12n
0210
(K12n
0210
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 10 4 11 5 8 6 9
Solving Sequence
8,11 4,9
3 7 10 6 12 1 5 2
c
8
c
3
c
7
c
10
c
6
c
11
c
12
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7u
16
− 135u
15
+ ··· + 256b − 55, 79u
16
− 1263u
15
+ ··· + 256a − 1471, u
17
− 16u
16
+ ··· − 11u − 1i
I
u
2
= h2202374768a
8
+ 4881742261799b + ··· + 3048286097801a + 1155541803378,
a
9
+ 3a
8
+ 20a
7
+ 27a
6
+ 39a
5
+ 35a
4
+ 54a
3
+ 232a
2
+ 63a + 557, u + 1i
I
u
3
= hb, u
7
− 2u
6
− 2u
5
+ 4u
4
+ 2u
3
− 2u
2
+ a − 2, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 34 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
= h7u
16
− 135u
15
+ · · · + 256b − 55, 79u
16
− 1263u
15
+ · · · + 256a −
1471, u
17
− 16u
16
+ · · · − 11u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−0.308594u
16
+ 4.93359u
15
+ ··· − 74.1016u + 5.74609
−0.0273438u
16
+ 0.527344u
15
+ ··· − 1.53906u + 0.214844
a
9
=
1
−u
2
a
3
=
−0.335938u
16
+ 5.46094u
15
+ ··· − 75.6406u + 5.96094
−0.0273438u
16
+ 0.527344u
15
+ ··· − 1.53906u + 0.214844
a
7
=
0.0898438u
16
− 1.35547u
15
+ ··· − 24.3828u − 4.87109
−0.0390625u
16
+ 0.578125u
15
+ ··· + 3.41406u − 0.0468750
a
10
=
−u
u
a
6
=
0.0546875u
16
− 0.843750u
15
+ ··· − 24.8203u − 4.90625
−0.00390625u
16
+ 0.0664063u
15
+ ··· + 3.85156u − 0.0117188
a
12
=
−0.375000u
16
+ 5.94531u
15
+ ··· + 5.21094u − 1.42969
0.0429688u
16
− 0.675781u
15
+ ··· + 3.79688u + 0.199219
a
1
=
−0.332031u
16
+ 5.27734u
15
+ ··· + 8.03125u − 1.28516
−0.0625000u
16
+ 0.617188u
15
+ ··· + 3.53906u + 0.179688
a
5
=
0.121094u
16
− 1.99609u
15
+ ··· + 25.7266u − 2.05859
0.0585938u
16
− 0.871094u
15
+ ··· + 0.726563u − 0.121094
a
2
=
−0.242188u
16
+ 3.99219u
15
+ ··· − 51.4531u + 4.11719
−0.0585938u
16
+ 0.871094u
15
+ ··· − 0.726563u + 0.121094
(ii) Obstruction class = −1
(iii) Cusp Shapes =
39
128
u
16
−
315
64
u
15
+ ··· +
2341
128
u −
531
64
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 37u
16
+ ··· + u + 1
c
2
, c
4
u
17
− 15u
16
+ ··· + 3u − 1
c
3
, c
7
u
17
+ u
16
+ ··· + 384u − 256
c
5
, c
11
u
17
+ 2u
16
+ ··· + 3u + 1
c
6
u
17
− 3u
16
+ ··· − 167922u − 192217
c
8
, c
10
u
17
+ 16u
16
+ ··· − 11u + 1
c
9
u
17
+ u
16
+ ··· − 512u − 512
c
12
u
17
− 6u
16
+ ··· − 19686u + 2393
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 57y
16
+ ··· − 7859y −1
c
2
, c
4
y
17
− 37y
16
+ ··· + y −1
c
3
, c
7
y
17
− 33y
