12n
0095
(K12n
0095
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 9 3 11 6 1 12 8 10
Solving Sequence
7,11
8
3,12
6 4 9 5 2 10 1
c
7
c
11
c
6
c
3
c
8
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.55792 × 10
15
u
51
− 2.00897 × 10
15
u
50
+ ··· + 5.52629 × 10
15
b − 2.66316 × 10
15
,
7.54263 × 10
16
u
51
+ 9.53580 × 10
16
u
50
+ ··· + 5.52629 × 10
15
a + 1.22505 × 10
17
, u
52
+ 2u
51
+ ··· − u + 1i
I
u
2
= hb, −3u
4
− u
3
+ u
2
+ a + 3u − 4, u
5
+ u
4
− u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 57 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−1.56×10
15
u
51
−2.01×10
15
u
50
+· · ·+5.53×10
15
b−2.66×10
15
, 7.54×
10
16
u
51
+9.54×10
16
u
50
+· · ·+5.53×10
15
a+1.23×10
17
, u
52
+2u
51
+· · ·−u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−13.6486u
51
− 17.2554u
50
+ ··· + 48.2225u − 22.1677
0.281910u
51
+ 0.363530u
50
+ ··· + 0.677139u + 0.481908
a
12
=
u
−u
3
+ u
a
6
=
3.42922u
51
+ 4.63065u
50
+ ··· − 12.3515u + 3.71531
−0.827825u
51
− 1.65459u
50
+ ··· + 1.54173u − 0.827822
a
4
=
−11.4441u
51
− 15.0654u
50
+ ··· + 49.3203u − 21.9727
−2.53719u
51
− 5.27177u
50
+ ··· + 4.90575u − 2.33717
a
9
=
−u
7
− 2u
3
u
9
− u
7
+ 3u
5
− 2u
3
+ u
a
5
=
2.03316u
51
+ 2.82064u
50
+ ··· − 9.13837u + 2.51030
0.154269u
51
− 0.0905893u
50
+ ··· − 1.03142u + 0.554276
a
2
=
−11.7150u
51
− 14.8966u
50
+ ··· + 44.4993u − 21.1883
−1.02663u
51
− 2.45529u
50
+ ··· + 2.73997u − 0.626644
a
10
=
−u
3
u
5
− u
3
+ u
a
1
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
820656989676521272
5526285094326109
u
51
−
1059949487703439182
5526285094326109
u
50
+ ··· +
2787762104200863436
5526285094326109
u −
1166602438311091155
5526285094326109
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 22u
51
+ ··· + 621u + 1
c
2
, c
4
u
52
− 6u
51
+ ··· + 33u − 1
c
3
, c
6
u
52
+ 7u
51
+ ··· − 1000u
2
+ 32
c
5
, c
8
u
52
+ 2u
51
+ ··· − u − 1
c
7
, c
11
u
52
− 2u
51
+ ··· + u + 1
c
9
, c
10
, c
12
u
52
− 14u
51
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
+ 22y
51
+ ··· − 353149y + 1
c
2
, c
4
y
52
− 22y
51
+ ··· − 621y + 1
c
3
, c
6
y
52
− 33y
51
+ ··· − 64000y + 1024
c
5
, c
8
y
52
+ 14y
51
+ ··· − 3y + 1
c
7
, c
11
y
52
− 14y
51
+ ··· − 3y + 1
c
9
, c
10
, c
12
y
52
+ 50y
51
+ ··· − 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016700 + 0.228557I
a = 2.72812 − 0.43036I
b = −1.51670 − 0.32511I
6.00023 + 3.38638I 10.71662 − 4.19927I
u = 1.016700 − 0.228557I
a = 2.72812 + 0.43036I
b = −1.51670 + 0.32511I
6.00023 − 3.38638I 10.71662 + 4.19927I
u = 0.823924 + 0.656561I
a = −0.484808 + 0.298032I
b = 0.495386 − 0.141113I
−2.12988 + 2.49537I 6.00000 − 4.33112I
u = 0.823924 − 0.656561I
a = −0.484808 − 0.298032I
b = 0.495386 + 0.141113I
−2.12988 − 2.49537I 6.00000 + 4.33112I
u = 0.671451 + 0.825112I
a = −0.172842 + 0.134029I
b = 0.986460 + 0.139928I
−1.94375 + 3.12402I 6.00000 − 5.50076I
u = 0.671451 − 0.825112I
a = −0.172842 − 0.134029I
b = 0.986460 − 0.139928I
−1.94375 − 3.12402I 6.00000 + 5.50076I
u = −1.019540 + 0.324660I
a = 1.95326 + 1.46461I
b = −1.375970 + 0.072193I
5.42581 − 2.84612I 6.00000 + 4.09308I
u = −1.019540 − 0.324660I
a = 1.95326 − 1.46461I
b = −1.375970 − 0.072193I
5.42581 + 2.84612I 6.00000 − 4.09308I
u = −1.067180 + 0.215417I
a = −2.01848 − 1.25744I
b = 1.328520 + 0.303236I
4.97698 + 2.99566I 0
u = −1.067180 − 0.215417I
a = −2.01848 + 1.25744I
b = 1.328520 − 0.303236I
