12n
0182
(K12n
0182
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 3 6 5 9 7 11
Solving Sequence
5,10 3,6
2 1 4 9 11 8 7 12
c
5
c
2
c
1
c
4
c
9
c
10
c
8
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.36510 × 10
17
u
43
+ 9.54484 × 10
15
u
42
+ ··· + 1.53293 × 10
18
b + 1.33198 × 10
18
,
− 1.62174 × 10
18
u
43
+ 1.01186 × 10
18
u
42
+ ··· + 1.53293 × 10
18
a − 2.65681 × 10
18
, u
44
− 2u
43
+ ··· − u − 1i
I
u
2
= hb + 1, −2u
8
+ u
7
+ 5u
6
− 3u
5
− 4u
4
+ 3u
3
− 2u
2
+ a + 2, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 53 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−1.37×10
17
u
43
+9.54×10
15
u
42
+· · ·+1.53×10
18
b+1.33×10
18
, −1.62×
10
18
u
43
+1.01×10
18
u
42
+· · ·+1.53×10
18
a−2.66×10
18
, u
44
−2u
43
+· · ·−u−1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1.05794u
43
− 0.660080u
42
+ ··· − 1.09633u + 1.73316
0.0890516u
43
− 0.00622654u
42
+ ··· − 0.0813299u − 0.868912
a
6
=
1
−u
2
a
2
=
1.14699u
43
− 0.666307u
42
+ ··· − 1.17766u + 0.864250
0.0890516u
43
− 0.00622654u
42
+ ··· − 0.0813299u − 0.868912
a
1
=
0.108274u
43
− 0.166759u
42
+ ··· − 0.652412u − 1.28055
0.0893388u
43
− 0.0640460u
42
+ ··· + 0.0125622u + 0.212283
a
4
=
1.02965u
43
− 0.560533u
42
+ ··· − 0.952635u + 1.81995
0.0297535u
43
+ 0.00665588u
42
+ ··· − 0.112208u − 0.958338
a
9
=
−u
u
a
11
=
u
3
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
−0.763419u
43
+ 1.17680u
42
+ ··· + 2.97987u − 0.290205
0.246436u
43
− 0.344490u
42
+ ··· − 0.623825u + 0.0577269
a
12
=
−0.143931u
43
+ 0.0553767u
42
+ ··· − 0.710282u − 1.19853
0.201658u
43
+ 0.0756056u
42
+ ··· + 0.749462u + 0.516983
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1914830631575013385
510976393730080697
u
43
+
344553853487150851
510976393730080697
u
42
+ ··· +
143617252098136043
510976393730080697
u −
6332818336569097832
510976393730080697
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 58u
43
+ ··· + 579u + 1
c
2
, c
4
u
44
− 10u
43
+ ··· − 39u − 1
c
3
, c
7
u
44
− u
43
+ ··· + 8192u + 512
c
5
, c
9
u
44
− 2u
43
+ ··· − u − 1
c
6
, c
11
u
44
− 2u
43
+ ··· − u − 1
c
8
u
44
− 6u
43
+ ··· + 537u + 117
c
10
u
44
− 18u
43
+ ··· − 15u + 1
c
12
u
44
+ 30u
43
+ ··· − 15u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 134y
43
+ ··· + 635013y + 1
c
2
, c
4
y
44
− 58y
43
+ ··· − 579y + 1
c
3
, c
7
y
44
− 57y
43
+ ··· − 14417920y + 262144
c
5
, c
9
y
44
− 18y
43
+ ··· − 15y + 1
c
6
, c
11
y
44
+ 30y
43
+ ··· − 15y + 1
c
8
y
44
− 18y
43
+ ··· − 749115y + 13689
c
10
y
44
+ 18y
43
+ ··· − 103y + 1
c
12
y
44
− 30y
43
+ ··· − 303y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688110 + 0.685606I
a = 0.863564 + 0.136667I
b = −1.10774 − 1.23190I
−5.98385 − 2.15414I −9.20742 + 2.18421I
u = 0.688110 − 0.685606I
a = 0.863564 − 0.136667I
b = −1.10774 + 1.23190I
−5.98385 + 2.15414I −9.20742 − 2.18421I
u = 0.845683 + 0.592317I
a = −1.25164 − 1.23315I
b = −1.243990 + 0.046469I
−3.00115 + 2.34547I 0.61315 − 3.20636I
u = 0.845683 − 0.592317I
a = −1.25164 + 1.23315I
b = −1.243990 − 0.046469I
−3.00115 − 2.34547I 0.61315 + 3.20636I
u = 0.905356 + 0.530754I
a = 1.20385 − 5.40977I
b = −0.922690 + 0.021453I
−3.18610 + 2.04679I −26.8865 + 3.7587I
u = 0.905356 − 0.530754I
a = 1.20385 + 5.40977I
b = −0.922690 − 0.021453I
−3.18610 − 2.04679I −26.8865 − 3.7587I
u = 0.515365 + 0.921554I
a = 0.0523760 − 0.1117110I
b = 1.80210 + 0.36838I
−15.2823 − 8.3356I −7.68501 + 3.11371I
u = 0.515365 − 0.921554I
a = 0.0523760 + 0.1117110I
b = 1.80210 − 0.36838I
