12n
0617
(K12n
0617
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 3 11 2 5 4 6 9 6
Solving Sequence
3,7
2 8
1,11
6 5 9 4 10 12
c
2
c
7
c
1
c
6
c
5
c
8
c
4
c
9
c
12
c
3
, c
10
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.03528 × 10
29
u
18
+ 2.20603 × 10
29
u
17
+ ··· + 1.42881 × 10
32
b − 1.94886 × 10
32
,
− 1.72871 × 10
32
u
18
+ 8.76867 × 10
31
u
17
+ ··· + 4.27215 × 10
34
a − 1.13938 × 10
35
,
u
19
+ 7u
17
+ ··· + 1241u + 299i
I
u
2
= h341324u
18
+ 743649u
17
+ ··· + 1775197b − 6939035,
− 4528372u
18
− 453288u
17
+ ··· + 5325591a − 8838485, u
19
+ 9u
17
+ ··· + 5u − 3i
I
u
3
= hb + 1, a + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 40 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−4.04 × 10
29
u
18
+ 2.21 × 10
29
u
17
+ · · · + 1.43 × 10
32
b − 1.95 ×
10
32
, −1.73 × 10
32
u
18
+ 8.77 × 10
31
u
17
+ · · · + 4.27 × 10
34
a − 1.14 ×
10
35
, u
19
+ 7u
17
+ · · · + 1241u + 299i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
0.00404647u
18
− 0.00205252u
17
+ ··· + 5.01173u + 2.66701
0.00282422u
18
− 0.00154396u
17
+ ··· + 3.08557u + 1.36397
a
6
=
0.00155291u
18
− 0.00147152u
17
+ ··· + 1.33246u + 0.620489
0.0000864825u
18
− 0.0000717914u
17
+ ··· + 0.294414u − 0.189493
a
5
=
0.00146643u
18
− 0.00139973u
17
+ ··· + 1.03805u + 0.809982
0.0000864825u
18
− 0.0000717914u
17
+ ··· + 0.294414u − 0.189493
a
9
=
0.000967454u
18
− 0.000263588u
17
+ ··· + 2.28928u + 0.510179
−0.00189360u
18
+ 0.00123884u
17
+ ··· − 1.20770u − 0.672255
a
4
=
−0.00114874u
18
+ 0.000504223u
17
+ ··· − 2.10077u + 0.100181
−0.00200460u
18
+ 0.00203579u
17
+ ··· − 2.29498u − 0.839146
a
10
=
−0.00755089u
18
+ 0.00505904u
17
+ ··· − 8.55381u − 3.61658
−0.00579600u
18
+ 0.00405386u
17
+ ··· − 6.14874u − 2.35891
a
12
=
0.00349992u
18
− 0.00250692u
17
+ ··· + 4.15098u + 2.32935
0.00305515u
18
− 0.00208189u
17
+ ··· + 3.55304u + 1.16410
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0112722u
18
− 0.00351862u
17
+ ··· + 14.6963u + 17.4566
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 14u
18
+ ··· + 674775u − 89401
c
2
, c
7
u
19
+ 7u
17
+ ··· + 1241u − 299
c
3
u
19
− 5u
18
+ ··· + 393u − 39
c
4
u
19
− 39u
17
+ ··· − 7472u + 3053
c
5
u
19
− u
18
+ ··· + 1014u − 111
c
6
, c
10
u
19
+ 3u
18
+ ··· − 360u + 108
c
8
u
19
− 4u
18
+ ··· + 783u − 789
c
9
u
19
+ u
18
+ ··· + 3474u + 4197
c
11
u
19
+ 4u
18
+ ··· − 12u − 3
c
12
u
19
+ 23u
17
+ ··· − 12u − 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 66y
18
+ ··· + 286804528071y −7992538801
c
2
, c
7
y
19
+ 14y
18
+ ··· + 674775y −89401
c
3
y
19
+ 7y
18
+ ··· + 57963y −1521
c
4
y
19
− 78y
18
+ ··· + 41701500y −9320809
c
5
y
19
− 47y
18
+ ··· + 419250y −12321
c
6
, c
10
y
19
− 37y
18
+ ··· − 80568y −11664
c
8
y
19
− 66y
18
+ ··· + 164937y −622521
c
9
y
19
− 47y
18
+ ··· + 31022328y −17614809
c
11
y
19
− 2y
18
+ ··· + 156y −9
c
12
y
19
+ 46y
18
+ ··· + 102y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791837 + 0.677469I
