12a
0201
(K12a
0201
)
A knot diagram
1
Linearized knot diagam
3 5 11 7 2 10 1 12 4 6 9 8
Solving Sequence
8,12 4,9
10 1 7 5 6 11 3 2
c
8
c
9
c
12
c
7
c
4
c
6
c
11
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.58867 × 10
91
u
83
+ 1.02171 × 10
92
u
82
+ ··· + 1.57098 × 10
92
b 1.00231 × 10
92
,
1.83263 × 10
92
u
83
+ 5.48113 × 10
92
u
82
+ ··· + 1.57098 × 10
92
a + 7.20038 × 10
92
, u
84
3u
83
+ ··· 3u + 1i
I
u
2
= hu
2
a + b, 10u
2
a + 25a
2
+ 5au + 13u
2
15a + 6u + 17, u
3
+ u
2
+ 2u + 1i
* 2 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
= h−3.59×10
91
u
83
+1.02×10
92
u
82
+· · ·+1.57×10
92
b1.00×10
92
, 1.83×
10
92
u
83
+5.48×10
92
u
82
+· · ·+1.57×10
92
a+7.20×10
92
, u
84
3u
83
+· · ·3u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
1.16655u
83
3.48898u
82
+ ··· + 6.40630u 4.58336
0.228435u
83
0.650361u
82
+ ··· + 0.796213u + 0.638014
a
9
=
1
u
2
a
10
=
0.00496120u
83
+ 0.0416024u
82
+ ··· 0.527099u 0.844089
0.0803009u
83
0.303932u
82
+ ··· + 0.736204u + 0.163754
a
1
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
0.869710u
83
2.51392u
82
+ ··· + 3.61734u 4.81101
0.108064u
83
+ 0.181385u
82
+ ··· 0.185590u + 1.02410
a
6
=
0.163754u
83
+ 0.571563u
82
+ ··· 3.05646u + 1.22747
0.0564860u
83
+ 0.102861u
82
+ ··· + 0.829205u + 0.00496120
a
11
=
u
u
3
+ u
a
3
=
0.835016u
83
2.40727u
82
+ ··· + 5.41664u 4.56959
0.175384u
83
0.0477895u
82
+ ··· + 1.19301u + 0.711354
a
2
=
0.667963u
83
+ 1.84046u
82
+ ··· 5.88896u 1.51691
0.0928646u
83
+ 0.425791u
82
+ ··· + 3.33040u 0.355437
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.16495u
83
5.74232u
82
+ ··· + 10.7785u 2.44552
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
84
+ 40u
83
+ ··· + 3294u + 625
c
2
, c
5
u
84
+ 4u
83
+ ··· + 166u + 25
c
3
25(25u
84
+ 105u
83
+ ··· 18688u + 2563)
c
4
25(25u
84
+ 10u
83
+ ··· + 227461u + 20617)
c
6
, c
10
u
84
3u
83
+ ··· 3u + 1
c
7
, c
8
, c
11
c
12
u
84
+ 3u
83
+ ··· + 3u + 1
c
9
u
84
u
83
+ ··· + 8800u + 8000
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
84
+ 12y
83
+ ··· 3086686y + 390625
c
2
, c
5
y
84
+ 40y
83
+ ··· + 3294y + 625
c
3
625(625y
84
31725y
83
+ ··· 1.22498 × 10
8
y + 6568969)
c
4
625(625y
84
13650y
83
+ ··· 5.34301 × 10
10
y + 4.25061 × 10
8
)
c
6
, c
10
y
84
+ 47y
83
+ ··· + 19y + 1
c
7
, c
8
, c
11
c
12
y
84
+ 99y
83
+ ··· + 19y + 1
c
9
y
84
35y
83
+ ··· 789120000y + 64000000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.559377 + 0.850834I
a = 1.34504 0.79140I
b = 0.0424165 + 0.1039430I
5.4555 + 13.7745I 0
u = 0.559377 0.850834I
a = 1.34504 + 0.79140I
b = 0.0424165 0.1039430I
5.4555 13.7745I 0
u = 0.603908 + 0.839047I
a = 0.818244 0.598416I
b = 0.0640806 + 0.0705229I
1.66257 7.72348I 0
u = 0.603908 0.839047I
