12a
0192
(K12a
0192
)
A knot diagram
1
Linearized knot diagam
3 5 9 8 2 11 10 1 12 7 6 4
Solving Sequence
6,11
7
2,12
5 3 1 10 8 4 9
c
6
c
11
c
5
c
2
c
1
c
10
c
7
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.37926 × 10
55
u
88
+ 9.52831 × 10
57
u
87
+ ··· + 4.66485 × 10
58
b + 1.81070 × 10
58
,
3.57832 × 10
57
u
88
− 1.08873 × 10
58
u
87
+ ··· + 4.66485 × 10
58
a − 5.48631 × 10
58
, u
89
+ u
88
+ ··· + 5u − 1i
* 1 irreducible components of dim
C
= 0, with total 89 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−7.38×10
55
u
88
+9.53×10
57
u
87
+· · ·+4.66×10
58
b+1.81×10
58
, 3.58×
10
57
u
88
−1.09×10
58
u
87
+· · ·+4.66×10
58
a−5.49×10
58
, u
89
+u
88
+· · ·+5u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
2
=
−0.0767082u
88
+ 0.233391u
87
+ ··· + 2.20793u + 1.17610
0.00158188u
88
− 0.204257u
87
+ ··· + 4.22139u − 0.388158
a
12
=
u
u
a
5
=
−0.0700335u
88
+ 0.955530u
87
+ ··· + 6.31059u − 0.164482
0.000780172u
88
− 0.187319u
87
+ ··· + 3.98539u − 1.30273
a
3
=
−0.0962203u
88
+ 0.711962u
87
+ ··· + 9.34457u − 1.31376
−0.0299682u
88
− 0.276739u
87
+ ··· + 3.53290u − 1.29576
a
1
=
−0.0570863u
88
+ 0.575773u
87
+ ··· + 0.462546u − 1.20248
0.780343u
88
+ 0.632859u
87
+ ··· + 3.82209u − 0.837430
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−0.368118u
88
− 0.575274u
87
+ ··· + 5.72052u − 0.661402
−0.0758137u
88
− 0.403033u
87
+ ··· − 2.02265u + 0.00119394
a
9
=
u
5
+ 2u
3
− u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.67855u
88
− 1.96081u
87
+ ··· − 19.9102u + 7.42306
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
+ 35u
88
+ ··· + 9u − 1
c
2
, c
5
u
89
+ u
88
+ ··· + 9u − 1
c
3
u
89
+ u
88
+ ··· − 1279u − 421
c
4
u
89
+ 3u
88
+ ··· + 1113u − 503
c
6
, c
7
, c
10
c
11
u
89
+ u
88
+ ··· + 5u − 1
c
8
u
89
− 5u
88
+ ··· + u − 1
c
9
u
89
− 19u
88
+ ··· + 158017u − 14627
c
12
u
89
+ 9u
88
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 39y
88
+ ··· − 651y −1
c
2
, c
5
y
89
+ 35y
88
+ ··· + 9y −1
c
3
y
89
− 109y
88
+ ··· + 13004525y −177241
c
4
y
89
− 81y
88
+ ··· − 6843435y −253009
c
6
, c
7
, c
10
c
11
y
89
+ 99y
88
+ ··· + 5y −1
c
8
y
89
− 9y
88
+ ··· + 5y −1
c
9
y
89
+ 27y
88
+ ··· − 8680509275y −213949129
c
12
y
89
− 5y
88
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629172 + 0.711509I
a = 1.44311 − 1.26130I
b = −0.589163 − 0.910663I
1.38416 + 5.67170I 0
u = 0.629172 − 0.711509I
a = 1.44311 + 1.26130I
b = −0.589163 + 0.910663I
1.38416 − 5.67170I 0
u = 0.222782 + 0.904277I
a = −0.111171 + 0.701310I
