12a
0382
(K12a
0382
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 7 2 12 1 11 4 5 8
Solving Sequence
5,10
4 11
8,12
1 7 6 9 3 2
c
4
c
10
c
11
c
12
c
7
c
5
c
9
c
3
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h5.25760 × 10
40
u
79
7.60567 × 10
40
u
78
+ ··· + 2.32478 × 10
40
b + 1.39471 × 10
38
,
2.10242 × 10
40
u
79
1.11824 × 10
40
u
78
+ ··· + 2.32478 × 10
40
a 6.38186 × 10
40
, u
80
u
79
+ ··· + 4u 4i
I
u
2
= hu
2
a + u
3
+ 2b + u, 2u
3
a 2u
2
a + 2a
2
+ 5u
2
4a + 2u + 6, u
4
+ 2u
2
+ 2i
I
v
1
= ha, b + v 1, v
2
v + 1i
* 3 irreducible components of dim
C
= 0, with total 90 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
= h5.26 × 10
40
u
79
7.61 × 10
40
u
78
+ · · · + 2.32 × 10
40
b + 1.39 × 10
38
, 2.10 ×
10
40
u
79
1.12×10
40
u
78
+· · ·+2.32×10
40
a6.38×10
40
, u
80
u
79
+· · ·+4u4i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
8
=
0.904354u
79
+ 0.481007u
78
+ ··· 1.07187u + 2.74514
2.26155u
79
+ 3.27156u
78
+ ··· + 11.4214u 0.00599931
a
12
=
u
3
u
3
+ u
a
1
=
0.904354u
79
0.481007u
78
+ ··· + 1.07187u 2.74514
1.40429u
79
+ 2.20008u
78
+ ··· + 9.49738u 1.69939
a
7
=
1.13657u
79
+ 1.84293u
78
+ ··· + 7.02460u 2.17652
1.70006u
79
+ 2.60937u
78
+ ··· + 9.55138u 0.627990
a
6
=
0.0263781u
79
+ 1.69363u
78
+ ··· + 11.1328u 6.06948
1.38845u
79
2.43528u
78
+ ··· 9.84146u + 1.92979
a
9
=
u
3
u
5
+ u
3
+ u
a
3
=
u
6
u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
2
=
2.09245u
79
2.33106u
78
+ ··· 5.71599u 2.00297
0.784122u
79
+ 0.549512u
78
+ ··· + 0.603346u + 2.47675
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5.47878u
79
9.68885u
78
+ ··· 54.6240u + 21.2301
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
80
+ 24u
79
+ ··· + 8u + 1
c
2
, c
6
u
80
2u
79
+ ··· 2u + 1
c
3
, c
11
u
80
+ u
79
+ ··· 452u 404
c
4
, c
10
u
80
u
79
+ ··· + 4u 4
c
7
, c
8
, c
12
u
80
3u
79
+ ··· 83u 13
c
9
u
80
45u
79
+ ··· 80u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
80
+ 72y
79
+ ··· 56y + 1
c
2
, c
6
y
80
+ 24y
79
+ ··· + 8y + 1
c
3
, c
11
y
80
75y
79
+ ··· 2017456y + 163216
c
4
, c
10
y
80
+ 45y
79
+ ··· + 80y + 16
c
7
, c
8
, c
12
y
80
85y
79
+ ··· 3353y + 169
c
9
y
80
15y
79
+ ··· 1792y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.465995 + 0.890027I
a = 0.441303 + 0.096283I
b = 1.45500 0.66755I
1.05476 + 4.92101I 0
u = 0.465995 0.890027I
a = 0.441303 0.096283I
b = 1.45500 + 0.66755I
1.05476 4.92101I 0
u = 0.138898 + 0.959842I
a = 1.40999 + 1.38132I
b = 0.376133 + 1.039330I
3.54764 + 1.95603I 12.28857 3.06785I
u = 0.138898 0.959842I
a = 1.40999 1.38132I
b = 0.376133 1.039330I