4.97698 − 2.99566I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.061390 + 0.321917I
a = −2.57122 + 0.55153I
b = 1.41215 + 0.59209I
4.33370 + 9.78968I 0
u = 1.061390 − 0.321917I
a = −2.57122 − 0.55153I
b = 1.41215 − 0.59209I
4.33370 − 9.78968I 0
u = −0.763594 + 0.816084I
a = −0.008414 + 0.288534I
b = −1.43047 − 0.79666I
−0.81354 + 2.41917I 0
u = −0.763594 − 0.816084I
a = −0.008414 − 0.288534I
b = −1.43047 + 0.79666I
−0.81354 − 2.41917I 0
u = 0.829935 + 0.258628I
a = 0.589363 + 1.277800I
b = −0.015897 − 1.194290I
−0.05696 + 3.40025I 6.00000 − 9.58209I
u = 0.829935 − 0.258628I
a = 0.589363 − 1.277800I
b = −0.015897 + 1.194290I
−0.05696 − 3.40025I 6.00000 + 9.58209I
u = 0.856907 + 0.769828I
a = 0.98921 − 2.18567I
b = −0.330878 − 0.523016I
−4.80216 + 2.18470I 0
u = 0.856907 − 0.769828I
a = 0.98921 + 2.18567I
b = −0.330878 + 0.523016I
−4.80216 − 2.18470I 0
u = −0.843215 + 0.806418I
a = −1.119580 − 0.651664I
b = 0.55289 − 1.60337I
−6.35990 + 0.70710I 0
u = −0.843215 − 0.806418I
a = −1.119580 + 0.651664I
b = 0.55289 + 1.60337I
−6.35990 − 0.70710I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.815699 + 0.149945I
a = −1.65430 − 0.16657I
b = −0.000259 − 0.620302I
0.447505 − 0.352674I 7.09954 + 0.50809I
u = −0.815699 − 0.149945I
a = −1.65430 + 0.16657I
b = −0.000259 + 0.620302I
0.447505 + 0.352674I 7.09954 − 0.50809I
u = −0.770843 + 0.892832I
a = −0.1123930 + 0.0783246I
b = 1.32848 + 0.83591I
−3.73354 + 8.81773I 0
u = −0.770843 − 0.892832I
a = −0.1123930 − 0.0783246I
b = 1.32848 − 0.83591I
−3.73354 − 8.81773I 0
u = 0.906595 + 0.760633I
a = −0.23718 + 1.51693I
b = −0.277122 + 0.612791I
−4.64898 + 3.59909I 0
u = 0.906595 − 0.760633I
a = −0.23718 − 1.51693I
b = −0.277122 − 0.612791I
−4.64898 − 3.59909I 0
u = 0.797815 + 0.885175I
a = −0.096669 + 0.136453I
b = −1.090370 + 0.347341I
−2.52853 − 1.37505I 0
u = 0.797815 − 0.885175I
a = −0.096669 − 0.136453I
b = −1.090370 − 0.347341I
−2.52853 + 1.37505I 0
u = −0.889829 + 0.799881I
a = −0.98021 − 1.11750I
b = 1.70487 + 0.08098I
−7.98633 − 2.99814I 0
u = −0.889829 − 0.799881I
a = −0.98021 + 1.11750I
b = 1.70487 − 0.08098I
−7.98633 + 2.99814I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.929422 + 0.783147I
a = 1.103730 − 0.206306I
b = 0.41722 + 1.67850I
−6.09427 − 6.67098I 0
u = −0.929422 − 0.783147I
a = 1.103730 + 0.206306I
b = 0.41722 − 1.67850I
−6.09427 + 6.67098I 0
u = 1.003030 + 0.726539I
a = −0.665678 + 1.244470I
b = 1.095740 + 0.014542I
−0.95751 + 2.64231I 0
u = 1.003030 − 0.726539I
a = −0.665678 − 1.244470I
b = 1.095740 − 0.014542I
−0.95751 − 2.64231I 0
u = 0.083300 + 0.756806I
a = −0.131209 − 0.090120I
b = 1.241510 − 0.510914I
1.11117 − 6.07445I 2.28728 + 4.99398I
u = 0.083300 − 0.756806I
a = −0.131209 + 0.090120I
b = 1.241510 + 0.510914I
1.11117 + 6.07445I 2.28728 − 4.99398I
u = −0.980620 + 0.759025I
a = 1.48052 + 1.47301I
b = −1.57827 + 0.76747I
−0.15374 − 8.33088I 0
u = −0.980620 − 0.759025I
a = 1.48052 − 1.47301I
b = −1.57827 − 0.76747I
−0.15374 + 8.33088I 0
u = 0.996725 + 0.804943I
a = 0.69605 − 1.42479I
b = −1.168190 − 0.406129I
−1.90172 + 7.64393I 0
u = 0.996725 − 0.804943I
a = 0.69605 + 1.42479I
b = −1.168190 + 0.406129I
−1.90172 − 7.64393I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011220 + 0.795658I
a = −1.51176 − 1.46953I
b = 1.39466 − 0.85421I
−2.9794 − 15.0713I 0
u = −1.011220 − 0.795658I
a = −1.51176 + 1.46953I
b = 1.39466 + 0.85421I
−2.9794 + 15.0713I 0
u = −0.698273
a = 8.42855
b = −0.206931
−0.693373 108.630
