12a
0140
(K12a
0140
)
A knot diagram
1
Linearized knot diagam
3 5 8 9 2 11 10 1 12 7 6 4
Solving Sequence
6,11
7
4,12
1 10 8 3 2 5 9
c
6
c
11
c
12
c
10
c
7
c
3
c
1
c
5
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.49803 × 10
58
u
89
+ 5.92542 × 10
58
u
88
+ ··· + 1.72660 × 10
59
b + 1.98078 × 10
59
,
1.02947 × 10
59
u
89
+ 2.41879 × 10
58
u
88
+ ··· + 1.72660 × 10
59
a + 1.67665 × 10
59
, u
90
+ u
89
+ ··· + 5u + 1i
* 1 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
= h1.50 × 10
58
u
89
+ 5.93 × 10
58
u
88
+ · · · + 1.73 × 10
59
b + 1.98 × 10
59
, 1.03 ×
10
59
u
89
+2.42×10
58
u
88
+· · ·+1.73×10
59
a+1.68×10
59
, u
90
+u
89
+· · ·+5u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
4
=
−0.596241u
89
− 0.140090u
88
+ ··· − 10.1457u − 0.971072
−0.0867618u
89
− 0.343185u
88
+ ··· − 1.42481u − 1.14721
a
12
=
−u
u
a
1
=
0.506491u
89
− 0.464959u
88
+ ··· − 2.21593u + 0.951695
0.858763u
89
+ 0.971450u
88
+ ··· + 4.50932u + 1.36525
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−0.922415u
89
+ 0.486437u
88
+ ··· − 9.28974u − 1.51851
−0.101016u
89
− 0.289665u
88
+ ··· − 6.01833u − 2.17824
a
2
=
0.598272u
89
− 0.135672u
88
+ ··· − 2.38042u − 1.48653
0.110717u
89
+ 0.268130u
88
+ ··· + 6.26801u + 1.12390
a
5
=
−0.653759u
89
+ 0.807509u
88
+ ··· − 4.03678u + 0.331898
−0.100166u
89
− 0.244164u
88
+ ··· − 5.85636u − 1.97404
a
9
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.95959u
89
− 1.57308u
88
+ ··· + 33.0318u + 12.1521
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 37u
89
+ ··· + 9u + 1
c
2
, c
5
u
90
+ u
89
+ ··· + 9u + 1
c
3
u
90
− u
89
+ ··· − 21u + 1
c
4
u
90
+ u
89
+ ··· + 53u + 7
c
6
, c
7
, c
10
c
11
u
90
− u
89
+ ··· − 5u + 1
c
8
u
90
+ 5u
89
+ ··· + u + 1
c
9
u
90
+ 21u
89
+ ··· + 30261u + 4067
c
12
u
90
+ 9u
89
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 33y
89
+ ··· − 403y + 1
c
2
, c
5
y
90
+ 37y
89
+ ··· + 9y + 1
c
3
y
90
+ 101y
89
+ ··· + 89y + 1
c
4
y
90
+ 93y
89
+ ··· + 1237y + 49
c
6
, c
7
, c
10
c
11
y
90
+ 101y
89
+ ··· + 5y + 1
c
8
y
90
+ 9y
89
+ ··· + 5y + 1
c
9
y
90
+ 13y
89
+ ··· + 583522625y + 16540489
c
12
y
90
+ 5y
89
+ ··· + 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.153386 + 0.949459I
a = 0.718759 + 0.923313I
b = 0.174097 − 0.184217I
4.37025 − 2.09737I 0
u = −0.153386 − 0.949459I
a = 0.718759 − 0.923313I
b = 0.174097 + 0.184217I
4.37025 + 2.09737I 0
u = 0.592585 + 0.748622I
a = 0.525999 − 0.073835I
b = −0.247712 + 0.718060I
−1.04239 − 5.87786I 0
u = 0.592585 − 0.748622I
