12n
0609
(K12n
0609
)
A knot diagram
1
Linearized knot diagam
3 7 8 7 10 2 11 12 3 5 4 9
Solving Sequence
7,11 5,8
4 12 3 2 1 6 10 9
c
7
c
4
c
11
c
3
c
2
c
1
c
6
c
10
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.50523 × 10
31
u
34
+ 3.77516 × 10
31
u
33
+ ··· + 2.98297 × 10
32
b + 5.56578 × 10
32
,
1.58581 × 10
33
u
34
− 2.10588 × 10
32
u
33
+ ··· + 2.08808 × 10
33
a − 7.24786 × 10
33
, u
35
− 7u
33
+ ··· − 15u − 7i
I
u
2
= h−3u
13
+ 4u
12
+ 12u
11
− 14u
10
− 24u
9
+ 33u
8
+ 22u
7
− 41u
6
− 4u
5
+ 33u
4
− 8u
3
− 16u
2
+ b + 5u + 5,
u
13
− u
12
− 4u
11
+ 3u
10
+ 8u
9
− 8u
8
− 8u
7
+ 10u
6
+ 3u
5
− 10u
4
+ u
3
+ 4u
2
+ a − u − 2,
u
15
− u
14
− 5u
13
+ 4u
12
+ 12u
11
− 11u
10
− 16u
9
+ 18u
8
+ 11u
7
− 20u
6
− 2u
5
+ 14u
4
− 2u
3
− 6u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 50 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
=
h4.51×10
31
u
34
+3.78×10
31
u
33
+· · ·+2.98×10
32
b+5.57×10
32
, 1.59×10
33
u
34
−
2.11 × 10
32
u
33
+ · · · + 2.09 × 10
33
a − 7.25 × 10
33
, u
35
− 7u
33
+ · · · − 15u − 7i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
−0.759458u
34
+ 0.100853u
33
+ ··· − 4.69237u + 3.47107
−0.151032u
34
− 0.126557u
33
+ ··· − 11.7344u − 1.86585
a
8
=
1
−u
2
a
4
=
−0.608426u
34
+ 0.227410u
33
+ ··· + 7.04204u + 5.33692
−0.151032u
34
− 0.126557u
33
+ ··· − 11.7344u − 1.86585
a
12
=
0.179494u
34
− 0.738948u
33
+ ··· − 15.5941u − 1.11702
−0.545677u
34
+ 0.0968206u
33
+ ··· − 9.38307u + 0.549020
a
3
=
−1.02030u
34
+ 0.148917u
33
+ ··· − 5.54020u + 5.06294
−0.0217840u
34
− 0.0983476u
33
+ ··· − 7.67390u − 1.31640
a
2
=
−1.04208u
34
+ 0.0505690u
33
+ ··· − 13.2141u + 3.74654
−0.0217840u
34
− 0.0983476u
33
+ ··· − 7.67390u − 1.31640
a
1
=
0.840961u
34
− 1.49063u
33
+ ··· − 33.0344u − 11.5939
−0.517267u
34
+ 0.810261u
33
+ ··· + 18.9933u + 12.5715
a
6
=
−0.851085u
34
− 0.116346u
33
+ ··· − 25.8199u − 1.77087
0.0725660u
34
− 0.436813u
33
+ ··· − 17.0168u − 7.55024
a
10
=
−0.456623u
34
− 0.375284u
33
+ ··· − 20.0850u + 2.76419
−0.0904401u
34
+ 0.266844u
33
+ ··· + 6.89220u + 3.33219
a
9
=
−3.40594u
34
+ 1.42898u
33
+ ··· − 12.4503u + 24.3578
1.40463u
34
− 0.957154u
33
+ ··· − 5.03678u − 8.25778
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.81804u
34
+ 1.88122u
33
+ ··· + 110.974u + 25.9634
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 62u
34