3.54764 1.95603I 12.28857 + 3.06785I
u = 0.255592 + 0.927697I
a = 1.34947 + 2.03332I
b = 0.009870 + 1.328880I
3.00368 + 3.13036I 10.09819 3.88096I
u = 0.255592 0.927697I
a = 1.34947 2.03332I
b = 0.009870 1.328880I
3.00368 3.13036I 10.09819 + 3.88096I
u = 0.407948 + 0.961740I
a = 1.228550 0.288226I
b = 0.209191 0.418092I
1.82577 + 1.64059I 0
u = 0.407948 0.961740I
a = 1.228550 + 0.288226I
b = 0.209191 + 0.418092I
1.82577 1.64059I 0
u = 0.482819 + 0.934965I
a = 1.079240 0.701792I
b = 0.200382 0.585726I
1.16955 6.69579I 0
u = 0.482819 0.934965I
a = 1.079240 + 0.701792I
b = 0.200382 + 0.585726I
1.16955 + 6.69579I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.304527 + 1.033480I
a = 0.389055 + 0.408709I
b = 0.914489 0.830590I
4.63163 3.09536I 0
u = 0.304527 1.033480I
a = 0.389055 0.408709I
b = 0.914489 + 0.830590I
4.63163 + 3.09536I 0
u = 0.718292 + 0.564408I
a = 0.30054 + 1.50770I
b = 0.699048 + 0.453179I
6.00409 4.34016I 7.41183 + 2.66481I
u = 0.718292 0.564408I
a = 0.30054 1.50770I
b = 0.699048 0.453179I
6.00409 + 4.34016I 7.41183 2.66481I
u = 0.222929 + 0.884136I
a = 0.215941 + 0.267184I
b = 1.07893 1.42958I
2.79044 1.07850I 9.91240 0.16778I
u = 0.222929 0.884136I
a = 0.215941 0.267184I
b = 1.07893 + 1.42958I
2.79044 + 1.07850I 9.91240 + 0.16778I
u = 0.897293 + 0.111616I
a = 0.271629 0.075634I
b = 2.77247 + 0.37666I
13.07070 4.01680I 9.61331 + 0.81202I
u = 0.897293 0.111616I
a = 0.271629 + 0.075634I
b = 2.77247 0.37666I
13.07070 + 4.01680I 9.61331 0.81202I
u = 0.890645 + 0.137467I
a = 0.265905 0.093191I
b = 2.73738 + 0.46410I
12.1328 + 10.4310I 8.31438 5.43420I
u = 0.890645 0.137467I
a = 0.265905 + 0.093191I
b = 2.73738 0.46410I
12.1328 10.4310I 8.31438 + 5.43420I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.473965 + 0.759787I
a = 0.499997 0.399523I
b = 0.386214 + 0.092533I
2.89498 1.99126I 3.21441 + 4.67828I
u = 0.473965 0.759787I
a = 0.499997 + 0.399523I
b = 0.386214 0.092533I
2.89498 + 1.99126I 3.21441 4.67828I
u = 0.730077 + 0.516813I
a = 0.33209 + 1.43938I
b = 0.692107 + 0.425189I
6.24399 1.64013I 7.94611 + 2.56376I
u = 0.730077 0.516813I
a = 0.33209 1.43938I
b = 0.692107 0.425189I
6.24399 + 1.64013I 7.94611 2.56376I
u = 0.621172 + 0.959007I
a = 0.596898 0.048619I
b = 1.37777 0.41758I
7.15122 + 9.41978I 0
u = 0.621172 0.959007I
a = 0.596898 + 0.048619I
b = 1.37777 + 0.41758I
7.15122 9.41978I 0
u = 0.853744
a = 0.244881
b = 3.05747
8.46558 10.3700
u = 0.835740 + 0.069667I
a = 0.121736 0.573005I
b = 0.860834 0.096641I
5.16321 5.92875I 6.57093 + 5.18628I
u = 0.835740 0.069667I
a = 0.121736 + 0.573005I