a = 0.525999 + 0.073835I
b = −0.247712 − 0.718060I
−1.04239 + 5.87786I 0
u = −0.574662 + 0.686016I
a = 1.314030 + 0.037343I
b = −1.09112 − 1.69898I
−0.2793 + 14.4752I 0
u = −0.574662 − 0.686016I
a = 1.314030 − 0.037343I
b = −1.09112 + 1.69898I
−0.2793 − 14.4752I 0
u = −0.150469 + 1.111890I
a = −0.878713 − 0.860540I
b = 0.042720 + 0.283468I
2.83318 − 7.25186I 0
u = −0.150469 − 1.111890I
a = −0.878713 + 0.860540I
b = 0.042720 − 0.283468I
2.83318 + 7.25186I 0
u = 0.417484 + 0.766577I
a = −0.398067 − 0.023582I
b = 0.098415 − 0.679860I
0.01934 − 1.98738I 0
u = 0.417484 − 0.766577I
a = −0.398067 + 0.023582I
b = 0.098415 + 0.679860I
0.01934 + 1.98738I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540546 + 0.681468I
a = −1.409290 + 0.010881I
b = 1.10186 + 1.70068I
1.74657 + 8.70254I 0
u = −0.540546 − 0.681468I
a = −1.409290 − 0.010881I
b = 1.10186 − 1.70068I
1.74657 − 8.70254I 0
u = 0.656158 + 0.547764I
a = 0.572560 − 0.062751I
b = −0.313753 + 0.727781I
−2.06605 − 0.65625I 0
u = 0.656158 − 0.547764I
a = 0.572560 + 0.062751I
b = −0.313753 − 0.727781I
−2.06605 + 0.65625I 0
u = 0.716623 + 0.371946I
a = −0.498659 − 0.100748I
b = 0.272381 − 0.633490I
−2.58726 − 3.92694I −12.8588 + 9.2593I
u = 0.716623 − 0.371946I
a = −0.498659 + 0.100748I
b = 0.272381 + 0.633490I
−2.58726 + 3.92694I −12.8588 − 9.2593I
u = −0.531750 + 0.597942I
a = 1.328430 − 0.323224I
b = −1.13869 − 1.67077I
−4.62635 + 6.13378I 0. − 8.46328I
u = −0.531750 − 0.597942I
a = 1.328430 + 0.323224I
b = −1.13869 + 1.67077I
−4.62635 − 6.13378I 0. + 8.46328I
u = −0.443199 + 0.608183I
a = −1.21211 − 1.52602I
b = −0.912945 + 0.867545I
0.35574 + 6.37386I 1.05559 − 12.60773I
u = −0.443199 − 0.608183I
a = −1.21211 + 1.52602I
b = −0.912945 − 0.867545I
0.35574 − 6.37386I 1.05559 + 12.60773I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387123 + 0.636739I
a = −0.193637 + 0.190795I
b = −0.006821 − 0.901193I
−0.01272 − 2.08828I −2.58132 + 5.68138I
u = 0.387123 − 0.636739I
a = −0.193637 − 0.190795I
b = −0.006821 + 0.901193I
−0.01272 + 2.08828I −2.58132 − 5.68138I
u = −0.375933 + 0.626578I
a = −2.06776 + 0.11377I
b = 1.01204 + 1.77494I
2.64454 + 3.98095I 7.57746 − 9.49711I
u = −0.375933 − 0.626578I
a = −2.06776 − 0.11377I
b = 1.01204 − 1.77494I
2.64454 − 3.98095I 7.57746 + 9.49711I
u = −0.669369 + 0.250763I
a = −1.249650 − 0.365953I
b = −0.458430 + 1.299980I
−1.56816 − 10.28520I −3.97736 + 6.02657I
u = −0.669369 − 0.250763I
a = −1.249650 + 0.365953I
b = −0.458430 − 1.299980I