a = 0.818244 + 0.598416I
b = 0.0640806 0.0705229I
1.66257 + 7.72348I 0
u = 0.354001 + 0.884267I
a = 1.44947 0.48407I
b = 0.151051 0.266514I
8.77859 + 4.94528I 0
u = 0.354001 0.884267I
a = 1.44947 + 0.48407I
b = 0.151051 + 0.266514I
8.77859 4.94528I 0
u = 0.501059 + 0.802771I
a = 1.45664 + 0.76972I
b = 0.0915011 0.0759455I
3.02003 + 8.18197I 0
u = 0.501059 0.802771I
a = 1.45664 0.76972I
b = 0.0915011 + 0.0759455I
3.02003 8.18197I 0
u = 0.575841 + 0.733284I
a = 0.084003 1.043710I
b = 0.182438 0.080722I
7.12558 + 2.31715I 0
u = 0.575841 0.733284I
a = 0.084003 + 1.043710I
b = 0.182438 + 0.080722I
7.12558 2.31715I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.352613 + 0.849364I
a = 0.561264 + 1.147210I
b = 0.162827 + 0.112680I
3.83598 0.83646I 0
u = 0.352613 0.849364I
a = 0.561264 1.147210I
b = 0.162827 0.112680I
3.83598 + 0.83646I 0
u = 0.059146 + 1.084560I
a = 0.794617 + 0.270479I
b = 0.322778 0.026997I
3.51431 1.41708I 0
u = 0.059146 1.084560I
a = 0.794617 0.270479I
b = 0.322778 + 0.026997I
3.51431 + 1.41708I 0
u = 0.505379 + 0.743093I
a = 0.966789 + 0.597818I
b = 0.0998708 + 0.0522679I
0.26259 2.97021I 0
u = 0.505379 0.743093I
a = 0.966789 0.597818I
b = 0.0998708 0.0522679I
0.26259 + 2.97021I 0
u = 0.498502 + 0.985151I
a = 0.394841 0.857254I
b = 0.080456 + 0.122688I
6.24548 5.02549I 0
u = 0.498502 0.985151I
a = 0.394841 + 0.857254I
b = 0.080456 0.122688I
6.24548 + 5.02549I 0
u = 0.823438 + 0.141577I
a = 0.235246 + 0.004564I
b = 0.607378 0.197816I
0.48308 + 2.97342I 0
u = 0.823438 0.141577I
a = 0.235246 0.004564I
b = 0.607378 + 0.197816I
0.48308 2.97342I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.350172 + 1.132160I
a = 0.625704 0.237671I
b = 0.198471 + 0.000769I
3.54157 1.27620I 0
u = 0.350172 1.132160I
a = 0.625704 + 0.237671I
b = 0.198471 0.000769I
3.54157 + 1.27620I 0
u = 0.774229 + 0.059652I
a = 0.319713 0.244575I
b = 0.930111 0.495675I
3.06074 9.34032I 1.08705 + 7.00360I
u = 0.774229 0.059652I
a = 0.319713 + 0.244575I
b = 0.930111 + 0.495675I
3.06074 + 9.34032I 1.08705 7.00360I
u = 0.057154 + 0.759277I
a = 2.92385 0.76517I
b = 1.44744 0.65670I
2.74047 1.50981I 1.82977 + 7.34075I
u = 0.057154 0.759277I
a = 2.92385 + 0.76517I
b = 1.44744 + 0.65670I
2.74047 + 1.50981I 1.82977 7.34075I
u = 0.283084 + 0.680233I
a = 0.176113 + 0.832722I
b = 0.305432 1.203210I
3.10028 5.80914I 1.88912 + 10.77046I
u = 0.283084 0.680233I
a = 0.176113 0.832722I
b = 0.305432 + 1.203210I
3.10028 + 5.80914I 1.88912 10.77046I
u = 0.663601 + 0.245565I
a = 0.299112 + 0.012132I
b = 0.426042 + 0.391408I
1.80973 0.97588I 6.29958 0.92330I
u = 0.663601 0.245565I
a = 0.299112 0.012132I
b = 0.426042 0.391408I
1.80973 + 0.97588I 6.29958 + 0.92330I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.666820 + 0.079514I