16
+ ··· + 245760y −65536
c
5
, c
11
y
17
+ 12y
16
+ ··· + 25y −1
c
6
y
17
− 45y
16
+ ··· + 806894237728y −36947375089
c
8
, c
10
y
17
− 40y
16
+ ··· + 221y −1
c
9
y
17
− 39y
16
+ ··· + 3670016y −262144
c
12
y
17
− 38y
16
+ ··· + 475084108y −5726449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.135290 + 0.215005I
a = −0.040636 − 0.276979I
b = −0.149177 − 0.310693I
0.959539 − 1.013620I 4.00582 − 0.77460I
u = −1.135290 − 0.215005I
a = −0.040636 + 0.276979I
b = −0.149177 + 0.310693I
0.959539 + 1.013620I 4.00582 + 0.77460I
u = −0.706391
a = −0.663382
b = −0.408620
1.02663 10.5660
u = −0.405211 + 0.413893I
a = 0.45966 + 1.59259I
b = 0.690024 + 0.240704I
−1.52593 − 2.30609I 0.84073 + 4.41351I
u = −0.405211 − 0.413893I
a = 0.45966 − 1.59259I
b = 0.690024 − 0.240704I
−1.52593 + 2.30609I 0.84073 − 4.41351I
u = 0.079841 + 0.128622I
a = −1.81733 − 9.04439I
b = −0.634179 + 0.647207I
−4.28789 − 1.16759I −4.15148 − 0.42617I
u = 0.079841 − 0.128622I
a = −1.81733 + 9.04439I
b = −0.634179 − 0.647207I
−4.28789 + 1.16759I −4.15148 + 0.42617I
u = −0.0625865
a = 10.3787
b = 0.442272
−1.26971 −9.85470
u = 1.95602 + 1.08672I
a = −1.45768 + 3.13444I
b = 2.02549 − 2.27905I
19.0196 + 12.9458I 0.98224 − 5.00778I
u = 1.95602 − 1.08672I
a = −1.45768 − 3.13444I
b = 2.02549 + 2.27905I
19.0196 − 12.9458I 0.98224 + 5.00778I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.05027 + 1.05712I
a = 1.67587 − 2.90707I
b = −2.13688 + 2.10608I
−16.2212 + 7.3387I 3.75665 − 2.42096I
u = 2.05027 − 1.05712I
a = 1.67587 + 2.90707I
b = −2.13688 − 2.10608I
−16.2212 − 7.3387I 3.75665 + 2.42096I
u = 2.10513 + 0.95501I
a = −2.03508 + 2.83272I
b = 2.36097 − 2.01644I
19.0497 + 1.6784I 0.985857 + 0.191287I
u = 2.10513 − 0.95501I
a = −2.03508 − 2.83272I
b = 2.36097 + 2.01644I
19.0497 − 1.6784I 0.985857 − 0.191287I
u = 2.46829 + 0.15035I
a = 3.58204 − 0.48409I
b = −3.25130 + 0.32944I
−0.61891 + 5.84472I 0.94829 − 2.62397I
u = 2.46829 − 0.15035I
a = 3.58204 + 0.48409I
b = −3.25130 − 0.32944I
−0.61891 − 5.84472I 0.94829 + 2.62397I
u = 2.53085
a = −3.44904
b = 3.15648
3.68181 3.55300
6
II. I
u
2
= h4.88 × 10
12
b + 2.20 × 10
9
a
8
+ · · · + 3.05 × 10
12
a + 1.16 × 10
12
, a
9
+
3a
8
+ · · · + 63a + 557, u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
−1
a
4
=
a
−0.000451145a
8
− 0.00112473a
7
+ ··· − 0.624426a − 0.236707
a
9
=
1
−1
a
3
=
−0.000451145a
8
− 0.00112473a
7