−1.56816 + 10.28520I −3.97736 − 6.02657I
u = 0.703492 + 0.126133I
a = −0.222901 − 0.350127I
b = 0.112898 − 0.515008I
−2.86278 + 1.53210I −14.6011 − 1.5393I
u = 0.703492 − 0.126133I
a = −0.222901 + 0.350127I
b = 0.112898 + 0.515008I
−2.86278 − 1.53210I −14.6011 + 1.5393I
u = −0.317537 + 0.631586I
a = 0.69364 + 1.58671I
b = 0.928055 − 0.324587I
2.99128 + 0.66231I 9.52889 − 2.63944I
u = −0.317537 − 0.631586I
a = 0.69364 − 1.58671I
b = 0.928055 + 0.324587I
2.99128 − 0.66231I 9.52889 + 2.63944I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165064 + 1.288320I
a = −1.113030 − 0.351119I
b = 0.563002 − 0.110438I
2.63709 − 7.22205I 0
u = 0.165064 − 1.288320I
a = −1.113030 + 0.351119I
b = 0.563002 + 0.110438I
2.63709 + 7.22205I 0
u = 0.418563 + 0.546343I
a = −2.50765 − 0.56009I
b = 1.94029 + 0.73720I
−0.24570 − 3.76742I 2.5969 − 21.3357I
u = 0.418563 − 0.546343I
a = −2.50765 + 0.56009I
b = 1.94029 − 0.73720I
−0.24570 + 3.76742I 2.5969 + 21.3357I
u = −0.569753 + 0.342177I
a = −1.57369 − 0.51879I
b = −0.457247 + 1.318270I
−5.37588 − 2.34777I −8.46003 + 1.41530I
u = −0.569753 − 0.342177I
a = −1.57369 + 0.51879I
b = −0.457247 − 1.318270I
−5.37588 + 2.34777I −8.46003 − 1.41530I
u = −0.622072 + 0.229860I
a = 1.333090 + 0.265168I
b = 0.458059 − 1.289570I
0.42234 − 4.75738I −1.60038 + 2.22004I
u = −0.622072 − 0.229860I
a = 1.333090 − 0.265168I
b = 0.458059 + 1.289570I
0.42234 + 4.75738I −1.60038 − 2.22004I
u = 0.351415 + 0.558810I
a = 2.39621 + 0.42195I
b = −1.69911 − 0.46842I
0.133011 + 0.337575I −11.1760 − 9.1703I
u = 0.351415 − 0.558810I
a = 2.39621 − 0.42195I
b = −1.69911 + 0.46842I
0.133011 − 0.337575I −11.1760 + 9.1703I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220551 + 0.576106I
a = 2.35810 + 0.27719I
b = −0.74063 − 1.49851I
1.73042 − 2.10860I 6.00206 + 2.72036I
u = −0.220551 − 0.576106I
a = 2.35810 − 0.27719I
b = −0.74063 + 1.49851I
1.73042 + 2.10860I 6.00206 − 2.72036I
u = 0.407501 + 0.439459I
a = −1.91928 − 0.47694I
b = 1.40687 + 0.99133I
−0.571516 + 0.804092I 14.6443 + 7.0088I
u = 0.407501 − 0.439459I
a = −1.91928 + 0.47694I
b = 1.40687 − 0.99133I
−0.571516 − 0.804092I 14.6443 − 7.0088I
u = 0.05663 + 1.42405I
a = 1.58377 + 0.57387I
b = −0.963257 − 0.289901I
4.57161 − 2.79628I 0
u = 0.05663 − 1.42405I
a = 1.58377 − 0.57387I
b = −0.963257 + 0.289901I
4.57161 + 2.79628I 0
u = 0.471994 + 0.317933I
a = 0.952599 + 0.435782I
b = −0.484844 + 0.384289I
−0.989919 − 0.990182I −5.04840 + 4.14744I
u = 0.471994 − 0.317933I
a = 0.952599 − 0.435782I
b = −0.484844 − 0.384289I