b = −0.556330 + 0.569146I
−0.83522 + 2.21982I 0
u = 0.222782 − 0.904277I
a = −0.111171 − 0.701310I
b = −0.556330 − 0.569146I
−0.83522 − 2.21982I 0
u = 0.652354 + 0.618933I
a = 0.016156 − 0.206879I
b = −0.568168 + 0.764733I
1.84881 + 1.03677I 0
u = 0.652354 − 0.618933I
a = 0.016156 + 0.206879I
b = −0.568168 − 0.764733I
1.84881 − 1.03677I 0
u = −0.587821 + 0.668605I
a = 1.84371 + 1.57426I
b = −0.689784 + 1.112970I
1.6805 − 14.3965I 0
u = −0.587821 − 0.668605I
a = 1.84371 − 1.57426I
b = −0.689784 − 1.112970I
1.6805 + 14.3965I 0
u = −0.576040 + 0.637409I
a = −0.180456 + 0.891479I
b = −0.912731 − 0.519289I
3.49714 − 8.50503I 0
u = −0.576040 − 0.637409I
a = −0.180456 − 0.891479I
b = −0.912731 + 0.519289I
3.49714 + 8.50503I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186133 + 0.807246I
a = 1.17307 + 2.02621I
b = −0.110685 + 1.090650I
−5.27581 + 0.77625I 0
u = −0.186133 − 0.807246I
a = 1.17307 − 2.02621I
b = −0.110685 − 1.090650I
−5.27581 − 0.77625I 0
u = 0.187001 + 1.165500I
a = 0.45304 − 1.37786I
b = −0.617348 − 0.979446I
−1.97335 + 7.02283I 0
u = 0.187001 − 1.165500I
a = 0.45304 + 1.37786I
b = −0.617348 + 0.979446I
−1.97335 − 7.02283I 0
u = −0.483117 + 0.643227I
a = −1.27197 − 1.41185I
b = 0.055573 − 1.266110I
−3.30433 − 6.34543I 0. + 9.41566I
u = −0.483117 − 0.643227I
a = −1.27197 + 1.41185I
b = 0.055573 + 1.266110I
−3.30433 + 6.34543I 0. − 9.41566I
u = 0.735954 + 0.310708I
a = 1.072010 − 0.285219I
b = −0.596779 − 0.860932I
2.75551 + 3.59145I 16.9119 − 7.8798I
u = 0.735954 − 0.310708I
a = 1.072010 + 0.285219I
b = −0.596779 + 0.860932I
2.75551 − 3.59145I 16.9119 + 7.8798I
u = −0.128379 + 1.218880I
a = 0.048603 − 1.126680I
b = −0.654242 − 1.028240I
−1.89864 + 7.13164I 0
u = −0.128379 − 1.218880I
a = 0.048603 + 1.126680I
b = −0.654242 + 1.028240I
−1.89864 − 7.13164I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302285 + 0.698873I
a = 0.372084 + 1.059710I
b = −0.097148 + 0.520009I
−0.88546 + 2.04291I 2.01521 − 6.41546I
u = 0.302285 − 0.698873I
a = 0.372084 − 1.059710I
b = −0.097148 − 0.520009I
−0.88546 − 2.04291I 2.01521 + 6.41546I
u = 0.729548 + 0.201616I
a = 0.787909 + 0.143124I
b = −0.594451 + 0.821113I
2.87995 − 1.13132I 17.8044 + 0.I
u = 0.729548 − 0.201616I
a = 0.787909 − 0.143124I
b = −0.594451 − 0.821113I
2.87995 + 1.13132I 17.8044 + 0.I
u = −0.487284 + 0.556003I
a = −2.04497 − 1.51099I
b = 0.721154 − 1.156170I
1.32467 − 6.17318I 8.6449 + 12.1067I
u = −0.487284 − 0.556003I
a = −2.04497 + 1.51099I
b = 0.721154 + 1.156170I
