12n
0194
(K12n
0194
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 11 3 12 1 7 6 9
Solving Sequence
7,10 4,11
3 8 6 12 5 2 1 9
c
10
c
3
c
7
c
6
c
11
c
5
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.49466 × 10
24
u
47
− 6.85289 × 10
24
u
46
+ ··· + 3.04521 × 10
25
b + 1.76125 × 10
25
,
− 7.26110 × 10
24
u
47
− 1.15653 × 10
25
u
46
+ ··· + 1.01507 × 10
25
a − 1.84956 × 10
25
, u
48
+ 2u
47
+ ··· + 2u + 1i
I
u
2
= hu
5
− 2u
4
+ 5u
3
− 4u
2
+ 3b + 3u − 1, a, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 54 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
= h1.49×10
24
u
47
−6.85×10
24
u
46
+· · ·+3.05×10
25
b+1.76×10
25
, −7.26×
10
24
u
47
−1.16×10
25
u
46
+· · ·+1.02×10
25
a−1.85×10
25
, u
48
+2u
47
+· · ·+2u+1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0.715331u
47
+ 1.13936u
46
+ ··· + 3.21104u + 1.82211
−0.0490826u
47
+ 0.225039u
46
+ ··· − 0.120857u − 0.578369
a
11
=
1
u
2
a
3
=
0.715331u
47
+ 1.13936u
46
+ ··· + 3.21104u + 1.82211
0.101581u
47
+ 0.453744u
46
+ ··· − 0.253590u − 0.287070
a
8
=
1.02410u
47
+ 1.70903u
46
+ ··· − 0.663879u + 2.04259
−0.142572u
47
− 0.142410u
46
+ ··· − 0.481991u − 0.617041
a
6
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
−0.298901u
47
− 0.182262u
46
+ ··· − 0.828027u − 1.26129
a
1
=
−1.47597u
47
− 2.15015u
46
+ ··· + 0.591045u − 4.37391
−0.438563u
47
− 0.494226u
46
+ ··· + 0.0633886u − 1.37511
a
9
=
1.86762u
47
+ 3.01187u
46
+ ··· − 0.400029u + 3.80060
0.297398u
47
+ 0.622443u
46
+ ··· − 0.229865u + 0.150066
(ii) Obstruction class = −1
(iii) Cusp Shapes =
24180032660295489705345802
30452057674032287811487569
u
47
+
40784802453743783652603914
30452057674032287811487569
u
46
+
··· +
461511678046237890102384932
30452057674032287811487569
u −
260983278311950731604691300
30452057674032287811487569
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 17u
47
+ ··· + 7933u + 81
c
2
, c
4
u
48
− 7u
47
+ ··· − 133u + 9
c
3
, c
7
u
48
− 3u
47
+ ··· − 1344u + 576
c
5
u
48
− 2u
47
+ ··· − 4494u + 1721
c
6
, c
10
, c
11
u
48
+ 2u
47
+ ··· + 2u + 1
c
8
, c
9
, c
12
u
48
+ 2u
47
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 35y
47
+ ··· − 36429289y + 6561
c
2
, c
4
y
48
− 17y
47
+ ··· − 7933y + 81
c
3
, c
7
y
48
− 39y
47
+ ··· − 8331264y + 331776
c
5
y
48
+ 22y
47
+ ··· + 1757040y + 2961841
c
6
, c
10
, c
11
y
48
+ 46y
47
+ ··· − 16y + 1
c
8
, c
9
, c
12
y
48
− 38y
47
+ ··· − 16y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.690041 + 0.629311I
a = 1.34542 + 0.54858I
b = 0.393714 + 0.635247I
−0.39368 − 5.38356I −9.68744 + 3.01224I
u = −0.690041 − 0.629311I
a = 1.34542 − 0.54858I
b = 0.393714 − 0.635247I
−0.39368 + 5.38356I −9.68744 − 3.01224I
u = 0.920254
a = 0.610728
b = 0.171718
−8.80254 −4.25000
u = −0.782668 + 0.456230I
a = −0.93137 − 1.43141I
b = 0.071750 − 1.022760I
−0.95064 + 10.34180I −10.86039 − 7.63801I
u = −0.782668 − 0.456230I
a = −0.93137 + 1.43141I
b = 0.071750 + 1.022760I
−0.95064 − 10.34180I −10.86039 + 7.63801I
u = 0.752519 + 0.427199I
a = 1.20108 − 1.15434I
b = 0.232758 − 0.968603I
3.81939 − 5.33756I −6.88950 + 5.69391I
u = 0.752519 − 0.427199I
a = 1.20108 + 1.15434I
b = 0.232758 + 0.968603I
3.81939 + 5.33756I −6.88950 − 5.69391I
u = 0.628454 + 0.590544I
a = −1.21299 + 1.06633I
b = −0.215800 + 0.693349I
4.41535 + 0.69519I −5.16048 + 0.01684I