+ ··· + 4330075u + 134689
c
2
, c
6
u
35
+ 2u
34
+ ··· + 4061u − 367
c
3
u
35
+ 2u
34
+ ··· − 7u + 1
c
4
u
35
+ 10u
34
+ ··· + 1712u + 311
c
5
, c
10
u
35
− u
34
+ ··· + 672u − 23
c
7
u
35
− 7u
33
+ ··· − 15u + 7
c
8
, c
12
u
35
+ 3u
34
+ ··· − 97u + 19
c
9
u
35
+ 4u
34
+ ··· − 54708u + 6023
c
11
u
35
− 5u
34
+ ··· + 422u − 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 206y
34
+ ··· + 2682621801371y −18141126721
c
2
, c
6
y
35
− 62y
34
+ ··· + 4330075y −134689
c
3
y
35
+ 2y
34
+ ··· + 63y −1
c
4
y
35
+ 10y
34
+ ··· − 500008y −96721
c
5
, c
10
y
35
− 3y
34
+ ··· + 454344y −529
c
7
y
35
− 14y
34
+ ··· + 1023y −49
c
8
, c
12
y
35
− 55y
34
+ ··· + 11689y −361
c
9
y
35
− 164y
34
+ ··· − 17527853484y −36276529
c
11
y
35
+ 9y
34
+ ··· + 217500y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.675365 + 0.752140I
a = 0.274011 + 1.179370I
b = −0.55916 + 1.59846I
−5.38269 − 0.91248I −10.44886 + 2.53258I
u = −0.675365 − 0.752140I
a = 0.274011 − 1.179370I
b = −0.55916 − 1.59846I
−5.38269 + 0.91248I −10.44886 − 2.53258I
u = −0.928230
a = −0.743205
b = −3.28718
−10.2373 −6.48310
u = −0.780540 + 0.794419I
a = 0.528114 + 0.428245I
b = −0.454633 + 0.505577I
−0.06975 − 2.50434I −7.09658 + 4.10230I
u = −0.780540 − 0.794419I
a = 0.528114 − 0.428245I
b = −0.454633 − 0.505577I
−0.06975 + 2.50434I −7.09658 − 4.10230I
u = −1.170970 + 0.199419I
a = 0.109806 − 0.892494I
b = 0.256411 − 0.529286I
2.93670 − 2.65045I −2.92426 + 3.85701I
u = −1.170970 − 0.199419I
a = 0.109806 + 0.892494I
b = 0.256411 + 0.529286I
2.93670 + 2.65045I −2.92426 − 3.85701I
u = −1.027690 + 0.614606I
a = −0.911917 − 0.413858I
b = 0.40767 − 1.44351I
−4.22355 − 4.34323I −8.88159 + 4.48072I
u = −1.027690 − 0.614606I
a = −0.911917 + 0.413858I
b = 0.40767 + 1.44351I
−4.22355 + 4.34323I −8.88159 − 4.48072I
u = −0.790308
a = 1.93557
b = −2.52371
−10.8736 0.541730
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.779444 + 0.122722I
a = 0.11921 + 1.82402I
b = 0.692344 + 0.750731I
4.75580 + 0.44115I −1.38131 + 2.20530I
u = 0.779444 − 0.122722I
a = 0.11921 − 1.82402I
b = 0.692344 − 0.750731I
4.75580 − 0.44115I −1.38131 − 2.20530I
u = 1.097490 + 0.543646I
a = −0.208642 + 0.776842I
b = 0.97202 + 1.45913I
1.07838 + 5.16629I −6.84650 − 9.62882I
u = 1.097490 − 0.543646I
a = −0.208642 − 0.776842I
b = 0.97202 − 1.45913I
1.07838 − 5.16629I −6.84650 + 9.62882I