+ ··· + 0.375574a − 0.236707
−0.000451145a
8
− 0.00112473a
7
+ ··· − 0.624426a − 0.236707
a
7
=
−0.000228701a
8
+ 0.00198520a
7
+ ··· + 0.208285a + 0.748712
−0.000596483a
8
− 0.00336172a
7
+ ··· − 0.154624a + 0.0980179
a
10
=
1
−1
a
6
=
0.000596483a
8
+ 0.00336172a
7
+ ··· + 0.154624a − 0.0980179
−0.00142167a
8
− 0.00473825a
7
+ ··· − 0.100963a + 0.944748
a
12
=
0.00210365a
8
+ 0.00495200a
7
+ ··· + 0.412355a + 0.509691
−0.00180466a
8
− 0.00643986a
7
+ ··· − 0.540321a − 1.18749
a
1
=
0.00240264a
8
+ 0.00346415a
7
+ ··· + 0.284388a − 0.168104
−0.00210365a
8
− 0.00495200a
7
+ ··· − 0.412355a − 0.509691
a
5
=
0.00391662a
8
+ 0.00543003a
7
+ ··· + 0.764313a − 0.311168
−0.00391662a
8
− 0.00543003a
7
+ ··· − 0.764313a + 0.311168
a
2
=
0.00301433a
8
+ 0.00318056a
7
+ ··· + 0.515461a − 0.784582
−0.00391662a
8
− 0.00543003a
7
+ ··· − 0.764313a + 0.311168
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
14902841729
4881742261799
a
8
+
166367890500
4881742261799
a
7
+ ··· +
12350657617094
4881742261799
a +
35285795123487
4881742261799
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
6
u
9
+ 2u
8
+ 5u
7
+ 22u
6
+ 52u
5
+ 63u
4
+ 41u
3
+ 10u
2
− 2u − 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
(u + 1)
9
c
9
u
9
c
10
(u − 1)
9
c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
12
u
9
+ 3u
8
+ 3u
7
− 2u
6
+ u
5
− 9u
4
+ 3u
3
+ 2u − 1
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
y
9
+ 6y
8
+ ··· + 24y −1
c
8
, c
10
(y −1)
9
c
9
y
9
c
12
y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.06261 + 1.45114I
b = −0.140343 − 0.966856I
3.42837 − 2.09337I 7.05683 + 6.62869I
u = −1.00000
a = 0.06261 − 1.45114I
b = −0.140343 + 0.966856I
3.42837 + 2.09337I 7.05683 − 6.62869I
u = −1.00000
a = 1.21902 + 0.95904I
b = −0.628449 − 0.875112I
1.02799 − 2.45442I 3.88318 + 3.00529I
u = −1.00000
a = 1.21902 − 0.95904I
b = −0.628449 + 0.875112I
1.02799 + 2.45442I 3.88318 − 3.00529I
u = −1.00000
a = −1.91873
b = −0.512358
0.446489 −13.4320
u = −1.00000
a = −1.03999 + 1.61486I
b = 0.728966 − 0.986295I
−1.95319 + 7.08493I −2.13339 − 8.87891I
u = −1.00000
a = −1.03999 − 1.61486I
b = 0.728966 + 0.986295I
−1.95319 − 7.08493I −2.13339 + 8.87891I
u = −1.00000
a = −0.78228 + 3.85888I
b = 0.796005 − 0.733148I
−2.72642 − 1.33617I 1.90921 − 3.07774I
u = −1.00000
a = −0.78228 − 3.85888I
b = 0.796005 + 0.733148I
−2.72642 + 1.33617I 1.90921 + 3.07774I
12
III.