u = 0.628454 − 0.590544I
a = −1.21299 − 1.06633I
b = −0.215800 − 0.693349I
4.41535 − 0.69519I −5.16048 − 0.01684I
u = −0.173421 + 1.158010I
a = 0.104728 + 0.511624I
b = 0.326208 + 0.117818I
2.41934 + 2.18121I −2.04928 − 4.16619I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173421 − 1.158010I
a = 0.104728 − 0.511624I
b = 0.326208 − 0.117818I
2.41934 − 2.18121I −2.04928 + 4.16619I
u = −0.700574 + 0.375620I
a = −1.38109 − 0.68287I
b = −0.565990 − 0.710333I
0.679050 + 0.119673I −8.77552 − 2.21849I
u = −0.700574 − 0.375620I
a = −1.38109 + 0.68287I
b = −0.565990 + 0.710333I
0.679050 − 0.119673I −8.77552 + 2.21849I
u = −0.582865 + 0.514097I
a = 0.93465 + 1.68545I
b = 0.017056 + 0.699009I
1.22382 + 4.04218I −8.14910 − 5.14084I
u = −0.582865 − 0.514097I
a = 0.93465 − 1.68545I
b = 0.017056 − 0.699009I
1.22382 − 4.04218I −8.14910 + 5.14084I
u = −0.073726 + 1.279840I
a = 0.763442 + 1.165900I
b = 0.95067 + 2.94188I
−2.23973 + 2.01164I 0
u = −0.073726 − 1.279840I
a = 0.763442 − 1.165900I
b = 0.95067 − 2.94188I
−2.23973 − 2.01164I 0
u = 0.454285 + 1.267740I
a = −0.084057 + 0.439948I
b = −0.212998 + 0.558035I
−4.87446 − 4.89245I 0
u = 0.454285 − 1.267740I
a = −0.084057 − 0.439948I
b = −0.212998 − 0.558035I
−4.87446 + 4.89245I 0
u = 0.039248 + 1.349580I
a = −0.345427 + 0.509536I
b = 0.63799 + 2.52080I
2.14165 − 1.06169I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.039248 − 1.349580I
a = −0.345427 − 0.509536I
b = 0.63799 − 2.52080I
2.14165 + 1.06169I 0
u = 0.155366 + 1.377490I
a = −1.307130 − 0.198976I
b = −2.06559 − 0.51195I
0.76215 − 5.52514I 0
u = 0.155366 − 1.377490I
a = −1.307130 + 0.198976I
b = −2.06559 + 0.51195I
0.76215 + 5.52514I 0
u = −0.116249 + 1.408890I
a = 0.761077 − 0.196541I
b = 0.629505 − 0.923500I
4.62872 + 2.83878I 0
u = −0.116249 − 1.408890I
a = 0.761077 + 0.196541I
b = 0.629505 + 0.923500I
4.62872 − 2.83878I 0
u = 0.062207 + 1.412420I
a = −0.430089 + 0.015361I
b = 1.62377 − 1.63866I
2.19914 − 0.22626I 0
u = 0.062207 − 1.412420I
a = −0.430089 − 0.015361I
b = 1.62377 + 1.63866I
2.19914 + 0.22626I 0
u = 0.502435 + 0.225000I
a = 1.62411 + 2.01656I
b = −0.083166 + 0.268273I
−4.30776 − 3.16023I −15.4533 + 7.2289I
u = 0.502435 − 0.225000I
a = 1.62411 − 2.01656I
b = −0.083166 − 0.268273I
−4.30776 + 3.16023I −15.4533 − 7.2289I
u = −0.27530 + 1.46413I
a = −0.012438 + 0.946406I
b = 1.06530 + 2.28274I
6.60020 + 3.71986I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27530 − 1.46413I
a = −0.012438 − 0.946406I
b = 1.06530 − 2.28274I
6.60020 − 3.71986I 0
u = −0.497658
a = −2.81262
b = 0.489265
−5.97931 −18.9670
u = −0.20208 + 1.49219I
a = 0.230181 − 1.263210I
b = 0.03507 − 3.40945I
7.72797 + 6.91935I 0
u = −0.20208 − 1.49219I
a = 0.230181 + 1.263210I
b = 0.03507 + 3.40945I
7.72797 − 6.91935I 0
u = 0.27968 + 1.48874I
a = 0.168905 + 1.066710I
b = −0.65284 + 2.93812I
10.01550 − 9.11070I 0
u = 0.27968 − 1.48874I
a = 0.168905 − 1.066710I
b = −0.65284 − 2.93812I
10.01550 + 9.11070I 0
u = −0.28574 + 1.50317I
a = −0.330652 + 1.097020I
b = 0.10316 + 3.23436I
5.3958 + 14.2406I 0
u = −0.28574 − 1.50317I
a = −0.330652 − 1.097020I
b = 0.10316 − 3.23436I
5.3958 − 14.2406I 0
u = 0.19752 + 1.51758I
a = 0.024863 − 1.091200I
b = 0.57543 − 3.00555I
11.29460 − 2.26941I 0
u = 0.19752 − 1.51758I
a = 0.024863 + 1.091200I
b = 0.57543 + 3.00555I