u = 0.879026 + 0.883079I
a = −1.65073 + 0.15661I
b = −0.276490 + 0.900117I
−16.3550 + 2.1833I −9.12494 − 2.49613I
u = 0.879026 − 0.883079I
a = −1.65073 − 0.15661I
b = −0.276490 − 0.900117I
−16.3550 − 2.1833I −9.12494 + 2.49613I
u = −1.004900 + 0.750402I
a = 0.159109 − 0.878002I
b = 0.886553 − 0.937980I
0.76221 − 3.35277I −9.00923 + 1.04834I
u = −1.004900 − 0.750402I
a = 0.159109 + 0.878002I
b = 0.886553 + 0.937980I
0.76221 + 3.35277I −9.00923 − 1.04834I
u = 0.980302 + 0.839353I
a = −0.12512 − 1.44580I
b = −0.56077 − 1.91870I
−16.0274 + 4.2362I −8.99278 − 2.47237I
u = 0.980302 − 0.839353I
a = −0.12512 + 1.44580I
b = −0.56077 + 1.91870I
−16.0274 − 4.2362I −8.99278 + 2.47237I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371475 + 0.598922I
a = 0.882706 − 0.414519I
b = −0.207818 − 0.631352I
−1.039020 − 0.567157I −9.02941 + 3.66448I
u = 0.371475 − 0.598922I
a = 0.882706 + 0.414519I
b = −0.207818 + 0.631352I
−1.039020 + 0.567157I −9.02941 − 3.66448I
u = 0.663303
a = 1.17343
b = −0.625094
−1.52399 −5.20750
u = 1.019370 + 0.891636I
a = 0.374425 − 0.936128I
b = −0.81320 − 1.16561I
−4.62293 + 8.02466I −8.99459 − 6.09889I
u = 1.019370 − 0.891636I
a = 0.374425 + 0.936128I
b = −0.81320 + 1.16561I
−4.62293 − 8.02466I −8.99459 + 6.09889I
u = −0.625529 + 1.237630I
a = −1.149750 − 0.604247I
b = −0.498371 − 1.184570I
−17.6881 + 5.3333I −10.32662 − 2.48689I
u = −0.625529 − 1.237630I
a = −1.149750 + 0.604247I
b = −0.498371 + 1.184570I
−17.6881 − 5.3333I −10.32662 + 2.48689I
u = 0.936546 + 1.042190I
a = −0.390412 + 0.550295I
b = −0.114051 + 0.985066I
−5.01490 − 1.02895I −12.04957 + 2.53411I
u = 0.936546 − 1.042190I
a = −0.390412 − 0.550295I
b = −0.114051 − 0.985066I
−5.01490 + 1.02895I −12.04957 − 2.53411I
u = 0.587494
a = −0.0584535
b = −1.70895
−2.29968 3.86260
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22874 + 0.83593I
a = 0.186277 + 1.290050I
b = −1.04714 + 1.80529I
−15.6932 − 12.6803I −6.00000 + 5.76735I
u = −1.22874 − 0.83593I
a = 0.186277 − 1.290050I
b = −1.04714 − 1.80529I
−15.6932 + 12.6803I −6.00000 − 5.76735I
u = −0.364021 + 0.159376I
a = −2.08592 + 2.84763I
b = 0.575909 + 0.656185I
−0.87711 − 2.42741I −7.50647 + 0.56307I
u = −0.364021 − 0.159376I
a = −2.08592 − 2.84763I
b = 0.575909 − 0.656185I
−0.87711 + 2.42741I −7.50647 − 0.56307I
u = 2.09595
a = −0.386813
b = −0.373598
−7.66684 0
8
II.