1.32467 + 6.17318I 8.6449 − 12.1067I
u = −0.672888 + 0.280476I
a = 0.789738 − 0.042118I
b = −0.684732 − 1.084880I
2.83010 + 10.15130I 7.61075 − 5.74179I
u = −0.672888 − 0.280476I
a = 0.789738 + 0.042118I
b = −0.684732 + 1.084880I
2.83010 − 10.15130I 7.61075 + 5.74179I
u = −0.639069 + 0.312530I
a = 1.053290 + 0.122104I
b = −0.869417 + 0.551430I
4.45557 + 4.38854I 10.08298 − 1.27597I
u = −0.639069 − 0.312530I
a = 1.053290 − 0.122104I
b = −0.869417 − 0.551430I
4.45557 − 4.38854I 10.08298 + 1.27597I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500387 + 0.501574I
a = −1.042820 − 0.811706I
b = 0.978738 − 0.544688I
3.39905 − 3.48992I 14.4983 + 7.8374I
u = −0.500387 − 0.501574I
a = −1.042820 + 0.811706I
b = 0.978738 + 0.544688I
3.39905 + 3.48992I 14.4983 − 7.8374I
u = 0.474265 + 0.491419I
a = 0.465564 + 0.028509I
b = 0.173591 + 0.109004I
0.68170 + 1.66226I 3.48924 − 4.60078I
u = 0.474265 − 0.491419I
a = 0.465564 − 0.028509I
b = 0.173591 − 0.109004I
0.68170 − 1.66226I 3.48924 + 4.60078I
u = 0.434724 + 0.524138I
a = −5.16293 + 0.82804I
b = 0.537717 + 0.883432I
0.38729 + 3.69638I −13.5626 + 18.8380I
u = 0.434724 − 0.524138I
a = −5.16293 − 0.82804I
b = 0.537717 − 0.883432I
0.38729 − 3.69638I −13.5626 − 18.8380I
u = −0.499673 + 0.459395I
a = −0.080168 − 1.151680I
b = 0.969659 + 0.422445I
3.52293 − 0.01044I 15.3738 + 0.9083I
u = −0.499673 − 0.459395I
a = −0.080168 + 1.151680I
b = 0.969659 − 0.422445I
3.52293 + 0.01044I 15.3738 − 0.9083I
u = −0.103485 + 1.347580I
a = 0.273259 + 0.747966I
b = −0.786906 + 0.627797I
−0.67403 + 1.69091I 0
u = −0.103485 − 1.347580I
a = 0.273259 − 0.747966I
b = −0.786906 − 0.627797I
−0.67403 − 1.69091I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.431180 + 0.470567I
a = −1.96595 + 3.06518I
b = 0.535306 − 0.833683I
0.550681 − 0.619676I −20.5386 + 0.0092I
u = 0.431180 − 0.470567I
a = −1.96595 − 3.06518I
b = 0.535306 + 0.833683I
0.550681 + 0.619676I −20.5386 − 0.0092I
u = 0.295375 + 0.540642I
a = 2.09399 − 3.18145I
b = 0.406553 − 0.839840I
−0.370699 − 0.487288I 9.82844 + 2.22925I
u = 0.295375 − 0.540642I
a = 2.09399 + 3.18145I
b = 0.406553 + 0.839840I
−0.370699 + 0.487288I 9.82844 − 2.22925I
u = −0.473391 + 0.392852I
a = −0.181126 − 0.558731I
b = 0.749485 + 1.073430I
1.80432 + 2.77862I 11.25470 − 4.17137I
u = −0.473391 − 0.392852I
a = −0.181126 + 0.558731I
b = 0.749485 − 1.073430I
1.80432 − 2.77862I 11.25470 + 4.17137I
u = −0.503795 + 0.211387I
a = 0.754696 + 0.227869I
b = 0.081301 + 1.158510I
