12n
0607
(K12n
0607
)
A knot diagram
1
Linearized knot diagam
3 7 12 8 9 2 11 5 3 7 4 10
Solving Sequence
4,8
5
9,11
12 3 7 2 1 6 10
c
4
c
8
c
11
c
3
c
7
c
2
c
1
c
6
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.98483 × 10
51
u
43
− 7.92706 × 10
51
u
42
+ ··· + 1.21780 × 10
52
b + 9.50729 × 10
52
,
− 6.39484 × 10
51
u
43
− 5.55868 × 10
51
u
42
+ ··· + 3.53162 × 10
53
a + 2.88768 × 10
53
,
u
44
+ 3u
43
+ ··· − 36u − 29i
I
u
2
= hu
13
− u
12
− 7u
11
+ 7u
10
+ 18u
9
− 18u
8
− 20u
7
+ 18u
6
+ 10u
5
− 2u
4
− 5u
3
− 4u
2
+ b + 2u + 1,
− u
14
+ 2u
13
+ 7u
12
− 16u
11
− 17u
10
+ 50u
9
+ 13u
8
− 74u
7
+ 6u
6
+ 50u
5
− 6u
4
− 12u
3
− 6u
2
+ a + 5,
u
15
− 2u
14
− 7u
13
+ 16u
12
+ 17u
11
− 50u
10
− 13u
9
+ 74u
8
− 6u
7
− 50u
6
+ 6u
5
+ 12u
4
+ 6u
3
+ u
2
− 5u − 1i
* 2 irreducible components of dim
C
= 0, with total 59 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−3.98 × 10
51
u
43
− 7.93 × 10
51
u
42
+ · · · + 1.22 × 10
52
b + 9.51 ×
10
52
, −6.39 × 10
51
u
43
− 5.56 × 10
51
u
42
+ · · · + 3.53 × 10
53
a + 2.89 ×
10
53
, u
44
+ 3u
43
+ · · · − 36u − 29i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
11
=
0.0181074u
43
+ 0.0157397u
42
+ ··· − 7.01705u − 0.817663
0.327216u
43
+ 0.650933u
42
+ ··· − 4.17363u − 7.80693
a
12
=
−0.309108u
43
− 0.635193u
42
+ ··· − 2.84342u + 6.98927
0.327216u
43
+ 0.650933u
42
+ ··· − 4.17363u − 7.80693
a
3
=
0.518338u
43
+ 1.03102u
42
+ ··· − 15.2327u − 13.7592
−0.303941u
43
− 0.580963u
42
+ ··· + 5.51276u + 8.99431
a
7
=
0.549754u
43
+ 1.13751u
42
+ ··· − 14.1047u − 14.7839
−0.193131u
43
− 0.327791u
42
+ ··· + 2.95340u + 6.21753
a
2
=
0.232795u
43
+ 0.476323u
42
+ ··· + 3.84795u − 8.66991
−0.371791u
43
− 0.806245u
42
+ ··· + 1.40362u + 10.8222
a
1
=
−0.350328u
43
− 0.903767u
42
+ ··· + 29.3966u + 10.2617
−0.431119u
43
− 0.755303u
42
+ ··· − 1.45502u + 5.30649
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
−0.00534609u
43
− 0.0637310u
42
+ ··· − 3.23886u − 5.04605
−0.0972752u
43
− 0.0928284u
42
+ ··· − 4.57450u + 2.98741
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.277792u
43
− 0.610725u
42
+ ··· + 9.19368u + 15.3613
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 54u
43
+ ··· + 157u + 1
c
2
, c
6
u
44
− 2u
43
+ ··· + 3u − 1
c
3
, c
11
u
44
− 3u
43
+ ··· − 25u + 1
c
4
, c
5
, c
8
u
44
− 3u
43
+ ··· + 36u − 29
c
7
, c
10
u
44
− 4u
43
+ ··· + 2004u − 563
c
9
u
44
− 2u
43
+ ··· + 2091u − 389
c
12
u
44
+ u
43
+ ··· + 1354u − 1081
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 114y
