11n
159
(K11n
159
)
A knot diagram
1
Linearized knot diagam
10 9 1 10 11 2 3 11 7 5 8
Solving Sequence
8,11
9
1,3
4 2 7 10 6 5
c
8
c
11
c
3
c
2
c
7
c
9
c
6
c
5
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.18672 × 10
96
u
50
− 1.99216 × 10
96
u
49
+ ··· + 1.57066 × 10
97
b − 7.53117 × 10
96
,
6.93809 × 10
95
u
50
− 3.65626 × 10
96
u
49
+ ··· + 1.57066 × 10
97
a − 2.77787 × 10
98
, u
51
+ 19u
49
+ ··· + 13u + 1i
I
u
2
= h−u
15
− u
14
− 3u
13
− u
12
+ u
11
+ 6u
10
+ 14u
9
+ 16u
8
+ 22u
7
+ 15u
6
+ 14u
5
+ 6u
4
+ 7u
3
+ u
2
+ b,
− 201u
15
− 115u
14
+ ··· + 85a − 229, u
16
+ u
15
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 67 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
=
h4.19×10
96
u
50
−1.99×10
96
u
49
+· · ·+1.57×10
97
b−7.53×10
96
, 6.94×10
95
u
50
−
3.66 × 10
96
u
49
+ · · · + 1.57 × 10
97
a − 2.78 × 10
98
, u
51
+ 19u
49
+ · · · + 13u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−0.0441731u
50
+ 0.232785u
49
+ ··· + 101.687u + 17.6860
−0.266558u
50
+ 0.126836u
49
+ ··· − 2.22590u + 0.479491
a
4
=
0.00694886u
50
+ 0.245771u
49
+ ··· + 100.087u + 17.5801
−0.215436u
50
+ 0.139822u
49
+ ··· − 3.82562u + 0.373542
a
2
=
−0.315201u
50
+ 0.322634u
49
+ ··· + 96.4791u + 17.9327
−0.255159u
50
+ 0.144501u
49
+ ··· − 1.32888u + 0.569340
a
7
=
0.492967u
50
− 0.795819u
49
+ ··· − 148.859u − 17.2613
−0.135931u
50
− 0.160168u
49
+ ··· − 20.5135u − 2.00969
a
10
=
−2.73260u
50
+ 0.0713461u
49
+ ··· − 195.275u − 13.1506
−0.141930u
50
+ 0.0517872u
49
+ ··· − 5.44851u + 0.0702398
a
6
=
2.17298u
50
− 0.00432810u
49
+ ··· + 193.781u + 17.3396
0.0132709u
50
+ 0.0275351u
49
+ ··· + 3.99076u + 0.0293163
a
5
=
2.17298u
50
− 0.00432810u
49
+ ··· + 193.781u + 17.3396
−0.0193853u
50
+ 0.0282101u
49
+ ··· + 1.87404u + 0.0336444
a
5
=
2.17298u
50
− 0.00432810u
49
+ ··· + 193.781u + 17.3396
−0.0193853u
50
+ 0.0282101u
49
+ ··· + 1.87404u + 0.0336444
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.101424u
50
+ 0.0191393u
49
+ ··· − 6.99335u + 1.74681
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 4u
50
+ ··· + 10304u + 1139
c
2
u
51
+ u
50
+ ··· + 197u + 3
c
3
u
51
+ 4u
50
+ ··· − 668u + 28
c
4
, c
5
, c
10
u
51
+ u
50
+ ··· − 15u − 1
c
6
u
51
+ 14u
49
+ ··· − 3611u + 487
c
7
u
51
− u
50
+ ··· + 2734u − 367
c
8
, c
11
u
51
+ 19u
49
+ ··· + 13u + 1
c
9
u
51
+ 3u
50
+ ··· + 17u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
+ 48y
50
+ ··· + 51493582y −1297321
c
2
y
51
− 11y
50
+ ··· + 48673y −9
c
3
y
51
− 54y
50
+ ··· + 361104y −784
c
4
, c
5
, c
10
y
51
− 13y
50
+ ··· + 69y −1
c
6
y
51
+ 28y
50
+ ··· − 14382675y −237169
c
7
y
51
− 13y
50
+ ··· + 4303142y −134689
c
8
, c
11
y
51
+ 38y
50
+ ··· − 63y −1
c
9
y
51
+ 3y
50
+ ··· + 231y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493427 + 0.809787I
a = −0.77037 + 1.28680I
b = −1.158320 − 0.268559I