I
u
2
= h−3u
13
+4u
12
+· · · +b + 5, u
13
−u
12
+· · · +a − 2, u
15
−u
14
+· · · +u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
−u
13
+ u
12
+ ··· + u + 2
3u
13
− 4u
12
+ ··· − 5u − 5
a
8
=
1
−u
2
a
4
=
−4u
13
+ 5u
12
+ ··· + 6u + 7
3u
13
− 4u
12
+ ··· − 5u − 5
a
12
=
−15u
14
+ 12u
13
+ ··· + 38u + 6
7u
14
− 4u
13
+ ··· − 22u − 6
a
3
=
u
14
− 5u
13
+ ··· + 5u + 6
3u
13
− 3u
12
+ ··· − 4u − 5
a
2
=
u
14
− 2u
13
+ ··· + u + 1
3u
13
− 3u
12
+ ··· − 4u − 5
a
1
=
20u
14
− 13u
13
+ ··· − 53u − 20
−10u
14
+ 4u
13
+ ··· + 32u + 12
a
6
=
−u
14
− 3u
13
+ ··· + 9u + 9
4u
14
− 3u
13
+ ··· − 11u − 7
a
10
=
−4u
14
+ 4u
13
+ ··· + 5u
2
+ 6u
4u
14
− 4u
13
+ ··· − 9u
2
− 8u
a
9
=
9u
14
+ 7u
13
+ ··· − 53u − 30
−7u
14
+ 37u
12
+ ··· + 30u + 17
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
14
+ 19u
13
+ 5u
12
− 83u
11
+ 6u
10
+ 184u
9
− 78u
8
− 223u
7
+
161u
6
+ 135u
5
− 187u
4
− 27u
3
+ 108u
2
− 9u − 37
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
15
− 15u
14
+ ··· + 5u − 1
c
2
u
15
− 3u
14
+ ··· + 3u − 1
c
3
u
15
+ u
14
+ ··· + 3u + 1
c
4
u
15
+ u
14
+ ··· + 2u − 1
c
5
u
15
+ 6u
13
+ ··· − 2u − 1
c
6
u
15
+ 3u
14
+ ··· + 3u + 1
c
7
u
15
− u
14
+ ··· + u + 1
c
8
u
15
− 10u
13
+ ··· + u + 1
c
9
u
15
− 5u
14
+ ··· − 14u + 1
c
10
u
15
+ 6u
13
+ ··· − 2u + 1
c
11
u
15
− 2u
13
+ ··· − 11u
2
− 1
c
12
u
15
− 10u
13
+ ··· + u − 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 59y
14
+ ··· + 5y −1
c
2
, c
6
y
15
− 15y
14
+ ··· + 5y −1
c
3
y
15
+ 5y
14
+ ··· + 17y −1
c
4
y
15
− 7y
14
+ ··· − 14y −1
c
5
, c
10
y
15
+ 12y
14
+ ··· − 6y −1
c
7
y
15
− 11y
14
+ ··· + 13y −1
c
8
, c
12
y
15
− 20y
14
+ ··· − 9y −1
c
9
y
15
− 53y
14
+ ··· + 38y −1
c
11
y
15
− 4y
14
+ ··· − 22y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945967 + 0.364350I
a = 0.447371 − 1.296300I
b = 0.54568 − 1.59008I
0.121261 + 0.585920I −6.11150 + 0.88466I
u = −0.945967 − 0.364350I
a = 0.447371 + 1.296300I
b = 0.54568 + 1.59008I
0.121261 − 0.585920I −6.11150 − 0.88466I
u = 0.910844 + 0.329867I
a = 0.63588 + 1.36871I
b = 0.434324 + 0.641040I
4.62454 + 1.37648I −3.28500 − 4.85991I
u = 0.910844 − 0.329867I
a = 0.63588 − 1.36871I
b = 0.434324 − 0.641040I
4.62454 − 1.37648I −3.28500 + 4.85991I
u = 0.483149 + 0.790685I
a = 0.552124 + 0.303102I
b = −0.006540 − 0.521541I
−3.32772 − 1.16564I −9.43576 + 1.29116I
u = 0.483149 − 0.790685I
a = 0.552124 − 0.303102I
b = −0.006540 + 0.521541I
−3.32772 + 1.16564I −9.43576 − 1.29116I
u = −0.858047 + 0.316539I