−15.2823 + 8.3356I −7.68501 − 3.11371I
u = 0.497628 + 0.931746I
a = 0.0477482 + 0.1144550I
b = 1.79749 − 0.07891I
−15.1569 + 3.5164I −7.98502 − 2.64030I
u = 0.497628 − 0.931746I
a = 0.0477482 − 0.1144550I
b = 1.79749 + 0.07891I
−15.1569 − 3.5164I −7.98502 + 2.64030I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804579 + 0.489610I
a = 1.071560 − 0.142770I
b = −0.0319136 − 0.0206061I
−1.74326 − 2.05593I −4.38426 + 3.93247I
u = −0.804579 − 0.489610I
a = 1.071560 + 0.142770I
b = −0.0319136 + 0.0206061I
−1.74326 + 2.05593I −4.38426 − 3.93247I
u = −0.511016 + 0.933628I
a = 0.0888703 − 0.0020707I
b = 1.71985 − 0.15282I
−10.83690 + 2.46216I −5.51655 − 0.44407I
u = −0.511016 − 0.933628I
a = 0.0888703 + 0.0020707I
b = 1.71985 + 0.15282I
−10.83690 − 2.46216I −5.51655 + 0.44407I
u = −0.849836 + 0.684332I
a = 0.27393 + 1.58284I
b = −2.08374 − 0.15007I
−7.96382 − 2.63414I −10.69768 + 3.24229I
u = −0.849836 − 0.684332I
a = 0.27393 − 1.58284I
b = −2.08374 + 0.15007I
−7.96382 + 2.63414I −10.69768 − 3.24229I
u = 0.880721 + 0.195510I
a = 0.851230 + 0.816240I
b = 0.027650 − 0.386682I
1.49461 + 0.44791I 5.81228 − 0.84575I
u = 0.880721 − 0.195510I
a = 0.851230 − 0.816240I
b = 0.027650 + 0.386682I
1.49461 − 0.44791I 5.81228 + 0.84575I
u = −0.698557 + 0.569479I
a = 0.474798 − 0.585716I
b = −0.826219 + 0.509582I
−1.84063 − 0.16201I −3.33593 + 0.20561I
u = −0.698557 − 0.569479I
a = 0.474798 + 0.585716I
b = −0.826219 − 0.509582I
−1.84063 + 0.16201I −3.33593 − 0.20561I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960365 + 0.600329I
a = −0.22638 + 1.69062I
b = −0.608152 − 0.737629I
−1.02255 − 4.55319I −0.74748 + 6.17596I
u = −0.960365 − 0.600329I
a = −0.22638 − 1.69062I
b = −0.608152 + 0.737629I
−1.02255 + 4.55319I −0.74748 − 6.17596I
u = −0.860051 + 0.047625I
a = 1.74194 + 1.29974I
b = −0.364953 − 0.686094I
−1.23921 − 2.55790I −0.72063 + 3.92676I
u = −0.860051 − 0.047625I
a = 1.74194 − 1.29974I
b = −0.364953 + 0.686094I
−1.23921 + 2.55790I −0.72063 − 3.92676I
u = 0.970487 + 0.654541I
a = −0.73443 − 1.96174I
b = −0.86872 + 1.43316I
−5.13822 + 7.34601I −6.99400 − 7.81515I
u = 0.970487 − 0.654541I
a = −0.73443 + 1.96174I
b = −0.86872 − 1.43316I
−5.13822 − 7.34601I −6.99400 + 7.81515I
u = 1.132370 + 0.387785I
a = −0.128368 + 0.373910I
b = 0.558289 + 0.000722I
3.49180 + 1.33135I 7.33904 − 0.67803I
u = 1.132370 − 0.387785I
a = −0.128368 − 0.373910I
b = 0.558289 − 0.000722I
3.49180 − 1.33135I 7.33904 + 0.67803I
u = −1.137390 + 0.514032I
a = −0.404883 − 0.128194I
b = 0.649155 − 0.317441I
2.59233 − 6.57074I 3.54533 + 3.81879I
u = −1.137390 − 0.514032I
a = −0.404883 + 0.128194I
b = 0.649155 + 0.317441I
2.59233 + 6.57074I 3.54533 − 3.81879I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.270670 + 0.015648I
a = −1.99358 − 0.44608I
b = 1.65558 + 0.23166I
−8.56328 − 6.02412I −2.00000 + 3.26167I
u = −1.270670 − 0.015648I
a = −1.99358 + 0.44608I
b = 1.65558 − 0.23166I
−8.56328 + 6.02412I −2.00000 − 3.26167I
u = 1.28468
a = −1.81405
b = 1.56686
−4.09522 −1.39870
u = 1.121640 + 0.694109I
a = −0.38211 + 2.16430I
b = 1.76719 − 0.45741I
−13.4269 + 14.2723I 0
u = 1.121640 − 0.694109I
a = −0.38211 − 2.16430I
b = 1.76719 + 0.45741I
−13.4269 − 14.2723I 0
u = −0.194814 + 0.648377I
a = 0.686468 − 0.152693I
b = 0.408342 + 0.262891I
−0.02630 + 2.06519I 0.09253 − 2.36039I
u = −0.194814 − 0.648377I
a = 0.686468 + 0.152693I
b = 0.408342 − 0.262891I
−0.02630 − 2.06519I 0.09253 + 2.36039I
u = −1.128940 + 0.699014I
a = −0.50088 − 1.83474I
b = 1.68302 + 0.25609I
−8.94545 − 8.44958I 0