−3.18456 − 2.09749I 1.52387 + 2.56668I
u = −0.493427 − 0.809787I
a = −0.77037 − 1.28680I
b = −1.158320 + 0.268559I
−3.18456 + 2.09749I 1.52387 − 2.56668I
u = 0.440430 + 1.030910I
a = 1.20909 + 0.73700I
b = 0.648815 + 0.030734I
−1.47252 + 3.57882I 5.00000 − 4.02671I
u = 0.440430 − 1.030910I
a = 1.20909 − 0.73700I
b = 0.648815 − 0.030734I
−1.47252 − 3.57882I 5.00000 + 4.02671I
u = −0.479467 + 1.026910I
a = −2.05858 + 0.43573I
b = −0.759278 − 0.845778I
−1.69267 − 6.49416I 2.47045 + 12.27311I
u = −0.479467 − 1.026910I
a = −2.05858 − 0.43573I
b = −0.759278 + 0.845778I
−1.69267 + 6.49416I 2.47045 − 12.27311I
u = 0.743842 + 0.386843I
a = 0.297848 + 0.032171I
b = 0.446197 + 0.593035I
1.328990 + 0.424799I 9.68382 − 3.33114I
u = 0.743842 − 0.386843I
a = 0.297848 − 0.032171I
b = 0.446197 − 0.593035I
1.328990 − 0.424799I 9.68382 + 3.33114I
u = 0.095349 + 1.173960I
a = −1.19574 − 0.93729I
b = −0.696664 − 0.158856I
−0.53609 − 2.28831I 3.93640 + 2.00082I
u = 0.095349 − 1.173960I
a = −1.19574 + 0.93729I
b = −0.696664 + 0.158856I
−0.53609 + 2.28831I 3.93640 − 2.00082I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599757 + 1.068150I
a = 1.59872 + 0.52153I
b = 1.166950 − 0.515248I
−0.82395 + 4.71884I 8.89552 − 4.87376I
u = 0.599757 − 1.068150I
a = 1.59872 − 0.52153I
b = 1.166950 + 0.515248I
−0.82395 − 4.71884I 8.89552 + 4.87376I
u = −0.037987 + 0.741711I
a = 0.487424 − 0.496015I
b = −0.263663 + 1.061380I
0.97092 + 2.65596I −1.16196 − 5.22442I
u = −0.037987 − 0.741711I
a = 0.487424 + 0.496015I
b = −0.263663 − 1.061380I
0.97092 − 2.65596I −1.16196 + 5.22442I
u = −0.105363 + 1.293330I
a = 0.842122 − 1.028860I
b = 1.15000 − 2.18955I
−6.78593 − 5.05905I 0. + 9.05421I
u = −0.105363 − 1.293330I
a = 0.842122 + 1.028860I
b = 1.15000 + 2.18955I
−6.78593 + 5.05905I 0. − 9.05421I
u = −0.605350 + 0.328798I
a = 0.030694 − 0.438381I
b = −0.582666 + 0.913456I
0.18643 + 2.24007I 4.31467 − 4.82703I
u = −0.605350 − 0.328798I
a = 0.030694 + 0.438381I
b = −0.582666 − 0.913456I
0.18643 − 2.24007I 4.31467 + 4.82703I
u = −0.103993 + 1.307300I
a = 1.289790 + 0.507751I
b = 1.30493 + 0.86402I
0.75736 − 4.17149I 0
u = −0.103993 − 1.307300I
a = 1.289790 − 0.507751I
b = 1.30493 − 0.86402I
0.75736 + 4.17149I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066040 + 1.316750I
a = −1.134200 + 0.598306I
b = −0.869888 − 0.655773I
−7.59339 + 1.64029I 0
u = 0.066040 − 1.316750I
a = −1.134200 − 0.598306I
b = −0.869888 + 0.655773I
−7.59339 − 1.64029I 0
u = −0.316521 + 1.283090I
a = −0.973576 + 0.636597I
b = −1.275330 + 0.375261I
−4.26515 − 0.63551I 0
u = −0.316521 − 1.283090I
a = −0.973576 − 0.636597I
b = −1.275330 − 0.375261I
−4.26515 + 0.63551I 0
u = −0.169671 + 1.316380I
a = −1.56522 − 0.54880I
b = −1.61853 − 1.92364I
−8.06935 − 3.19037I 0
u = −0.169671 − 1.316380I
a = −1.56522 + 0.54880I
b = −1.61853 + 1.92364I