a = 0.85127 − 1.27055I
b = −0.183732 + 0.291743I
−0.26649 − 3.45017I −3.88329 + 5.28365I
u = −0.858047 − 0.316539I
a = 0.85127 + 1.27055I
b = −0.183732 − 0.291743I
−0.26649 + 3.45017I −3.88329 − 5.28365I
u = 1.047160 + 0.587752I
a = 0.157821 + 0.780474I
b = 1.54439 + 1.24046I
−1.69704 + 6.28081I −7.36459 − 5.95096I
u = 1.047160 − 0.587752I
a = 0.157821 − 0.780474I
b = 1.54439 − 1.24046I
−1.69704 − 6.28081I −7.36459 + 5.95096I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686348
a = 1.89062
b = −3.01568
−11.2981 −19.7640
u = −1.189670 + 0.653681I
a = 0.004952 − 0.642912I
b = 0.747056 − 0.985367I
1.40673 − 4.12593I −4.27551 + 5.62522I
u = −1.189670 − 0.653681I
a = 0.004952 + 0.642912I
b = 0.747056 + 0.985367I
1.40673 + 4.12593I −4.27551 − 5.62522I
u = −0.428593
a = 1.22503
b = −1.45207
−2.69518 −18.0200
u = 1.84731
a = −0.414496
b = −0.694610
−7.46852 5.49540
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 15u
14
+ ··· + 5u − 1)(u
35
+ 62u
34
+ ··· + 4330075u + 134689)
c
2
(u
15
− 3u
14
+ ··· + 3u − 1)(u
35
+ 2u
34
+ ··· + 4061u − 367)
c
3
(u
15
+ u
14
+ ··· + 3u + 1)(u
35
+ 2u
34
+ ··· − 7u + 1)
c
4
(u
15
+ u
14
+ ··· + 2u − 1)(u
35
+ 10u
34
+ ··· + 1712u + 311)
c
5
(u
15
+ 6u
13
+ ··· − 2u − 1)(u
35
− u
34
+ ··· + 672u − 23)
c
6
(u
15
+ 3u
14
+ ··· + 3u + 1)(u
35
+ 2u
34
+ ··· + 4061u − 367)
c
7
(u
15
− u
14
+ ··· + u + 1)(u
35
− 7u
33
+ ··· − 15u + 7)
c
8
(u
15
− 10u
13
+ ··· + u + 1)(u
35
+ 3u
34
+ ··· − 97u + 19)
c
9
(u
15
− 5u
14
+ ··· − 14u + 1)(u
35
+ 4u
34
+ ··· − 54708u + 6023)
c
10
(u
15
+ 6u
13
+ ··· − 2u + 1)(u
35
− u
34
+ ··· + 672u − 23)
c
11
(u
15
− 2u
13
+ ··· − 11u
2
− 1)(u
35
− 5u
34
+ ··· + 422u − 13)
c
12
(u
15
− 10u
13
+ ··· + u − 1)(u
35
+ 3u
34
+ ··· − 97u + 19)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 59y
14
+ ··· + 5y −1)
· (y
35
− 206y
34
+ ··· + 2682621801371y −18141126721)
c
2
, c
6
(y
15
− 15y
14
+ ··· + 5y −1)(y
35
− 62y
34
+ ··· + 4330075y −134689)
c
3
(y
15
+ 5y
14
+ ··· + 17y −1)(y
35
+ 2y
34
+ ··· + 63y −1)
c
4
(y
15
− 7y
14
+ ··· − 14y −1)(y
35
+ 10y
34
+ ··· − 500008y −96721)
c
5
, c
10
(y
15
+ 12y
14
+ ··· − 6y −1)(y
35
− 3y
34
+ ··· + 454344y −529)
c
7
(y
15
− 11y
14
+ ··· + 13y −1)(y
35
− 14y
34
+ ··· + 1023y −49)
c
8
, c
12
(y
15
− 20y
14
+ ··· − 9y −1)(y
35
− 55y
34
+ ··· + 11689y −361)
c
9
(y
15
− 53y
14
+ ··· + 38y −1)
· (y
35
− 164y
34
+ ··· − 17527853484y −36276529)
c
11
(y
15
− 4y
14
+ ··· − 22y −1)(y
35
+ 9y
34
+ ··· + 217500y −169)
17
