 0
u = −0.657910
a = −2.47446
b = 0.397664
−4.04738 1.08600
u = −0.509311 + 0.393833I
a = 1.131640 − 0.668056I
b = −0.669143 + 0.583071I
−1.77451 + 0.52923I −4.16249 + 0.21334I
u = −0.509311 − 0.393833I
a = 1.131640 + 0.668056I
b = −0.669143 − 0.583071I
−1.77451 − 0.52923I −4.16249 − 0.21334I
u = 0.420827 + 1.304130I
a = 1.42832 + 1.31723I
b = −0.626328 − 1.065560I
1.33689 + 6.54913I 0
u = 0.420827 − 1.304130I
a = 1.42832 − 1.31723I
b = −0.626328 + 1.065560I
1.33689 − 6.54913I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.181384 + 1.359970I
a = 0.407588 + 0.745307I
b = 0.699749 − 0.288589I
−4.01419 + 3.49485I 0
u = 0.181384 − 1.359970I
a = 0.407588 − 0.745307I
b = 0.699749 + 0.288589I
−4.01419 − 3.49485I 0
u = −0.423050 + 1.318510I
a = −0.24113 − 2.42704I
b = 1.046820 + 0.917522I
4.63663 − 8.30735I 0
u = −0.423050 − 1.318510I
a = −0.24113 + 2.42704I
b = 1.046820 − 0.917522I
4.63663 + 8.30735I 0
u = −0.192973 + 1.390020I
a = 0.1114790 + 0.0226378I
b = −0.666441 + 0.485044I
−7.33799 − 1.99899I 0
u = −0.192973 − 1.390020I
a = 0.1114790 − 0.0226378I
b = −0.666441 − 0.485044I
−7.33799 + 1.99899I 0
u = 0.397923 + 1.355450I
a = 0.17147 − 2.46591I
b = −1.17690 + 0.80462I
−0.40257 + 13.35110I 0
u = 0.397923 − 1.355450I
a = 0.17147 + 2.46591I
b = −1.17690 − 0.80462I
−0.40257 − 13.35110I 0
u = 0.536600 + 0.237972I
a = 0.147433 + 1.338600I
b = 0.375946 − 0.435344I
1.05918 + 0.97127I 3.52880 − 3.41320I
u = 0.536600 − 0.237972I
a = 0.147433 − 1.338600I
b = 0.375946 + 0.435344I
1.05918 − 0.97127I 3.52880 + 3.41320I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13547 + 1.42408I
a = −0.481300 + 0.967134I
b = −0.921093 − 0.597509I
−8.04171 − 6.36604I 0
u = −0.13547 − 1.42408I
a = −0.481300 − 0.967134I
b = −0.921093 + 0.597509I
−8.04171 + 6.36604I 0
u = −0.302868
a = 2.56595
b = −0.846938
−1.10522 −12.4510
u = −0.0966649
a = 11.5425
b = 1.04441
−6.54665 −14.0770
9
II. I
u
2
= hb − 1, 2u
2
a + a
2
− 2au + 4a + u − 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
a
1
a
7
=
1
−u
2
a
2
=
a + 1
1
a
1
=
1
0
a
5
=
−a
−1
a
11
=
−u
u
2
− u + 1
a
8
=
u
2
+ 1
−u
2
+ u − 1
a
9
=
−u
2
a + 2u
2
− a + 1
u
2
a − au + a + u
a
10
=
−u
2
− 1
u
2
− u + 1
a
4
=
−u
2
− 2a + u − 2
au
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 4u − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
− 2)
3
c
6
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
10
(u
3
− u
2
+ 1)
2
c
11
(u
3
+ u
2
+ 2u + 1)
2
c
12
(u
3
+ u
2
− 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y −2)
6
c
6
, c
7
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
10
, c
12
(y
3
− y
2
+ 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.814156 − 0.050322I
b = 1.00000
−9.60386 + 2.82812I −11.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = −1.05928 + 1.54005I
b = 1.00000
−9.60386 + 2.82812I −11.50976 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.814156 + 0.050322I
b = 1.00000
−9.60386 − 2.82812I −11.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −1.05928 − 1.54005I
b = 1.00000
−9.60386 − 2.82812I −11.50976 + 2.97945I
u = 0.569840
a = 0.118556
b = 1.00000
−5.46628 −4.98050
u = 0.569840
a = −3.62831
b = 1.00000
−5.46628 −4.98050
13
III. I
u
3
= hb + 1, −u
2
+ a − u − 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
u
2
+ u + 2
−1
a
7
=
1
−u
2
a
2
=
u
2
+ u + 1
−1
a
1
=
−1
0
a
5
=
u
2
+ u + 2
−1
a
11
=
−u
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
10
=
u
2
+ 1
−u
2
− u − 1
a
4
=
u
2
+ u + 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
2
+ 4u + 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
7
u
3
+ u
2
+ 2u + 1
c
10
, c
12
u
3
+ u
2
− 1
c
11
u
3
− u
2
+ 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
7
, c
11
y
3
+ 3y
2
+ 2y −1
c
10
, c
12
y
3
− y
2
+ 2y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.122561 + 0.744862I
b = −1.00000
−4.66906 − 2.82812I −6.83447 + 1.85489I
u = −0.215080 − 1.307140I
a = 0.122561 − 0.744862I
b = −1.00000
−4.66906 + 2.82812I −6.83447 − 1.85489I
u = −0.569840
a = 1.75488
b = −1.00000
−0.531480 3.66890
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
44
+ 14u
43
+ ··· + 687u + 49)
c
2
((u − 1)
3
)(u + 1)
6
(u
44
+ 4u
43
+ ··· + 13u − 7)
c
3
, c
4
, c
9
u
3
(u
2
− 2)
3
(u
44
− u
43
+ ··· − 8u − 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
44
+ 4u
43
+ ··· + 13u − 7)
c
6
, c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
44
− 2u
43
+ ··· − 12u − 1)
c
8
u
3
(u
2
− 2)
3
(u
44
+ 3u
43
+ ··· + 8u + 8)
c
10
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
44
+ 2u
43
+ ··· − 216u − 13)
c
11
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
44
− 2u
43
+ ··· − 12u − 1)
c
12
((u
3
+ u
2
− 1)
3
)(u
44
+ 20u
43
+ ··· − 582288u + 12161)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
44
+ 42y
43
+ ··· − 11859y + 2401)
c
2
, c
5
((y −1)
9
)(y
44
− 14y
43
+ ··· − 687y + 49)
c
3
, c
4
, c
9
y
3
(y −2)
6
(y
44
− 37y
43
+ ··· − 64y + 64)
c
6
, c
7
, c
11
((y
3
+ 3y
2
+ 2y −1)
3
)(y
44
+ 36y
43
+ ··· − 120y + 1)
c
8
y
3
(y −2)
6
(y
44
+ 47y
43
+ ··· − 960y + 64)
c
10
((y
3
− y
2
+ 2y −1)
3
)(y
44
− 44y
43
+ ··· − 21852y + 169)
c
12
(y
3
− y
2
+ 2y −1)
3
· (y
44
− 68y
43
+ ··· − 423863999800y + 147889921)
19