a = 0.382678 + 0.101341I
b = 0.868529 + 0.564372I
0.84887 4.24920I 4.48446 + 3.03882I
u = 0.666820 0.079514I
a = 0.382678 0.101341I
b = 0.868529 0.564372I
0.84887 + 4.24920I 4.48446 3.03882I
u = 0.627872 + 0.171062I
a = 0.669086 + 0.483574I
b = 0.703760 + 0.442978I
5.54769 + 1.76630I 2.07508 2.33583I
u = 0.627872 0.171062I
a = 0.669086 0.483574I
b = 0.703760 0.442978I
5.54769 1.76630I 2.07508 + 2.33583I
u = 0.196060 + 0.617529I
a = 1.239230 0.333181I
b = 0.247349 1.018570I
0.71568 + 3.16029I 2.36917 2.88022I
u = 0.196060 0.617529I
a = 1.239230 + 0.333181I
b = 0.247349 + 1.018570I
0.71568 3.16029I 2.36917 + 2.88022I
u = 0.181114 + 0.588314I
a = 2.47298 + 3.00036I
b = 1.47689 + 0.99560I
3.13471 + 1.93596I 4.26373 + 2.32250I
u = 0.181114 0.588314I
a = 2.47298 3.00036I
b = 1.47689 0.99560I
3.13471 1.93596I 4.26373 2.32250I
u = 0.285706 + 1.360680I
a = 0.240060 + 0.370676I
b = 0.219517 + 0.162799I
3.25781 4.38865I 0
u = 0.285706 1.360680I
a = 0.240060 0.370676I
b = 0.219517 0.162799I
3.25781 + 4.38865I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.273958 + 0.517742I
a = 2.14473 + 0.91311I
b = 0.732241 0.347542I
0.27546 + 3.96105I 3.31158 10.67062I
u = 0.273958 0.517742I
a = 2.14473 0.91311I
b = 0.732241 + 0.347542I
0.27546 3.96105I 3.31158 + 10.67062I
u = 0.278794 + 0.406348I
a = 1.60602 + 0.57998I
b = 0.281917 + 0.460637I
0.456460 1.219620I 6.20987 + 4.56453I
u = 0.278794 0.406348I
a = 1.60602 0.57998I
b = 0.281917 0.460637I
0.456460 + 1.219620I 6.20987 4.56453I
u = 0.293880 + 0.377603I
a = 1.078430 0.084585I
b = 0.042583 + 0.717975I
0.538633 1.103160I 7.21508 + 6.37604I
u = 0.293880 0.377603I
a = 1.078430 + 0.084585I
b = 0.042583 0.717975I
0.538633 + 1.103160I 7.21508 6.37604I
u = 0.00893 + 1.56295I
a = 0.97735 + 1.24513I
b = 1.66511 + 1.48668I
6.12688 1.59937I 0
u = 0.00893 1.56295I
a = 0.97735 1.24513I
b = 1.66511 1.48668I
6.12688 + 1.59937I 0
u = 0.01945 + 1.57262I
a = 1.93490 + 0.40789I
b = 3.50479 + 0.31797I
6.44558 1.79187I 0
u = 0.01945 1.57262I
a = 1.93490 0.40789I
b = 3.50479 0.31797I
6.44558 + 1.79187I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.04000 + 1.57921I
a = 2.69888 0.37859I
b = 4.75339 0.35957I
7.51330 + 4.86891I 0
u = 0.04000 1.57921I
a = 2.69888 + 0.37859I
b = 4.75339 + 0.35957I
7.51330 4.86891I 0
u = 0.01120 + 1.58483I
a = 0.33329 1.70734I
b = 0.40623 4.78895I
10.56600 + 1.42603I 0
u = 0.01120 1.58483I
a = 0.33329 + 1.70734I
b = 0.40623 + 4.78895I
10.56600 1.42603I 0
u = 0.288131 + 0.291830I
a = 0.748039 1.103380I
b = 0.695579 + 0.725202I
0.29629 1.71529I 6.13579 + 1.42425I
u = 0.288131 0.291830I
a = 0.748039 + 1.103380I
b = 0.695579 0.725202I
0.29629 + 1.71529I 6.13579 1.42425I
u = 0.04376 + 1.60820I
a = 1.102070 0.442715I