u = −0.939941 + 0.914479I
a = 0.055763 − 0.275557I
b = 0.491327 − 0.017560I
−12.27210 − 3.36480I 0
u = −0.939941 − 0.914479I
a = 0.055763 + 0.275557I
b = 0.491327 + 0.017560I
−12.27210 + 3.36480I 0
u = −0.095263 + 0.656941I
a = −0.107033 − 0.214568I
b = −1.209340 + 0.178713I
2.53391 − 0.61006I 4.82513 + 0.42624I
u = −0.095263 − 0.656941I
a = −0.107033 + 0.214568I
b = −1.209340 − 0.178713I
2.53391 + 0.61006I 4.82513 − 0.42624I
u = 0.581935 + 0.257196I
a = −2.52005 + 0.53236I
b = 0.898782 − 0.422027I
−2.37470 + 1.17859I −0.43614 − 4.23765I
u = 0.581935 − 0.257196I
a = −2.52005 − 0.53236I
b = 0.898782 + 0.422027I
−2.37470 − 1.17859I −0.43614 + 4.23765I
u = −0.607842
a = −0.654513
b = −0.202346
0.846925 12.0260
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.149713 + 0.331460I
a = −2.09121 + 1.21238I
b = 0.350124 + 0.778422I
−1.82510 − 1.05647I −2.50964 + 1.48510I
u = 0.149713 − 0.331460I
a = −2.09121 − 1.21238I
b = 0.350124 − 0.778422I
−1.82510 + 1.05647I −2.50964 − 1.48510I
10
II. I
u
2
= hb, −3u
4
− u
3
+ u
2
+ a + 3u − 4, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
3u
4
+ u
3
− u
2
− 3u + 4
0
a
12
=
u
−u
3
+ u
a
6
=
1
0
a
4
=
3u
4
+ u
3
− u
2
− 3u + 4
0
a
9
=
−u
2
+ 1
−u
2
a
5
=
u
4
− u
2
+ 1
u
4
a
2
=
2u
4
+ u
3
− 3u + 3
−u
4
a
10
=
−u
3
−u
4
− u
3
+ u
2
− 1
a
1
=
−u
4
+ u
2
− 1
−u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
4
− 7u
3
− u
2
+ 10u − 19
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
6
u
5
c
4
(u + 1)
5
c
5
, c
9
, c
10
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
7
u
5
+ u
4
− u
2
+ u + 1
c
8
, c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
11
u
5
− u
4
+ u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
, c
8
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
7
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = −1.036940 − 0.588205I
b = 0
−3.46474 + 2.21397I −1.97599 − 4.83884I
u = 0.758138 − 0.584034I
a = −1.036940 + 0.588205I
b = 0
−3.46474 − 2.21397I −1.97599 + 4.83884I
u = −0.935538 + 0.903908I
a = −0.348360 + 0.023996I
b = 0
−12.60320 − 3.33174I −10.16346 + 1.25445I
u = −0.935538 − 0.903908I
a = −0.348360 − 0.023996I
b = 0
−12.60320 + 3.33174I −10.16346 − 1.25445I
u = −0.645200
a = 5.77061
b = 0
−0.762751 −25.7210
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
52
+ 22u
51
+ ··· + 621u + 1)
c
2
((u − 1)
5
)(u
52
− 6u
51
+ ··· + 33u − 1)
c
3
, c
6
u
5
(u
52
+ 7u
51
+ ··· − 1000u
2
+ 32)
c
4
((u + 1)
5
)(u
52
− 6u
51
+ ··· + 33u − 1)
c
5
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
52
+ 2u
51
+ ··· − u − 1)
c
7
(u
5
+ u
4
− u
2
+ u + 1)(u
52
− 2u
51
+ ··· + u + 1)
c
8
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
52
+ 2u
51
+ ··· − u − 1)
c
9
, c
10
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
52
− 14u
51
+ ··· − 3u + 1)
c
11
(u
5
− u
4
+ u
2
+ u − 1)(u
52
− 2u
51
+ ··· + u + 1)
c
12
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
52
− 14u
51
+ ··· − 3u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
52
+ 22y
51
+ ··· − 353149y + 1)
c
2
, c
4
((y −1)
5
)(y
52
− 22y
51
+ ··· − 621y + 1)
c
3
, c
6
y
5
(y
52
− 33y
51
+ ··· − 64000y + 1024)
c
5
, c
8
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
52
+ 14y
51
+ ··· − 3y + 1)
c
7
, c
11
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)(y
52
− 14y
51
+ ··· − 3y + 1)
c
9
, c
10
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
52
+ 50y
51
+ ··· − 3y + 1)
16