a = −0.619990 + 0.658481I
b = −1.173080 − 0.756067I
3.59219 − 0.75835I 12.53082 − 1.44797I
u = 0.791837 − 0.677469I
a = −0.619990 − 0.658481I
b = −1.173080 + 0.756067I
3.59219 + 0.75835I 12.53082 + 1.44797I
u = 0.668469 + 1.020450I
a = 0.517672 − 0.080176I
b = 1.98730 + 0.83213I
3.00456 + 6.40703I 1.37835 − 6.31753I
u = 0.668469 − 1.020450I
a = 0.517672 + 0.080176I
b = 1.98730 − 0.83213I
3.00456 − 6.40703I 1.37835 + 6.31753I
u = −0.709865 + 0.235609I
a = −1.24244 + 1.33477I
b = −1.233030 + 0.441203I
−1.78162 + 2.24100I 7.64182 − 5.49504I
u = −0.709865 − 0.235609I
a = −1.24244 − 1.33477I
b = −1.233030 − 0.441203I
−1.78162 − 2.24100I 7.64182 + 5.49504I
u = −0.443396 + 0.513943I
a = 0.464073 − 0.228663I
b = 0.114778 − 0.413169I
0.81666 − 1.62841I 5.50356 + 4.37919I
u = −0.443396 − 0.513943I
a = 0.464073 + 0.228663I
b = 0.114778 + 0.413169I
0.81666 + 1.62841I 5.50356 − 4.37919I
u = 0.220968 + 1.307740I
a = 0.559258 + 0.670454I
b = −0.221871 + 0.268759I
−5.42189 − 4.80173I 4.68015 + 6.13601I
u = 0.220968 − 1.307740I
a = 0.559258 − 0.670454I
b = −0.221871 − 0.268759I
−5.42189 + 4.80173I 4.68015 − 6.13601I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34390
a = −1.75903
b = −1.60303
7.99042 38.4260
u = −0.387274
a = 1.08970
b = 0.460660
0.789923 12.9890
u = 0.04812 + 2.23479I
a = 0.270283 − 0.668799I
b = 0.626673 + 0.094069I
−8.32137 + 0.26499I 5.83131 − 0.13665I
u = 0.04812 − 2.23479I
a = 0.270283 + 0.668799I
b = 0.626673 − 0.094069I
−8.32137 − 0.26499I 5.83131 + 0.13665I
u = −1.37830 + 2.10976I
a = −1.085980 − 0.344467I
b = −1.96178 + 0.21547I
16.1957 − 11.9447I 6.54103 + 4.41921I
u = −1.37830 − 2.10976I
a = −1.085980 + 0.344467I
b = −1.96178 − 0.21547I
16.1957 + 11.9447I 6.54103 − 4.41921I
u = −1.31382 + 2.41201I
a = 1.051960 + 0.419604I
b = 1.94078 − 0.12636I
16.2683 − 3.2857I 6.98967 + 0.65186I
u = −1.31382 − 2.41201I
a = 1.051960 − 0.419604I
b = 1.94078 + 0.12636I
16.2683 + 3.2857I 6.98967 − 0.65186I
u = 3.27534
a = 1.42832
b = 1.98283
11.6017 8.39160
6
II.
I
u
2
= h3.41 × 10
5
u
18
+ 7.44 × 10
5
u
17
+ · · · + 1.78 × 10
6
b − 6.94 × 10
6
, −4.53 ×
10
6
u
18
−4.53×10
5
u
17
+· · · +5.33×10
6
a−8.84×10
6
, u
19
+9u
17
+· · · +5u −3i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
0.850304u
18
+ 0.0851151u
17
+ ··· − 12.4234u + 1.65963
−0.192274u
18
− 0.418911u
17
+ ··· − 5.06973u + 3.90888
a
6
=
−1.28785u
18
− 0.428274u
17
+ ··· + 8.62193u + 0.381312
−0.543496u
18
+ 0.141234u
17
+ ··· + 4.84292u − 1.96536
a
5
=
−0.744352u
18
− 0.569507u
17
+ ··· + 3.77902u + 2.34667
−0.543496u
18
+ 0.141234u
17
+ ··· + 4.84292u − 1.96536
a
9
=
1.33678u
18
+ 0.0558727u
17
+ ··· − 10.8180u + 4.84550
−0.392077u
18
+ 0.00853821u
17
+ ··· + 3.50128u + 1.73453
a
4
=
−0.774842u
18
− 0.604057u
17
+ ··· + 6.25830u − 0.275189
0.00405983u
18
+ 0.179806u
17
+ ··· + 5.94869u − 2.53039
a
10
=
0.598889u
18
− 0.135703u
17
+ ··· − 12.8058u + 3.66527
−0.567102u
18
− 0.369487u
17
+ ··· − 1.56347u + 2.36723
a
12
=
0.658741u
18