b = 2.15482 + 0.08868I
8.48978 + 3.97458I 0
u = 0.04376 1.60820I
a = 1.102070 + 0.442715I
b = 2.15482 0.08868I
8.48978 3.97458I 0
u = 0.06572 + 1.61236I
a = 0.25388 1.78486I
b = 0.55057 2.45686I
11.01890 7.03717I 0
u = 0.06572 1.61236I
a = 0.25388 + 1.78486I
b = 0.55057 + 2.45686I
11.01890 + 7.03717I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.02406 + 1.63596I
a = 1.27658 + 1.06452I
b = 3.37497 + 3.38315I
11.09410 1.87001I 0
u = 0.02406 1.63596I
a = 1.27658 1.06452I
b = 3.37497 3.38315I
11.09410 + 1.87001I 0
u = 0.10980 + 1.63370I
a = 1.243870 0.667925I
b = 2.51489 1.49587I
12.27640 + 0.94689I 0
u = 0.10980 1.63370I
a = 1.243870 + 0.667925I
b = 2.51489 + 1.49587I
12.27640 0.94689I 0
u = 0.14236 + 1.63151I
a = 1.60169 0.04119I
b = 3.11449 0.09048I
7.86900 5.39498I 0
u = 0.14236 1.63151I
a = 1.60169 + 0.04119I
b = 3.11449 + 0.09048I
7.86900 + 5.39498I 0
u = 0.18027 + 1.63208I
a = 1.118390 + 0.583138I
b = 2.08381 + 1.15494I
15.1614 + 5.2174I 0
u = 0.18027 1.63208I
a = 1.118390 0.583138I
b = 2.08381 1.15494I
15.1614 5.2174I 0
u = 0.14361 + 1.64435I
a = 2.11765 0.04963I
b = 4.19419 0.00744I
11.3977 + 10.6415I 0
u = 0.14361 1.64435I
a = 2.11765 + 0.04963I
b = 4.19419 + 0.00744I
11.3977 10.6415I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.09631 + 1.66230I
a = 2.20269 0.24901I
b = 4.20217 0.38809I
17.5922 + 6.6845I 0
u = 0.09631 1.66230I
a = 2.20269 + 0.24901I
b = 4.20217 + 0.38809I
17.5922 6.6845I 0
u = 0.328502 + 0.059345I
a = 2.21199 2.70852I
b = 0.726650 0.503743I
1.42146 + 3.57364I 4.61344 2.53748I
u = 0.328502 0.059345I
a = 2.21199 + 2.70852I
b = 0.726650 + 0.503743I
1.42146 3.57364I 4.61344 + 2.53748I
u = 0.17610 + 1.65959I
a = 1.52509 + 0.08404I
b = 3.02998 + 0.08952I
10.1779 10.7238I 0
u = 0.17610 1.65959I
a = 1.52509 0.08404I
b = 3.02998 0.08952I
10.1779 + 10.7238I 0
u = 0.16399 + 1.66168I
a = 1.98755 + 0.07708I
b = 4.04967 + 0.09312I
14.0467 + 16.5764I 0
u = 0.16399 1.66168I
a = 1.98755 0.07708I
b = 4.04967 0.09312I
14.0467 16.5764I 0
u = 0.184110 + 0.262726I
a = 2.32875 0.09910I
b = 0.492273 + 0.447222I
0.19160 1.53066I 0.415592 + 0.997580I
u = 0.184110 0.262726I
a = 2.32875 + 0.09910I
b = 0.492273 0.447222I
0.19160 + 1.53066I 0.415592 0.997580I
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.07757 + 1.68352I
a = 1.51866 0.11008I
b = 3.13003 0.08518I
13.07090 2.69496I 0
u = 0.07757 1.68352I
a = 1.51866 + 0.11008I
b = 3.13003 + 0.08518I
13.07090 + 2.69496I 0
u = 0.10895 + 1.70761I
a = 1.271630 + 0.476012I
b = 2.67034 + 0.89787I
15.7142 2.6891I 0
u = 0.10895 1.70761I
a = 1.271630 0.476012I
b = 2.67034 0.89787I
15.7142 + 2.6891I 0
13
II. I
u
2
= hu
2
a + b, 10u
2
a + 13u
2
+ · · · 15a + 17, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