I
u
3
= hb, u
7
−2u
6
−2u
5
+4u
4
+2u
3
−2u
2
+a−2, u
8
−u
7
−3u
6
+2u
5
+3u
4
−2u−1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
4
=
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ 2u
2
+ 2
0
a
9
=
1
−u
2
a
3
=
−u
7
+ 2u
6
+ 2u
5
− 4u
4
− 2u
3
+ 2u
2
+ 2
0
a
7
=
1
0
a
10
=
−u
u
a
6
=
−u
2
+ 1
u
2
a
12
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
1
=
u
7
− 2u
5
+ 2u
−u
7
− u
6
+ 2u
5
+ 3u
4
− 2u
2
− 2u − 1
a
5
=
−u
7
+ 2u
5
− 2u
u
7
+ u
6
− 2u
5
− 3u
4
+ 2u
2
+ 2u + 1
a
2
=
2u
6
− 4u
4
− 2u
3
+ 2u
2
+ 2u + 2
−u
7
− u
6
+ 2u
5
+ 3u
4
− 2u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
7
+ 9u
6
− u
5
− 22u
4
− 3u
3
+ 12u
2
+ 13u + 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
, c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
, c
12
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = 1.21928 − 2.03110I
b = 0
−0.604279 − 1.131230I −3.30729 − 4.28492I
u = −1.180120 − 0.268597I
a = 1.21928 + 2.03110I
b = 0
−0.604279 + 1.131230I −3.30729 + 4.28492I
u = −0.108090 + 0.747508I
a = −1.230330 − 0.083902I
b = 0
−3.80435 − 2.57849I −1.56478 + 3.68514I
u = −0.108090 − 0.747508I
a = −1.230330 + 0.083902I
b = 0
−3.80435 + 2.57849I −1.56478 − 3.68514I
u = 1.37100
a = 0.337834
b = 0
4.85780 14.7400
u = 1.334530 + 0.318930I
a = −0.370895 − 0.073482I
b = 0
0.73474 + 6.44354I 8.02705 − 7.90662I
u = 1.334530 − 0.318930I
a = −0.370895 + 0.073482I
b = 0
0.73474 − 6.44354I 8.02705 + 7.90662I
u = −0.463640
a = 2.42604
b = 0
−0.799899 9.95010
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
17
+ 37u
16
+ ··· + u + 1)
c
2
(u − 1)
8
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
17
− 15u
16
+ ··· + 3u − 1)
c
3
u
8
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
17
+ u
16
+ ··· + 384u − 256)
c
4
(u + 1)
8
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
17
− 15u
16
+ ··· + 3u − 1)
c
5
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
17
+ 2u
16
+ ··· + 3u + 1)
c
6
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
9
+ 2u
8
+ 5u
7
+ 22u
6
+ 52u
5
+ 63u
4
+ 41u
3
+ 10u
2
− 2u − 1)
· (u
17
− 3u
16
+ ··· − 167922u − 192217)
c
7
u
8
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
17
+ u
16
+ ··· + 384u − 256)
c
8
(u + 1)
9
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
17
+ 16u
16
+ ··· − 11u + 1)
c
9
u
9
(u
8
− u
7
+ ··· + 2u − 1)(u
17
+ u
16
+ ··· − 512u − 512)
c
10
(u − 1)
9
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
17
+ 16u
16
+ ··· − 11u + 1)
c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
17
+ 2u
16
+ ··· + 3u + 1)
c
12
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
9
+ 3u
8
+ 3u
7
− 2u
6
+ u
5
− 9u
4
+ 3u
3
+ 2u − 1)
· (u
17
− 6u
16
+ ··· − 19686u + 2393)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
17
− 57y
16
+ ··· − 7859y −1)
c
2
, c
4
(y −1)
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
17
− 37y
16
+ ··· + y −1)
c
3
, c
7
y
8
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
17
− 33y
16
+ ··· + 245760y −65536)
c
5
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
17
+ 12y
16
+ ··· + 25y −1)
c
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
9
+ 6y
8
+ ··· + 24y −1)
· (y
17
− 45y
16
+ ··· + 806894237728y −36947375089)
c
8
, c
10
(y −1)
9
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
17
− 40y
16
+ ··· + 221y −1)
c
9
y
9
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
17
− 39y
16
+ ··· + 3670016y −262144)
c
12
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
9
− 3y
8
+ 23y
7
+ 62y
6
− 13y
5
− 57y
4
+ 9y
3
− 6y
2
+ 4y −1)
· (y
17
− 38y
16
+ ··· + 475084108y −5726449)
18