b = 0.860834 + 0.096641I
5.16321 + 5.92875I 6.57093 5.18628I
u = 0.608825 + 0.993182I
a = 0.636243 0.025508I
b = 1.345400 0.421772I
7.63224 3.42695I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.608825 0.993182I
a = 0.636243 + 0.025508I
b = 1.345400 + 0.421772I
7.63224 + 3.42695I 0
u = 0.830514 + 0.028983I
a = 0.168471 0.606307I
b = 0.834469 0.116020I
5.51190 0.08562I 7.53170 0.02621I
u = 0.830514 0.028983I
a = 0.168471 + 0.606307I
b = 0.834469 + 0.116020I
5.51190 + 0.08562I 7.53170 + 0.02621I
u = 0.814288 + 0.058409I
a = 0.218467 0.037164I
b = 3.20383 + 0.31940I
4.47676 + 4.08811I 5.94358 3.55557I
u = 0.814288 0.058409I
a = 0.218467 + 0.037164I
b = 3.20383 0.31940I
4.47676 4.08811I 5.94358 + 3.55557I
u = 0.420036 + 1.121960I
a = 1.312780 + 0.338786I
b = 0.980693 0.347373I
2.29503 + 1.39582I 0
u = 0.420036 1.121960I
a = 1.312780 0.338786I
b = 0.980693 + 0.347373I
2.29503 1.39582I 0
u = 0.022114 + 1.201810I
a = 0.026017 + 0.667704I
b = 0.051525 0.715255I
12.02500 3.18270I 0
u = 0.022114 1.201810I
a = 0.026017 0.667704I
b = 0.051525 + 0.715255I
12.02500 + 3.18270I 0
u = 0.427711 + 1.135650I
a = 0.800534 + 0.574575I
b = 0.980152 0.405539I
4.29603 3.85211I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.427711 1.135650I
a = 0.800534 0.574575I
b = 0.980152 + 0.405539I
4.29603 + 3.85211I 0
u = 0.462927 + 0.633291I
a = 0.53377 + 1.87620I
b = 0.529788 + 0.626997I
0.307290 0.999281I 1.095810 0.533831I
u = 0.462927 0.633291I
a = 0.53377 1.87620I
b = 0.529788 0.626997I
0.307290 + 0.999281I 1.095810 + 0.533831I
u = 0.484079 + 1.119780I
a = 0.866749 + 0.224504I
b = 1.140810 0.396001I
3.93599 3.81750I 0
u = 0.484079 1.119780I
a = 0.866749 0.224504I
b = 1.140810 + 0.396001I
3.93599 + 3.81750I 0
u = 0.213622 + 0.748341I
a = 0.526734 + 0.180517I
b = 0.072777 + 0.311265I
0.469913 + 1.044090I 6.86138 6.22374I
u = 0.213622 0.748341I
a = 0.526734 0.180517I
b = 0.072777 0.311265I
0.469913 1.044090I 6.86138 + 6.22374I
u = 0.477124 + 1.149760I
a = 1.013430 + 0.942548I
b = 1.032000 0.244669I
1.86076 + 6.51679I 0
u = 0.477124 1.149760I
a = 1.013430 0.942548I
b = 1.032000 + 0.244669I
1.86076 6.51679I 0
u = 0.478853 + 0.518342I
a = 0.157255 0.210245I
b = 0.243674 + 0.798703I
0.01114 + 2.66370I 0.22333 3.59171I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.478853 0.518342I
a = 0.157255 + 0.210245I
b = 0.243674 0.798703I
0.01114 2.66370I 0.22333 + 3.59171I
u = 0.430621 + 1.222960I
a = 3.99939 1.81832I
b = 3.41999 + 0.85134I
8.27741 0.27610I 0
u = 0.430621 1.222960I
a = 3.99939 + 1.81832I
b = 3.41999 0.85134I
8.27741 + 0.27610I 0
u = 0.423343 + 1.234360I