43
+ ··· − 6565y + 1
c
2
, c
6
y
44
− 54y
43
+ ··· − 157y + 1
c
3
, c
11
y
44
+ 43y
43
+ ··· − 415y + 1
c
4
, c
5
, c
8
y
44
− 43y
43
+ ··· + 154y + 841
c
7
, c
10
y
44
− 26y
43
+ ··· − 2861866y + 316969
c
9
y
44
+ 54y
43
+ ··· + 12410735y + 151321
c
12
y
44
+ 49y
43
+ ··· + 24190678y + 1168561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232314 + 0.891394I
a = −1.182840 + 0.641241I
b = −0.785573 + 0.181213I
−9.31236 + 3.20269I −1.63968 − 3.08905I
u = 0.232314 − 0.891394I
a = −1.182840 − 0.641241I
b = −0.785573 − 0.181213I
−9.31236 − 3.20269I −1.63968 + 3.08905I
u = −0.421682 + 0.772572I
a = −0.86640 − 1.32108I
b = 0.027933 − 1.313490I
4.97162 + 0.16549I 5.68850 + 0.34807I
u = −0.421682 − 0.772572I
a = −0.86640 + 1.32108I
b = 0.027933 + 1.313490I
4.97162 − 0.16549I 5.68850 − 0.34807I
u = −0.837269 + 0.017279I
a = −0.688236 − 0.510031I
b = 0.052866 + 0.391971I
1.359070 + 0.099848I 6.44713 + 0.44768I
u = −0.837269 − 0.017279I
a = −0.688236 + 0.510031I
b = 0.052866 − 0.391971I
1.359070 − 0.099848I 6.44713 − 0.44768I
u = −1.16381
a = 1.26734
b = 0.816752
2.85076 2.72130
u = −1.187230 + 0.325824I
a = 1.367400 + 0.224408I
b = 0.332131 + 1.373840I
7.30043 − 4.16721I 6.35771 + 3.21063I
u = −1.187230 − 0.325824I
a = 1.367400 − 0.224408I
b = 0.332131 − 1.373840I
7.30043 + 4.16721I 6.35771 − 3.21063I
u = 1.229270 + 0.131786I
a = 0.802568 + 0.161525I
b = 0.892070 − 0.665689I
2.18790 + 3.06008I 7.00945 − 4.71003I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.229270 − 0.131786I
a = 0.802568 − 0.161525I
b = 0.892070 + 0.665689I
2.18790 − 3.06008I 7.00945 + 4.71003I
u = −0.132670 + 0.748244I
a = 0.413490 + 1.238040I
b = 0.14531 + 1.46229I
4.65271 − 3.21249I 2.19622 + 5.43824I
u = −0.132670 − 0.748244I
a = 0.413490 − 1.238040I
b = 0.14531 − 1.46229I
4.65271 + 3.21249I 2.19622 − 5.43824I
u = 0.413623 + 1.194950I
a = −0.734599 + 0.755593I
b = −0.29763 + 1.39048I
−4.29060 + 7.07615I 2.00000 − 4.71324I
u = 0.413623 − 1.194950I
a = −0.734599 − 0.755593I
b = −0.29763 − 1.39048I
−4.29060 − 7.07615I 2.00000 + 4.71324I
u = 1.150740 + 0.556416I
a = 0.032760 − 0.925047I
b = −0.328510 − 0.006839I
−6.59118 + 1.93121I 0
u = 1.150740 − 0.556416I
a = 0.032760 + 0.925047I
b = −0.328510 + 0.006839I
−6.59118 − 1.93121I 0
u = −1.303890 + 0.194858I
a = −0.855836 + 0.581357I
b = −0.03406 − 1.56374I
8.41843 − 0.01026I 0
u = −1.303890 − 0.194858I
a = −0.855836 − 0.581357I
b = −0.03406 + 1.56374I
8.41843 + 0.01026I 0
u = 1.355820 + 0.181971I
a = 0.18635 − 1.43687I