−2.10438 + 2.91296I 3.85872 − 3.54311I
u = −0.503795 − 0.211387I
a = 0.754696 − 0.227869I
b = 0.081301 − 1.158510I
−2.10438 − 2.91296I 3.85872 + 3.54311I
u = −0.031844 + 0.498137I
a = 1.79243 + 1.98491I
b = 0.452894 + 1.035280I
−1.16253 + 2.81373I 0.94545 − 4.27965I
u = −0.031844 − 0.498137I
a = 1.79243 − 1.98491I
b = 0.452894 − 1.035280I
−1.16253 − 2.81373I 0.94545 + 4.27965I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09570 + 1.51606I
a = 0.484133 + 0.651673I
b = 0.846108 + 1.016410I
−4.55578 + 0.98631I 0
u = −0.09570 − 1.51606I
a = 0.484133 − 0.651673I
b = 0.846108 − 1.016410I
−4.55578 − 0.98631I 0
u = −0.12003 + 1.52137I
a = 0.788400 − 0.472468I
b = 1.028650 + 0.306936I
−3.06055 − 2.11654I 0
u = −0.12003 − 1.52137I
a = 0.788400 + 0.472468I
b = 1.028650 − 0.306936I
−3.06055 + 2.11654I 0
u = 0.12194 + 1.53251I
a = 0.524459 + 0.057134I
b = 0.287639 + 0.284127I
−6.09091 + 3.74135I 0
u = 0.12194 − 1.53251I
a = 0.524459 − 0.057134I
b = 0.287639 − 0.284127I
−6.09091 − 3.74135I 0
u = −0.05215 + 1.53803I
a = 0.78383 + 2.12557I
b = 0.394001 + 1.219470I
−7.99338 + 2.27220I 0
u = −0.05215 − 1.53803I
a = 0.78383 − 2.12557I
b = 0.394001 − 1.219470I
−7.99338 − 2.27220I 0
u = 0.10814 + 1.53630I
a = −0.46791 + 1.35996I
b = 0.557170 − 0.784157I
−6.21839 + 1.22639I 0
u = 0.10814 − 1.53630I
a = −0.46791 − 1.35996I
b = 0.557170 + 0.784157I
−6.21839 − 1.22639I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13046 + 1.53461I
a = −0.009257 − 1.133030I
b = 1.023540 − 0.632653I
−3.39866 − 5.69060I 0
u = −0.13046 − 1.53461I
a = −0.009257 + 1.133030I
b = 1.023540 + 0.632653I
−3.39866 + 5.69060I 0
u = 0.11815 + 1.55305I
a = −3.04685 + 2.18791I
b = 0.547660 + 0.917462I
−6.64186 + 5.64915I 0
u = 0.11815 − 1.55305I
a = −3.04685 − 2.18791I
b = 0.547660 − 0.917462I
−6.64186 − 5.64915I 0
u = −0.13579 + 1.55414I
a = −0.92689 − 2.28994I
b = 0.714058 − 1.215670I
−5.76285 − 8.40304I 0
u = −0.13579 − 1.55414I
a = −0.92689 + 2.28994I
b = 0.714058 + 1.215670I
−5.76285 + 8.40304I 0
u = 0.08285 + 1.55949I
a = 0.69935 − 3.37892I
b = 0.379375 − 0.924960I
−7.53072 + 0.87574I 0
u = 0.08285 − 1.55949I
a = 0.69935 + 3.37892I
b = 0.379375 + 0.924960I
−7.53072 − 0.87574I 0
u = 0.18967 + 1.55696I
a = −0.180533 + 0.193860I
b = −0.569360 + 0.635557I
−5.32319 + 4.10488I 0
u = 0.18967 − 1.55696I
a = −0.180533 − 0.193860I
b = −0.569360 − 0.635557I
−5.32319 − 4.10488I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17406 + 1.57857I
a = −0.732146 + 0.316878I
b = −0.945850 − 0.492890I