u = −1.128940 − 0.699014I
a = −0.50088 + 1.83474I
b = 1.68302 − 0.25609I
−8.94545 + 8.44958I 0
u = 1.136310 + 0.692427I
a = −0.83675 + 1.65755I
b = 1.75390 − 0.02647I
−13.20280 + 2.44542I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136310 − 0.692427I
a = −0.83675 − 1.65755I
b = 1.75390 + 0.02647I
−13.20280 − 2.44542I 0
u = 0.228003 + 0.393046I
a = 2.05111 − 0.21934I
b = −1.129040 + 0.431943I
−4.33669 + 1.37214I −7.87004 − 0.50855I
u = 0.228003 − 0.393046I
a = 2.05111 + 0.21934I
b = −1.129040 − 0.431943I
−4.33669 − 1.37214I −7.87004 + 0.50855I
u = −0.295609
a = 1.91719
b = −0.837652
−1.20532 −9.09590
9
II.
I
u
2
= hb+1, −2u
8
+u
7
+· · ·+a+2, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 2
−1
a
6
=
1
−u
2
a
2
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 3
−1
a
1
=
−1
0
a
4
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 2
−1
a
9
=
−u
u
a
11
=
u
3
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
−u
3
u
5
− u
3
+ u
a
12
=
−u
6
+ u
4
− 1
u
6
− 2u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
8
− 3u
7
− 10u
6
+ 8u
5
+ 2u
4
− 8u
3
+ 12u
2
− 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
, c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
10
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −1.67861 + 2.31573I
b = −1.00000
−3.42837 + 2.09337I −0.35753 + 5.88316I
u = 0.772920 − 0.510351I
a = −1.67861 − 2.31573I
b = −1.00000
−3.42837 − 2.09337I −0.35753 − 5.88316I
u = −0.825933
a = 0.871015
b = −1.00000
−0.446489 3.46070
u = −1.173910 + 0.391555I
a = 0.893484 + 0.630694I
b = −1.00000
2.72642 − 1.33617I −4.05086 + 0.75351I
u = −1.173910 − 0.391555I
a = 0.893484 − 0.630694I
b = −1.00000
2.72642 + 1.33617I −4.05086 − 0.75351I
u = 0.141484 + 0.739668I
a = −0.309843 + 0.043204I
b = −1.00000
−1.02799 − 2.45442I −7.24378 + 3.91612I
u = 0.141484 − 0.739668I
a = −0.309843 − 0.043204I
b = −1.00000
−1.02799 + 2.45442I −7.24378 − 3.91612I
u = 1.172470 + 0.500383I
a = 0.659464 − 0.874093I
b = −1.00000
1.95319 + 7.08493I −4.07818 − 8.89461I
u = 1.172470 − 0.500383I
a = 0.659464 + 0.874093I
b = −1.00000
1.95319 − 7.08493I −4.07818 + 8.89461I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
44
+ 58u
43
+ ··· + 579u + 1)
c
2
((u − 1)
9
)(u
44
− 10u
43
+ ··· − 39u − 1)
c
3
, c
7
u
9
(u
44
− u
43
+ ··· + 8192u + 512)
c
4
((u + 1)
9
)(u
44
− 10u
43
+ ··· − 39u − 1)
c
5
(u
9
− u
8
+ ··· − u + 1)(u
44
− 2u
43
+ ··· − u − 1)
c
6
(u
9
− u
8
+ ··· + u + 1)(u
44
− 2u
43
+ ··· − u − 1)
c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
44
− 6u
43
+ ··· + 537u + 117)
c
9
(u
9
+ u
8
+ ··· − u − 1)(u
44
− 2u
43
+ ··· − u − 1)
c
10
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
44
− 18u
43
+ ··· − 15u + 1)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
44
− 2u
43
+ ··· − u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
44
+ 30u
43
+ ··· − 15u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
44
− 134y
43
+ ··· + 635013y + 1)
c
2
, c
4
((y −1)
9
)(y
44
− 58y
43
+ ··· − 579y + 1)
c
3
, c
7
y
9
(y
44
− 57y
43
+ ··· − 1.44179 × 10
7
y + 262144)
c
5
, c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
44
− 18y
43
+ ··· − 15y + 1)
c
6
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
44
+ 30y
43
+ ··· − 15y + 1)
c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
44
− 18y
43
+ ··· − 749115y + 13689)
c
10
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
44
+ 18y
43
+ ··· − 103y + 1)
c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
44
− 30y
43
+ ··· − 303y + 1)
15