b = −0.110848 + 1.367110I
−2.05757 + 3.46602I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.355820 − 0.181971I
a = 0.18635 + 1.43687I
b = −0.110848 − 1.367110I
−2.05757 − 3.46602I 0
u = −1.363940 + 0.224481I
a = −0.752199 − 0.014028I
b = −0.777456 + 1.110380I
−1.75499 − 1.31745I 0
u = −1.363940 − 0.224481I
a = −0.752199 + 0.014028I
b = −0.777456 − 1.110380I
−1.75499 + 1.31745I 0
u = 1.41075 + 0.33605I
a = 1.010620 + 0.344192I
b = 0.26866 − 1.59656I
9.67423 + 7.25773I 0
u = 1.41075 − 0.33605I
a = 1.010620 − 0.344192I
b = 0.26866 + 1.59656I
9.67423 − 7.25773I 0
u = 0.532070 + 0.131930I
a = 0.546352 + 0.863213I
b = 0.339438 − 0.970682I
0.83167 + 2.36657I −0.87472 − 6.65650I
u = 0.532070 − 0.131930I
a = 0.546352 − 0.863213I
b = 0.339438 + 0.970682I
0.83167 − 2.36657I −0.87472 + 6.65650I
u = −1.43896 + 0.36287I
a = −0.916232 + 0.157045I
b = −1.063760 − 0.354092I
−3.95592 − 7.70748I 0
u = −1.43896 − 0.36287I
a = −0.916232 − 0.157045I
b = −1.063760 + 0.354092I
−3.95592 + 7.70748I 0
u = 1.16519 + 0.93278I
a = 0.430958 − 0.453922I
b = −0.130936 − 1.336900I
−2.17172 + 0.20438I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16519 − 0.93278I
a = 0.430958 + 0.453922I
b = −0.130936 + 1.336900I
−2.17172 − 0.20438I 0
u = 1.50599
a = −0.890789
b = −0.701130
7.41930 0
u = −1.51357
a = 0.442367
b = 0.615094
4.10092 0
u = 0.093435 + 0.449887I
a = 0.704295 + 0.829058I
b = 0.537602 + 0.282669I
−1.096590 − 0.866114I −3.90601 + 3.40711I
u = 0.093435 − 0.449887I
a = 0.704295 − 0.829058I
b = 0.537602 − 0.282669I
−1.096590 + 0.866114I −3.90601 − 3.40711I
u = 0.044561 + 0.449061I
a = −2.51002 + 1.22441I
b = −0.445864 − 1.148650I
−6.42558 − 1.22817I 1.23064 + 0.76065I
u = 0.044561 − 0.449061I
a = −2.51002 − 1.22441I
b = −0.445864 + 1.148650I
−6.42558 + 1.22817I 1.23064 − 0.76065I
u = −0.437583
a = −1.73381
b = −0.0495045
0.995678 12.7470
u = 1.58442 + 0.22351I
a = −0.988026 − 0.209610I
b = −0.273784 + 1.367010I
11.87800 + 3.53758I 0
u = 1.58442 − 0.22351I
a = −0.988026 + 0.209610I
b = −0.273784 − 1.367010I
11.87800 − 3.53758I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57334 + 0.45526I
a = −1.096720 + 0.211977I
b = −0.40918 − 1.51901I
2.06161 − 12.99220I 0
u = −1.57334 − 0.45526I
a = −1.096720 − 0.211977I
b = −0.40918 + 1.51901I
2.06161 + 12.99220I 0
u = −1.64873 + 0.07955I
a = 0.484789 − 0.551045I
b = 0.220970 + 1.380770I
8.71374 − 3.02881I 0
u = −1.64873 − 0.07955I
a = 0.484789 + 0.551045I
b = 0.220970 − 1.380770I
8.71374 + 3.02881I 0
9
II.