−3.92592 − 11.27190I 0
u = −0.17406 − 1.57857I
a = −0.732146 − 0.316878I
b = −0.945850 + 0.492890I
−3.92592 + 11.27190I 0
u = −0.14170 + 1.58228I
a = −0.81875 − 2.26841I
b = 0.029274 − 1.322190I
−10.81660 − 8.64854I 0
u = −0.14170 − 1.58228I
a = −0.81875 + 2.26841I
b = 0.029274 + 1.322190I
−10.81660 + 8.64854I 0
u = −0.17969 + 1.59088I
a = 1.07922 + 2.20177I
b = −0.690669 + 1.135390I
−5.9008 − 17.2515I 0
u = −0.17969 − 1.59088I
a = 1.07922 − 2.20177I
b = −0.690669 − 1.135390I
−5.9008 + 17.2515I 0
u = 0.02185 + 1.60984I
a = −0.334028 + 0.512887I
b = −0.660273 + 0.247851I
−9.21525 + 2.86609I 0
u = 0.02185 − 1.60984I
a = −0.334028 − 0.512887I
b = −0.660273 − 0.247851I
−9.21525 − 2.86609I 0
u = 0.19671 + 1.59879I
a = 0.95926 − 1.78876I
b = −0.587714 − 0.974481I
−6.33075 + 8.77850I 0
u = 0.19671 − 1.59879I
a = 0.95926 + 1.78876I
b = −0.587714 + 0.974481I
−6.33075 − 8.77850I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11385 + 1.60819I
a = −0.01550 + 1.75233I
b = −0.159993 + 0.835696I
−8.85016 + 3.75057I 0
u = 0.11385 − 1.60819I
a = −0.01550 − 1.75233I
b = −0.159993 − 0.835696I
−8.85016 − 3.75057I 0
u = −0.03980 + 1.61583I
a = 0.59179 + 2.44233I
b = −0.207157 + 1.168620I
−13.56530 − 0.00825I 0
u = −0.03980 − 1.61583I
a = 0.59179 − 2.44233I
b = −0.207157 − 1.168620I
−13.56530 + 0.00825I 0
u = 0.01953 + 1.65553I
a = −0.02044 − 2.11856I
b = −0.548611 − 1.071920I
−11.38720 + 7.42542I 0
u = 0.01953 − 1.65553I
a = −0.02044 + 2.11856I
b = −0.548611 + 1.071920I
−11.38720 − 7.42542I 0
u = 0.320073
a = 1.19050
b = 0.294304
0.909318 11.9760
u = 0.215339 + 0.116095I
a = 1.65550 + 0.61588I
b = 0.580913 + 0.842383I
0.56266 + 2.30732I 0.56794 − 4.25502I
u = 0.215339 − 0.116095I
a = 1.65550 − 0.61588I
b = 0.580913 − 0.842383I
0.56266 − 2.30732I 0.56794 + 4.25502I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
89
+ 35u
88
+ ··· + 9u − 1
c
2
, c
5
u
89
+ u
88
+ ··· + 9u − 1
c
3
u
89
+ u
88
+ ··· − 1279u − 421
c
4
u
89
+ 3u
88
+ ··· + 1113u − 503
c
6
, c
7
, c
10
c
11
u
89
+ u
88
+ ··· + 5u − 1
c
8
u
89
− 5u
88
+ ··· + u − 1
c
9
u
89
− 19u
88
+ ··· + 158017u − 14627
c
12
u
89
+ 9u
88
+ ··· − u − 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
89
+ 39y
88
+ ··· − 651y −1
c
2
, c
5
y
89
+ 35y
88
+ ··· + 9y −1
c
3
y
89
− 109y
88
+ ··· + 13004525y −177241
c
4
y
89
− 81y
88
+ ··· − 6843435y −253009
c
6
, c
7
, c
10
c
11
y
89
+ 99y
88
+ ··· + 5y −1
c
8
y
89
− 9y
88
+ ··· + 5y −1
c
9
y
89
+ 27y
88
+ ··· − 8680509275y −213949129
c
12
y
89
− 5y
88
+ ··· + 9y −1
15