+ 0.00570697u
17
+ ··· − 4.71566u + 1.45371
0.422567u
18
+ 0.0260112u
17
+ ··· − 5.98056u + 0.887322
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7917565
1775197
u
18
−
841506
1775197
u
17
+ ··· +
16153658
1775197
u +
29863827
1775197
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
19
− 18u
18
+ ··· − 125u + 9
c
2
u
19
+ 9u
17
+ ··· + 5u − 3
c
3
u
19
+ 4u
18
+ ··· − 2u − 1
c
4
u
19
+ 2u
18
+ ··· + 2u − 3
c
5
u
19
− 7u
18
+ ··· + 2u − 1
c
6
u
19
+ u
18
+ ··· − 2u + 1
c
7
u
19
+ 9u
17
+ ··· + 5u + 3
c
8
u
19
− 5u
18
+ ··· + 290u − 139
c
9
u
19
− 5u
18
+ ··· − 10u
2
− 1
c
10
u
19
− u
18
+ ··· − 2u − 1
c
11
u
19
− 6u
18
+ ··· − 2u + 1
c
12
u
19
+ 2u
18
+ ··· + 102u − 29
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 34y
18
+ ··· + 343y −81
c
2
, c
7
y
19
+ 18y
18
+ ··· − 125y −9
c
3
y
19
+ 8y
18
+ ··· − 10y −1
c
4
y
19
− 2y
18
+ ··· + 28y −9
c
5
y
19
− 3y
18
+ ··· + 2y −1
c
6
, c
10
y
19
+ y
18
+ ··· + 2y −1
c
8
y
19
− 25y
18
+ ··· − 100492y −19321
c
9
y
19
− 19y
18
+ ··· − 20y −1
c
11
y
19
+ 2y
18
+ ··· + 8y −1
c
12
y
19
+ 30y
18
+ ··· + 3270y −841
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.120264 + 0.951026I
a = −1.298530 − 0.086419I
b = −0.796550 + 0.567431I
−2.83073 + 0.47879I 6.36948 + 1.61646I
u = 0.120264 − 0.951026I
a = −1.298530 + 0.086419I
b = −0.796550 − 0.567431I
−2.83073 − 0.47879I 6.36948 − 1.61646I
u = −0.309080 + 0.822665I
a = −1.231090 + 0.430785I
b = −1.51871 + 0.39241I
−2.40859 + 1.79507I −0.97377 − 1.20868I
u = −0.309080 − 0.822665I
a = −1.231090 − 0.430785I
b = −1.51871 − 0.39241I
−2.40859 − 1.79507I −0.97377 + 1.20868I
u = −0.565790 + 0.993465I
a = 0.464701 + 0.325729I
b = 2.41965 − 0.62277I
3.48186 − 6.48285I 17.9524 + 9.5212I
u = −0.565790 − 0.993465I
a = 0.464701 − 0.325729I
b = 2.41965 + 0.62277I
3.48186 + 6.48285I 17.9524 − 9.5212I
u = −0.724005 + 1.005750I
a = −0.318967 − 0.481555I
b = −1.82441 + 0.68066I
3.49084 + 1.72012I 11.46074 − 5.25453I
u = −0.724005 − 1.005750I
a = −0.318967 + 0.481555I
b = −1.82441 − 0.68066I
3.49084 − 1.72012I 11.46074 + 5.25453I
u = 0.463872 + 0.485503I
a = 1.86693 + 1.26312I
b = 0.693431 − 0.123308I
−3.85974 + 5.13272I 7.67492 − 5.46593I
u = 0.463872 − 0.485503I
a = 1.86693 − 1.26312I
b = 0.693431 + 0.123308I
−3.85974 − 5.13272I 7.67492 + 5.46593I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.089855 + 1.336230I
a = −0.632293 + 0.749086I
b = −1.53550 − 0.37470I
−0.69955 + 3.25819I 5.31453 − 5.59109I
u = 0.089855 − 1.336230I
a = −0.632293 − 0.749086I
b = −1.53550 + 0.37470I
−0.69955 − 3.25819I 5.31453 + 5.59109I
u = 1.39341
a = 1.71022
b = 1.63158
7.82904 −11.7070
u = −0.11696 + 1.47623I
a = −0.271822 + 0.210703I
b = 0.092197 + 0.445873I
−5.77761 − 3.98981I 1.124365 − 0.741804I
u = −0.11696 − 1.47623I
a = −0.271822 − 0.210703I
b = 0.092197 − 0.445873I
−5.77761 + 3.98981I 1.124365 + 0.741804I
u = 0.147710 + 0.491095I
a = −0.00567 − 1.87177I
b = 1.138500 + 0.167993I
2.46837 − 2.43749I 10.16983 + 4.01127I