I
u
2
= hu
13
−u
12
+· · ·+b+1, −u
14
+2u
13
+· · ·+a+5, u
15
−2u
14
+· · ·−5u−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
11
=
u
14
− 2u
13
+ ··· + 6u
2
− 5
−u
13
+ u
12
+ ··· − 2u − 1
a
12
=
u
14
− u
13
+ ··· + 2u − 4
−u
13
+ u
12
+ ··· − 2u − 1
a
3
=
u
11
− 7u
9
+ u
8
+ 18u
7
− 5u
6
− 20u
5
+ 7u
4
+ 8u
3
− u
2
− 1
−u
13
+ u
12
+ ··· − 4u − 1
a
7
=
−u
14
+ 2u
13
+ ··· + u + 5
−u
14
+ u
13
+ ··· − 4u
2
− 2u
a
2
=
u
14
− 2u
13
+ ··· + 4u − 4
u
14
− 2u
13
+ ··· + 3u
2
+ 3u
a
1
=
2u
14
− 2u
13
+ ··· + 6u − 3
u
14
− 2u
13
+ ··· + 7u
2
+ 3u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
10
=
u
5
− 3u
3
+ 2u
−u
13
+ u
12
+ ··· + 4u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
14
− 5u
13
− 13u
12
+ 39u
11
+ 26u
10
− 118u
9
− 2u
8
+ 166u
7
−
44u
6
− 101u
5
+ 29u
4
+ 17u
3
+ 10u
2
+ 2u − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 17u
14
+ ··· − 10u − 1
c
2
u
15
− u
14
+ ··· − 5u
2
− 1
c
3
u
15
+ 2u
14
+ ··· + 2u − 1
c
4
, c
5
u
15
− 2u
14
+ ··· − 5u − 1
c
6
u
15
+ u
14
+ ··· + 5u
2
+ 1
c
7
u
15
− 3u
14
+ ··· + 5u + 1
c
8
u
15
+ 2u
14
+ ··· − 5u + 1
c
9
u
15
− u
14
+ ··· − 4u − 1
c
10
u
15
+ 3u
14
+ ··· + 5u − 1
c
11
u
15
− 2u
14
+ ··· + 2u + 1
c
12
u
15
+ 3u
13
+ ··· − u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 25y
14
+ ··· + 166y −1
c
2
, c
6
y
15
− 17y
14
+ ··· − 10y −1
c
3
, c
11
y
15
+ 16y
14
+ ··· + 28y −1
c
4
, c
5
, c
8
y
15
− 18y
14
+ ··· + 27y −1
c
7
, c
10
y
15
− 9y
14
+ ··· + 11y −1
c
9
y
15
+ 7y
14
+ ··· + 38y −1
c
12
y
15
+ 6y
14
+ ··· + 7y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.934249 + 0.468327I
a = −0.078829 − 0.897138I
b = 0.285799 − 0.922611I
−5.20797 + 2.96284I 4.54487 − 3.34260I
u = 0.934249 − 0.468327I
a = −0.078829 + 0.897138I
b = 0.285799 + 0.922611I
−5.20797 − 2.96284I 4.54487 + 3.34260I
u = −0.869322 + 0.091277I
a = −0.268456 − 0.210742I
b = −0.457860 + 0.901308I
1.38423 + 1.85573I 6.45379 − 0.08829I
u = −0.869322 − 0.091277I
a = −0.268456 + 0.210742I
b = −0.457860 − 0.901308I
1.38423 − 1.85573I 6.45379 + 0.08829I
u = 1.104070 + 0.476456I
a = −0.340525 − 0.805960I
b = 0.292941 + 1.082610I
−4.60809 + 0.68620I 3.07033 − 0.28009I
u = 1.104070 − 0.476456I
a = −0.340525 + 0.805960I
b = 0.292941 − 1.082610I
−4.60809 − 0.68620I 3.07033 + 0.28009I