−0.989919 + 0.990182I −5.04840 − 4.14744I
u = −0.09077 + 1.42884I
a = −1.29677 − 1.10983I
b = 0.450417 + 0.767926I
0.201142 − 0.116256I 0
u = −0.09077 − 1.42884I
a = −1.29677 + 1.10983I
b = 0.450417 − 0.767926I
0.201142 + 0.116256I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.405371 + 0.280603I
a = −0.199952 − 1.378270I
b = −0.959262 − 0.968605I
−0.56516 − 3.28407I −3.30805 + 5.23829I
u = −0.405371 − 0.280603I
a = −0.199952 + 1.378270I
b = −0.959262 + 0.968605I
−0.56516 + 3.28407I −3.30805 − 5.23829I
u = 0.16937 + 1.52158I
a = 1.51766 − 0.30903I
b = −1.130990 + 0.625814I
4.65622 − 3.58702I 0
u = 0.16937 − 1.52158I
a = 1.51766 + 0.30903I
b = −1.130990 − 0.625814I
4.65622 + 3.58702I 0
u = 0.09271 + 1.53236I
a = −1.27280 − 2.03682I
b = 1.17772 + 2.44286I
6.09255 − 0.84757I 0
u = 0.09271 − 1.53236I
a = −1.27280 + 2.03682I
b = 1.17772 − 2.44286I
6.09255 + 0.84757I 0
u = −0.05357 + 1.53456I
a = 1.45113 + 0.11741I
b = −1.46172 − 1.07706I
5.68381 − 2.27432I 0
u = −0.05357 − 1.53456I
a = 1.45113 − 0.11741I
b = −1.46172 + 1.07706I
5.68381 + 2.27432I 0
u = 0.11432 + 1.56167I
a = −2.93352 − 1.95251I
b = 2.65903 + 2.16225I
6.90903 − 5.66157I 0
u = 0.11432 − 1.56167I
a = −2.93352 + 1.95251I
b = 2.65903 − 2.16225I
6.90903 + 5.66157I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09617 + 1.56590I
a = 3.12411 + 1.27896I
b = −2.77213 − 1.39716I
7.37300 − 1.26295I 0
u = 0.09617 − 1.56590I
a = 3.12411 − 1.27896I
b = −2.77213 + 1.39716I
7.37300 + 1.26295I 0
u = −0.15237 + 1.56573I
a = 2.50255 + 1.03565I
b = −1.82102 − 1.91169I
2.62908 + 8.61485I 0
u = −0.15237 − 1.56573I
a = 2.50255 − 1.03565I
b = −1.82102 + 1.91169I
2.62908 − 8.61485I 0
u = −0.07670 + 1.57131I
a = 2.36617 + 1.61202I
b = −1.31873 − 1.95306I
9.07886 − 0.93094I 0
u = −0.07670 − 1.57131I
a = 2.36617 − 1.61202I
b = −1.31873 + 1.95306I
9.07886 + 0.93094I 0
u = −0.12500 + 1.57476I
a = 0.06493 − 1.49401I
b = −0.906132 + 0.621652I
7.74476 + 8.43784I 0
u = −0.12500 − 1.57476I
a = 0.06493 + 1.49401I
b = −0.906132 − 0.621652I
7.74476 − 8.43784I 0
u = 0.10144 + 1.57704I
a = −0.66918 + 1.52360I
b = 0.49284 − 1.89219I
7.47987 − 3.80306I 0
u = 0.10144 − 1.57704I
a = −0.66918 − 1.52360I
b = 0.49284 + 1.89219I
7.47987 + 3.80306I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09384 + 1.58164I
a = −0.702815 + 1.007970I
b = 1.244420 + 0.005868I
10.52950 + 2.19494I 0
u = −0.09384 − 1.58164I
a = −0.702815 − 1.007970I
b = 1.244420 − 0.005868I
10.52950 − 2.19494I 0
u = −0.10790 + 1.58110I