a = 1.180390 + 0.077989I
b = 1.128210 0.192853I
9.08229 1.53556I 0
u = 0.423343 1.234360I
a = 1.180390 0.077989I
b = 1.128210 + 0.192853I
9.08229 + 1.53556I 0
u = 0.484159 + 1.214790I
a = 3.23346 2.92931I
b = 3.61500 0.04388I
7.89154 8.79580I 0
u = 0.484159 1.214790I
a = 3.23346 + 2.92931I
b = 3.61500 + 0.04388I
7.89154 + 8.79580I 0
u = 0.445621 + 1.230110I
a = 1.142860 + 0.074777I
b = 1.143680 0.218383I
9.26755 4.60038I 0
u = 0.445621 1.230110I
a = 1.142860 0.074777I
b = 1.143680 + 0.218383I
9.26755 + 4.60038I 0
u = 0.473133 + 1.225410I
a = 0.674158 + 1.005180I
b = 0.842255 0.176963I
9.06923 4.59966I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.473133 1.225410I
a = 0.674158 1.005180I
b = 0.842255 + 0.176963I
9.06923 + 4.59966I 0
u = 0.491722 + 1.221380I
a = 0.696670 + 1.055440I
b = 0.864778 0.142267I
8.58962 + 10.73420I 0
u = 0.491722 1.221380I
a = 0.696670 1.055440I
b = 0.864778 + 0.142267I
8.58962 10.73420I 0
u = 0.461673 + 1.239500I
a = 3.34624 2.19469I
b = 3.30822 + 0.35003I
12.19070 + 4.68445I 0
u = 0.461673 1.239500I
a = 3.34624 + 2.19469I
b = 3.30822 0.35003I
12.19070 4.68445I 0
u = 0.659131 + 0.138583I
a = 0.131715 0.302385I
b = 0.783683 + 0.078001I
1.00843 2.17613I 0.72572 + 4.89946I
u = 0.659131 0.138583I
a = 0.131715 + 0.302385I
b = 0.783683 0.078001I
1.00843 + 2.17613I 0.72572 4.89946I
u = 0.376961 + 1.272580I
a = 3.27843 0.87003I
b = 2.59679 + 0.91122I
16.5475 + 6.0856I 0
u = 0.376961 1.272580I
a = 3.27843 + 0.87003I
b = 2.59679 0.91122I
16.5475 6.0856I 0
u = 0.395993 + 1.275570I
a = 3.25352 1.08729I
b = 2.70154 + 0.80021I
17.3961 + 0.4584I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.395993 1.275570I
a = 3.25352 + 1.08729I
b = 2.70154 0.80021I
17.3961 0.4584I 0
u = 0.532038 + 1.229040I
a = 2.22989 2.75471I
b = 3.06819 0.43695I
15.4242 15.5867I 0
u = 0.532038 1.229040I
a = 2.22989 + 2.75471I
b = 3.06819 + 0.43695I
15.4242 + 15.5867I 0
u = 0.522093 + 1.238600I
a = 2.39580 2.61515I
b = 3.07981 0.29683I
16.4786 + 9.1429I 0
u = 0.522093 1.238600I
a = 2.39580 + 2.61515I
b = 3.07981 + 0.29683I
16.4786 9.1429I 0
u = 0.589183 + 0.225941I
a = 0.856805 + 1.015170I
b = 0.572688 + 0.230131I
1.41466 0.43042I 4.49722 0.21738I
u = 0.589183 0.225941I
a = 0.856805 1.015170I
b = 0.572688 0.230131I
1.41466 + 0.43042I 4.49722 + 0.21738I
u = 0.603179
a = 0.604155
b = 0.636890
1.24472 8.33220
u = 0.441124 + 0.397291I
a = 0.091294 0.136266I
b = 0.316370 + 0.765160I
0.25766 + 1.95200I 0.06852 3.23110I
u = 0.441124 0.397291I
a = 0.091294 + 0.136266I
b = 0.316370 0.765160I
0.25766 1.95200I 0.06852 + 3.23110I
12
II.