u = −0.143480 + 0.548716I
a = −0.30256 − 2.25452I
b = −0.16552 − 1.42393I
5.28846 − 2.33485I 6.06895 + 0.77612I
u = −0.143480 − 0.548716I
a = −0.30256 + 2.25452I
b = −0.16552 + 1.42393I
5.28846 + 2.33485I 6.06895 − 0.77612I
u = −1.45684
a = 0.770423
b = 0.184352
5.01004 8.46440
u = 1.52546
a = −0.869923
b = −0.935208
6.67613 2.28060
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51915 + 0.26492I
a = 0.880313 − 0.376323I
b = 0.05993 + 1.45415I
10.22370 − 0.90460I 8.60899 + 0.29397I
u = −1.51915 − 0.26492I
a = 0.880313 + 0.376323I
b = 0.05993 − 1.45415I
10.22370 + 0.90460I 8.60899 − 0.29397I
u = 1.55868 + 0.15458I
a = −0.923357 − 0.217594I
b = −0.40039 + 1.46959I
11.52840 + 4.89291I 7.41262 − 4.45672I
u = 1.55868 − 0.15458I
a = −0.923357 + 0.217594I
b = −0.40039 − 1.46959I
11.52840 − 4.89291I 7.41262 + 4.45672I
u = −0.198713
a = −4.83367
b = −0.478944
0.444342 −4.06410
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 17u
14
+ ··· − 10u − 1)(u
44
+ 54u
43
+ ··· + 157u + 1)
c
2
(u
15
− u
14
+ ··· − 5u
2
− 1)(u
44
− 2u
43
+ ··· + 3u − 1)
c
3
(u
15
+ 2u
14
+ ··· + 2u − 1)(u
44
− 3u
43
+ ··· − 25u + 1)
c
4
, c
5
(u
15
− 2u
14
+ ··· − 5u − 1)(u
44
− 3u
43
+ ··· + 36u − 29)
c
6
(u
15
+ u
14
+ ··· + 5u
2
+ 1)(u
44
− 2u
43
+ ··· + 3u − 1)
c
7
(u
15
− 3u
14
+ ··· + 5u + 1)(u
44
− 4u
43
+ ··· + 2004u − 563)
c
8
(u
15
+ 2u
14
+ ··· − 5u + 1)(u
44
− 3u
43
+ ··· + 36u − 29)
c
9
(u
15
− u
14
+ ··· − 4u − 1)(u
44
− 2u
43
+ ··· + 2091u − 389)
c
10
(u
15
+ 3u
14
+ ··· + 5u − 1)(u
44
− 4u
43
+ ··· + 2004u − 563)
c
11
(u
15
− 2u
14
+ ··· + 2u + 1)(u
44
− 3u
43
+ ··· − 25u + 1)
c
12
(u
15
+ 3u
13
+ ··· − u − 1)(u
44
+ u
43
+ ··· + 1354u − 1081)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 25y
14
+ ··· + 166y −1)(y
44
− 114y
43
+ ··· − 6565y + 1)
c
2
, c
6
(y
15
− 17y
14
+ ··· − 10y −1)(y
44
− 54y
43
+ ··· − 157y + 1)
c
3
, c
11
(y
15
+ 16y
14
+ ··· + 28y −1)(y
44
+ 43y
43
+ ··· − 415y + 1)
c
4
, c
5
, c
8
(y
15
− 18y
14
+ ··· + 27y −1)(y
44
− 43y
43
+ ··· + 154y + 841)
c
7
, c
10
(y
15
− 9y
14
+ ··· + 11y −1)(y
44
− 26y
43
+ ··· − 2861866y + 316969)
c
9
(y
15
+ 7y
14
+ ··· + 38y −1)
· (y
44
+ 54y
43
+ ··· + 12410735y + 151321)
c
12
(y
15
+ 6y
14
+ ··· + 7y −1)
· (y
44
+ 49y
43
+ ··· + 24190678y + 1168561)
16