u = 0.147710 − 0.491095I
a = −0.00567 + 1.87177I
b = 1.138500 − 0.167993I
2.46837 + 2.43749I 10.16983 − 4.01127I
u = 0.19742 + 1.78925I
a = 0.404951 + 0.383658I
b = 0.515604 − 0.393143I
−9.29391 − 1.41791I −0.23891 + 4.94600I
u = 0.19742 − 1.78925I
a = 0.404951 − 0.383658I
b = 0.515604 + 0.393143I
−9.29391 + 1.41791I −0.23891 − 4.94600I
13
III. I
u
3
= hb + 1, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u − 1
a
8
=
u
u + 1
a
1
=
−u
−u − 1
a
11
=
−u − 1
−1
a
6
=
u + 1
u + 1
a
5
=
0
u + 1
a
9
=
u
0
a
4
=
1
1
a
10
=
0
−u
a
12
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
9
, c
12
u
2
+ u + 1
c
2
, c
7
, c
11
u
2
− u + 1
c
3
, c
6
, c
8
c
10
(u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
9
c
11
, c
12
y
2
+ y + 1
c
3
, c
6
, c
8
c
10
(y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = −1.00000
−1.64493 − 2.02988I 3.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = −1.00000
−1.64493 + 2.02988I 3.00000 − 3.46410I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
19
− 18u
18
+ ··· − 125u + 9)
· (u
19
+ 14u
18
+ ··· + 674775u − 89401)
c
2
(u
2
− u + 1)(u
19
+ 7u
17
+ ··· + 1241u − 299)(u
19
+ 9u
17
+ ··· + 5u − 3)
c
3
((u + 1)
2
)(u
19
− 5u
18
+ ··· + 393u − 39)(u
19
+ 4u
18
+ ··· − 2u − 1)
c
4
(u
2
+ u + 1)(u
19
− 39u
17
+ ··· − 7472u + 3053)
· (u
19
+ 2u
18
+ ··· + 2u − 3)
c
5
(u
2
+ u + 1)(u
19
− 7u
18
+ ··· + 2u − 1)(u
19
− u
18
+ ··· + 1014u − 111)
c
6
((u + 1)
2
)(u
19
+ u
18
+ ··· − 2u + 1)(u
19
+ 3u
18
+ ··· − 360u + 108)
c
7
(u
2
− u + 1)(u
19
+ 7u
17
+ ··· + 1241u − 299)(u
19
+ 9u
17
+ ··· + 5u + 3)
c
8
((u + 1)
2
)(u
19
− 5u
18
+ ··· + 290u − 139)
· (u
19
− 4u
18
+ ··· + 783u − 789)
c
9
(u
2
+ u + 1)(u
19
− 5u
18
+ ··· − 10u
2
− 1)
· (u
19
+ u
18
+ ··· + 3474u + 4197)
c
10
((u + 1)
2
)(u
19
− u
18
+ ··· − 2u − 1)(u
19
+ 3u
18
+ ··· − 360u + 108)
c
11
(u
2
− u + 1)(u
19
− 6u
18
+ ··· − 2u + 1)(u
19
+ 4u
18
+ ··· − 12u − 3)
c
12
(u
2
+ u + 1)(u
19
+ 23u
17
+ ··· − 12u − 3)(u
19
+ 2u
18
+ ··· + 102u − 29)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
19
− 66y
18
+ ··· + 2.86805 × 10
11
y −7.99254 × 10
9
)
· (y
19
− 34y
18
+ ··· + 343y −81)
c
2
, c
7
(y
2
+ y + 1)(y
19
+ 14y
18
+ ··· + 674775y −89401)
· (y
19
+ 18y
18
+ ··· − 125y −9)
c
3
((y −1)
2
)(y
19
+ 7y
18
+ ··· + 57963y −1521)
· (y
19
+ 8y
18
+ ··· − 10y −1)
c
4
(y
2
+ y + 1)(y
19
− 78y
18
+ ··· + 4.17015 × 10
7
y −9320809)
· (y
19
− 2y
18
+ ··· + 28y −9)
c
5
(y
2
+ y + 1)(y
19
− 47y
18
+ ··· + 419250y −12321)
· (y
19
− 3y
18
+ ··· + 2y −1)
c
6
, c
10
((y −1)
2
)(y
19
− 37y
18
+ ··· − 80568y −11664)
· (y
19
+ y
18
+ ··· + 2y −1)
c
8
((y −1)
2
)(y
19
− 66y
18
+ ··· + 164937y −622521)
· (y
19
− 25y
18
+ ··· − 100492y −19321)
c
9
(y
2
+ y + 1)(y
19
− 47y
18
+ ··· + 3.10223 × 10
7
y −1.76148 × 10
7
)
· (y
19
− 19y
18
+ ··· − 20y −1)
c
11
(y
2
+ y + 1)(y
19
− 2y
18
+ ··· + 156y −9)(y
19
+ 2y
18
+ ··· + 8y −1)
c
12
(y
2
+ y + 1)(y
19
+ 30y
18
+ ··· + 3270y −841)
· (y
19
+ 46y
18
+ ··· + 102y −9)
19