u
2
a
a
9
=
1
u
2
a
10
=
1
u
2
a
1
=
u
u
a
7
=
u
2
+ 1
u
2
a
5
=
2a
2u
2
a au
a
6
=
u
u
a
11
=
u
u
2
u 1
a
3
=
u
2
a + a
u
2
a au a
a
2
=
u
2
a
4
5
u
2
+ a +
2
5
u
6
5
u
2
a au +
1
5
u
2
a +
7
5
u +
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
27
5
u
2
a +
74
5
au +
87
25
u
2
+
53
5
a +
94
25
u +
133
25
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
25(25u
6
20u
5
+ 21u
4
6u
3
+ 5u
2
u + 1)
c
4
25(25u
6
35u
5
+ 29u
4
18u
3
+ 9u
2
4u + 1)
c
6
(u
3
u
2
+ 1)
2
c
7
, c
8
(u
3
+ u
2
+ 2u + 1)
2
c
9
u
6
c
10
(u
3
+ u
2
1)
2
c
11
, c
12
(u
3
u
2
+ 2u 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
625(625y
6
+ 650y
5
+ 451y
4
+ 184y
3
+ 55y
2
+ 9y + 1)
c
4
625(625y
6
+ 225y
5
+ 31y
4
32y
3
5y
2
+ 2y + 1)
c
6
, c
10
(y
3
y
2
+ 2y 1)
2
c
7
, c
8
, c
11
c
12
(y
3
+ 3y
2
+ 2y 1)
2
c
9
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.432147 0.224180I
b = 0.592331 0.615655I
3.02413 4.85801I 2.36205 + 10.05749I
u = 0.215080 + 1.307140I
a = 0.410219 0.262160I
b = 0.829338 0.205146I
3.02413 0.79824I 3.05664 3.74022I
u = 0.215080 1.307140I
a = 0.432147 + 0.224180I
b = 0.592331 + 0.615655I
3.02413 + 4.85801I 2.36205 10.05749I
u = 0.215080 1.307140I
a = 0.410219 + 0.262160I
b = 0.829338 + 0.205146I
3.02413 + 0.79824I 3.05664 + 3.74022I
u = 0.569840
a = 0.421928 + 0.730800I
b = 0.137007 0.237304I
1.11345 2.02988I 5.96131 + 2.86462I
u = 0.569840
a = 0.421928 0.730800I
b = 0.137007 + 0.237304I
1.11345 + 2.02988I 5.96131 2.86462I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
u + 1)
3
)(u
84
+ 40u
83
+ ··· + 3294u + 625)
c
2
((u
2
+ u + 1)
3
)(u
84
+ 4u
83
+ ··· + 166u + 25)
c
3
625(25u
6
20u
5
+ 21u
4
6u
3
+ 5u
2
u + 1)
· (25u
84
+ 105u
83
+ ··· 18688u + 2563)
c
4
625(25u
6
35u
5
+ 29u
4
18u
3
+ 9u
2
4u + 1)
· (25u
84
+ 10u
83
+ ··· + 227461u + 20617)
c
5
((u
2
u + 1)
3
)(u
84
+ 4u
83
+ ··· + 166u + 25)
c
6
((u
3
u
2
+ 1)
2
)(u
84
3u
83
+ ··· 3u + 1)
c
7
, c
8
((u
3
+ u
2
+ 2u + 1)
2
)(u
84
+ 3u
83
+ ··· + 3u + 1)
c
9
u
6
(u
84
u
83
+ ··· + 8800u + 8000)
c
10
((u
3
+ u
2
1)
2
)(u
84
3u
83
+ ··· 3u + 1)
c
11
, c
12
((u
3
u
2
+ 2u 1)
2
)(u
84
+ 3u
83
+ ··· + 3u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
84
+ 12y
83
+ ··· 3086686y + 390625)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
84
+ 40y
83
+ ··· + 3294y + 625)
c
3
390625(625y
6
+ 650y
5
+ 451y
4
+ 184y
3
+ 55y
2
+ 9y + 1)
· (625y
84
31725y
83
+ ··· 122497860y + 6568969)
c
4
390625(625y
6
+ 225y
5
+ 31y
4
32y
3
5y
2
+ 2y + 1)
· (625y
84
13650y
83
+ ··· 53430131371y + 425060689)
c
6
, c
10
((y
3
y
2
+ 2y 1)
2
)(y
84
+ 47y
83
+ ··· + 19y + 1)
c
7
, c
8
, c
11
c
12
((y
3
+ 3y
2
+ 2y 1)
2
)(y
84
+ 99y
83
+ ··· + 19y + 1)
c
9
y
6
(y
84
35y
83
+ ··· 7.89120 × 10
8
y + 6.40000 × 10
7
)
19