I
u
2
= hu
2
a + u
3
+ 2b + u, 2u
3
a 2u
2
a + 2a
2
+ 5u
2
4a + 2u + 6, u
4
+ 2u
2
+ 2i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
8
=
a
1
2
u
2
a
1
2
u
3
1
2
u
a
12
=
u
3
u
3
+ u
a
1
=
u
3
+ a
1
2
u
2
a +
1
2
u
3
+
1
2
u
a
7
=
u
3
+ a
1
2
u
2
a +
1
2
u
3
+
1
2
u
a
6
=
1
2
u
3
a +
1
2
u
3
+ ··· + a
1
2
1
2
u
2
a +
1
2
u
3
+
1
2
u 1
a
9
=
u
3
u
3
u
a
3
=
1
0
a
2
=
1
2
u
2
a +
1
2
u
3
+ a
1
2
u
1
2
u
2
a +
1
2
u
3
+
1
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
a + 2u
3
+ 4u
2
+ 2u + 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
u + 1)
4
c
3
, c
11
(u
4
2u
2
+ 2)
2
c
4
, c
10
(u
4
+ 2u
2
+ 2)
2
c
6
(u
2
+ u + 1)
4
c
7
, c
8
(u 1)
8
c
9
(u
2
+ 2u + 2)
4
c
12
(u + 1)
8
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
4
c
3
, c
11
(y
2
2y + 2)
4
c
4
, c
10
(y
2
+ 2y + 2)
4
c
7
, c
8
, c
12
(y 1)
8
c
9
(y
2
+ 4)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.455090 + 1.098680I
a = 0.41086 + 1.68782I
b = 1.59868 + 0.41094I
4.11234 5.69375I 10.00000 + 7.46410I
u = 0.455090 + 1.098680I
a = 2.14291 0.04423I
b = 1.59868 1.32112I
4.11234 1.63398I 10.00000 + 0.53590I
u = 0.455090 1.098680I
a = 0.41086 1.68782I
b = 1.59868 0.41094I
4.11234 + 5.69375I 10.00000 7.46410I
u = 0.455090 1.098680I
a = 2.14291 + 0.04423I
b = 1.59868 + 1.32112I
4.11234 + 1.63398I 10.00000 0.53590I
u = 0.455090 + 1.098680I
a = 0.589138 + 0.687823I
b = 0.598684 + 0.410936I
4.11234 + 1.63398I 10.00000 0.53590I
u = 0.455090 + 1.098680I
a = 1.14291 1.04423I
b = 0.59868 1.32112I
4.11234 + 5.69375I 10.00000 7.46410I
u = 0.455090 1.098680I
a = 0.589138 0.687823I
b = 0.598684 0.410936I
4.11234 1.63398I 10.00000 + 0.53590I
u = 0.455090 1.098680I
a = 1.14291 + 1.04423I
b = 0.59868 + 1.32112I
4.11234 5.69375I 10.00000 + 7.46410I
16
III. I
v
1
= ha, b + v 1, v
2
v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
4
=
1
0
a
11
=
v
0
a
8
=
0
v + 1
a
12
=
v
0
a
1
=
v
v 1
a
7
=
v
v + 1
a
6
=
0
v
a
9
=
v
0
a
3
=
1
0
a
2
=
1
v 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 8
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
u
2
u + 1
c
2
u
2
+ u + 1
c
3
, c
4
, c
9
c
10
, c
11
u
2
c
7
, c
8
(u + 1)
2
c
12
(u 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
9
c
10
, c
11
y
2
c
7
, c
8
, c
12
(y 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
1(vol +
1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 0.866025I
1.64493 + 2.02988I 6.00000 3.46410I
v = 0.500000 0.866025I
a = 0
b = 0.500000 + 0.866025I
1.64493 2.02988I 6.00000 + 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
u + 1)
5
)(u
80
+ 24u
79
+ ··· + 8u + 1)
c
2
((u
2
u + 1)
4
)(u
2
+ u + 1)(u
80
2u
79
+ ··· 2u + 1)
c
3
, c
11
u
2
(u
4
2u
2
+ 2)
2
(u
80
+ u
79
+ ··· 452u 404)
c
4
, c
10
u
2
(u
4
+ 2u
2
+ 2)
2
(u
80
u
79
+ ··· + 4u 4)
c
6
(u
2
u + 1)(u
2
+ u + 1)
4
(u
80
2u
79
+ ··· 2u + 1)
c
7
, c
8
((u 1)
8
)(u + 1)
2
(u
80
3u
79
+ ··· 83u 13)
c
9
u
2
(u
2
+ 2u + 2)
4
(u
80
45u
79
+ ··· 80u + 16)
c
12
((u 1)
2
)(u + 1)
8
(u
80
3u
79
+ ··· 83u 13)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
5
)(y
80
+ 72y
79
+ ··· 56y + 1)
c
2
, c
6
((y
2
+ y + 1)
5
)(y
80
+ 24y
79
+ ··· + 8y + 1)
c
3
, c
11
y
2
(y
2
2y + 2)
4
(y
80
75y
79
+ ··· 2017456y + 163216)
c
4
, c
10
y
2
(y
2
+ 2y + 2)
4
(y
80
+ 45y
79
+ ··· + 80y + 16)
c
7
, c
8
, c
12
((y 1)
10
)(y
80
85y
79
+ ··· 3353y + 169)
c
9
y
2
(y
2
+ 4)
4
(y
80
15y
79
+ ··· 1792y + 256)
22