a = −2.64329 − 1.41564I
b = 1.66442 + 2.10196I
10.15180 + 5.76027I 0
u = −0.10790 − 1.58110I
a = −2.64329 + 1.41564I
b = 1.66442 − 2.10196I
10.15180 − 5.76027I 0
u = −0.16145 + 1.59638I
a = −2.42197 − 1.17248I
b = 1.75629 + 1.92985I
9.4286 + 11.3153I 0
u = −0.16145 − 1.59638I
a = −2.42197 + 1.17248I
b = 1.75629 − 1.92985I
9.4286 − 11.3153I 0
u = −0.17437 + 1.59798I
a = 2.37867 + 1.16311I
b = −1.74876 − 1.91913I
7.4050 + 17.2703I 0
u = −0.17437 − 1.59798I
a = 2.37867 − 1.16311I
b = −1.74876 + 1.91913I
7.4050 − 17.2703I 0
u = 0.14486 + 1.61314I
a = −0.922533 + 0.684068I
b = 0.625007 − 1.078630I
8.05248 − 4.24619I 0
u = 0.14486 − 1.61314I
a = −0.922533 − 0.684068I
b = 0.625007 + 1.078630I
8.05248 + 4.24619I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18353 + 1.61376I
a = 1.027430 − 0.490906I
b = −0.695784 + 0.881112I
6.89750 − 8.82487I 0
u = 0.18353 − 1.61376I
a = 1.027430 + 0.490906I
b = −0.695784 − 0.881112I
6.89750 + 8.82487I 0
u = 0.227195 + 0.284908I
a = 1.90995 − 0.81708I
b = −0.954823 − 0.478011I
−0.50806 − 2.64460I 2.81091 + 6.46234I
u = 0.227195 − 0.284908I
a = 1.90995 + 0.81708I
b = −0.954823 + 0.478011I
−0.50806 + 2.64460I 2.81091 − 6.46234I
u = −0.02421 + 1.64276I
a = −0.0903645 + 0.0173208I
b = 0.439641 + 0.634212I
13.23290 − 1.53819I 0
u = −0.02421 − 1.64276I
a = −0.0903645 − 0.0173208I
b = 0.439641 − 0.634212I
13.23290 + 1.53819I 0
u = −0.339095 + 0.048393I
a = 1.85470 − 0.96460I
b = 0.425963 − 0.989713I
1.24876 − 1.48001I 1.04199 + 3.33888I
u = −0.339095 − 0.048393I
a = 1.85470 + 0.96460I
b = 0.425963 + 0.989713I
1.24876 + 1.48001I 1.04199 − 3.33888I
u = −0.00034 + 1.65939I
a = −0.0768283 + 0.1112280I
b = −0.262523 − 0.705756I
12.22560 − 7.06179I 0
u = −0.00034 − 1.65939I
a = −0.0768283 − 0.1112280I
b = −0.262523 + 0.705756I
12.22560 + 7.06179I 0
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
90
+ 37u
89
+ ··· + 9u + 1
c
2
, c
5
u
90
+ u
89
+ ··· + 9u + 1
c
3
u
90
− u
89
+ ··· − 21u + 1
c
4
u
90
+ u
89
+ ··· + 53u + 7
c
6
, c
7
, c
10
c
11
u
90
− u
89
+ ··· − 5u + 1
c
8
u
90
+ 5u
89
+ ··· + u + 1
c
9
u
90
+ 21u
89
+ ··· + 30261u + 4067
c
12
u
90
+ 9u
89
+ ··· + u + 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 33y
89
+ ··· − 403y + 1
c
2
, c
5
y
90
+ 37y
89
+ ··· + 9y + 1
c
3
y
90
+ 101y
89
+ ··· + 89y + 1
c
4
y
90
+ 93y
89
+ ··· + 1237y + 49
c
6
, c
7
, c
10
c
11
y
90
+ 101y
89
+ ··· + 5y + 1
c
8
y
90
+ 9y
89
+ ··· + 5y + 1
c
9
y
90
+ 13y
89
+ ··· + 583522625y + 16540489
c
12
y
90
+ 5y
89
+ ··· + 9y + 1
15