11.29460 + 2.26941I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374037 + 0.273421I
a = −0.98022 + 1.25843I
b = 0.051210 + 0.628665I
−0.755503 + 1.062600I −8.41291 − 6.25143I
u = −0.374037 − 0.273421I
a = −0.98022 − 1.25843I
b = 0.051210 − 0.628665I
−0.755503 − 1.062600I −8.41291 + 6.25143I
u = −0.19300 + 1.54906I
a = −0.209237 − 0.861034I
b = −0.98283 − 2.41559I
6.83914 − 2.22391I 0
u = −0.19300 − 1.54906I
a = −0.209237 + 0.861034I
b = −0.98283 + 2.41559I
6.83914 + 2.22391I 0
u = 0.220939 + 0.378134I
a = 0.89297 + 1.37411I
b = 0.48463 + 1.82610I
−3.36304 + 0.79471I −10.44549 + 7.25850I
u = 0.220939 − 0.378134I
a = 0.89297 − 1.37411I
b = 0.48463 − 1.82610I
−3.36304 − 0.79471I −10.44549 − 7.25850I
u = −0.419380
a = −0.806662
b = −0.421185
−0.865778 −11.4160
u = 0.310865
a = 1.35509
b = −1.07781
−2.07975 2.78660
9
II.
I
u
2
= hu
5
− 2u
4
+ 5u
3
− 4u
2
+ 3b + 3u − 1, a, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
0
−
1
3
u
5
+
2
3
u
4
+ ··· − u +
1
3
a
11
=
1
u
2
a
3
=
0
−
1
3
u
5
+
2
3
u
4
+ ··· − u +
1
3
a
8
=
0
u
a
6
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
−u
3
− 2u
−
1
3
u
5
+
2
3
u
4
+ ··· − 2u +
1
3
a
1
=
−u
3
− 2u
−u
3
− u
a
9
=
−u
5
− 2u
3
− u
−u
5
+ u
4
− 2u
3
+ u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
9
u
5
−
41
9
u
4
+
62
9
u
3
−
103
9
u
2
+ 6u −
178
9
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
9
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
6
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
, c
11
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
12
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
6
, c
10
, c
11
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = 0
b = −0.414549
−9.30502 −20.9320
u = −0.138835 + 1.234450I
a = 0
b = −0.632705 + 1.176960I
1.31531 + 1.97241I −10.03735 − 3.88708I
u = −0.138835 − 1.234450I
a = 0
b = −0.632705 − 1.176960I
1.31531 − 1.97241I −10.03735 + 3.88708I
u = 0.408802 + 1.276380I
a = 0
b = 0.449122 + 0.449614I
−5.34051 − 4.59213I −15.2999 − 0.2296I
u = 0.408802 − 1.276380I
a = 0
b = 0.449122 − 0.449614I
−5.34051 + 4.59213I −15.2999 + 0.2296I
u = −0.413150
a = 0
b = 1.11505
−2.38379 −24.8380
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
48
+ 17u
47
+ ··· + 7933u + 81)
c
2
((u − 1)
6
)(u
48
− 7u
47
+ ··· − 133u + 9)
c
3
, c
7
u
6
(u
48
− 3u
47
+ ··· − 1344u + 576)
c
4
((u + 1)
6
)(u
48
− 7u
47
+ ··· − 133u + 9)
c
5
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
48
− 2u
47
+ ··· − 4494u + 1721)
c
6
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
48
+ 2u
47
+ ··· + 2u + 1)
c
8
, c
9
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
48
+ 2u
47
+ ··· + 2u + 1)
c
10
, c
11
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
48
+ 2u
47
+ ··· + 2u + 1)
c
12
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
48
+ 2u
47
+ ··· + 2u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
48
+ 35y
47
+ ··· − 36429289y + 6561)
c
2
, c
4
((y −1)
6
)(y
48
− 17y
47
+ ··· − 7933y + 81)
c
3
, c
7
y
6
(y
48
− 39y
47
+ ··· − 8331264y + 331776)
c
5
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
48
+ 22y
47
+ ··· + 1757040y + 2961841)
c
6
, c
10
, c
11
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
48
+ 46y
47
+ ··· − 16y + 1)
c
8
, c
9
, c
12
(y
6
− 7y
5
+ ··· − 5y + 1)(y
48
− 38y
47
+ ··· − 16y + 1)
15