−8.06935 + 3.19037I 0
u = 1.32897
a = 0.301273
b = 0.554539
2.55208 −16.4860
u = −1.386170 + 0.040542I
a = 0.0061725 + 0.0594784I
b = 1.060320 + 0.487450I
−4.33426 − 8.28696I 0
u = −1.386170 − 0.040542I
a = 0.0061725 − 0.0594784I
b = 1.060320 − 0.487450I
−4.33426 + 8.28696I 0
u = 0.119578 + 1.392790I
a = 1.112220 + 0.798814I
b = 0.741572 − 0.551742I
−8.21456 + 4.85073I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119578 − 1.392790I
a = 1.112220 − 0.798814I
b = 0.741572 + 0.551742I
−8.21456 − 4.85073I 0
u = 1.40409 + 0.33821I
a = 0.0516236 − 0.0304155I
b = −0.946779 + 0.253375I
−4.12435 + 1.05287I 0
u = 1.40409 − 0.33821I
a = 0.0516236 + 0.0304155I
b = −0.946779 − 0.253375I
−4.12435 − 1.05287I 0
u = 0.531665
a = 0.598400
b = 0.509912
1.10699 8.71620
u = 0.32774 + 1.48242I
a = 1.280410 − 0.075549I
b = 1.059310 − 0.382106I
−3.16584 + 5.71287I 0
u = 0.32774 − 1.48242I
a = 1.280410 + 0.075549I
b = 1.059310 + 0.382106I
−3.16584 − 5.71287I 0
u = −1.54491
a = −0.149552
b = 0.343321
7.66230 0
u = −0.60455 + 1.48396I
a = 1.358730 − 0.175270I
b = 1.44476 + 0.99917I
−9.1940 − 15.1810I 0
u = −0.60455 − 1.48396I
a = 1.358730 + 0.175270I
b = 1.44476 − 0.99917I
−9.1940 + 15.1810I 0
u = 0.45015 + 1.55699I
a = −1.287260 − 0.004117I
b = −1.50034 + 0.96394I
−10.36510 + 7.36778I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.45015 − 1.55699I
a = −1.287260 + 0.004117I
b = −1.50034 − 0.96394I
−10.36510 − 7.36778I 0
u = −0.013247 + 0.321612I
a = 1.17101 − 1.69632I
b = 0.490132 − 1.210900I
4.50411 + 3.58227I 16.0667 − 6.6127I
u = −0.013247 − 0.321612I
a = 1.17101 + 1.69632I
b = 0.490132 + 1.210900I
4.50411 − 3.58227I 16.0667 + 6.6127I
u = 0.70380 + 1.55046I
a = −0.751838 − 0.224127I
b = −1.028030 + 0.642864I
−8.17422 + 6.90097I 0
u = 0.70380 − 1.55046I
a = −0.751838 + 0.224127I
b = −1.028030 − 0.642864I
−8.17422 − 6.90097I 0
u = −0.56390 + 1.65705I
a = 0.727943 − 0.273768I
b = 1.075260 + 0.420157I
−9.56909 + 0.79682I 0
u = −0.56390 − 1.65705I
a = 0.727943 + 0.273768I
b = 1.075260 − 0.420157I
−9.56909 − 0.79682I 0
u = −0.169815 + 0.103297I
a = 5.86596 + 4.64169I
b = −0.852548 − 0.435407I
−3.57803 − 1.46219I 0.29485 + 4.98451I
u = −0.169815 − 0.103297I
a = 5.86596 − 4.64169I
b = −0.852548 + 0.435407I
−3.57803 + 1.46219I 0.29485 − 4.98451I
u = −0.059185 + 0.143199I
a = 9.53198 + 7.67652I
b = 0.759897 + 0.569891I
−2.97946 + 4.11273I 4.99561 + 1.01748I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059185 − 0.143199I
a = 9.53198 − 7.67652I
b = 0.759897 − 0.569891I
−2.97946 − 4.11273I 4.99561 − 1.01748I
10
II. I
u
2
= h−u
15
− u
14
+ · · · + u
2
+ b, −201u
15
− 115u
14
+ · · · + 85a −
229, u
16
+ u
15
+ · · · − u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
2.36471u
15
+ 1.35294u
14
+ ··· − 6.82353u + 2.69412
u
15
+ u
14
+ ··· − 7u
3
− u
2
a
4
=
3.49412u
15
+ 3.05882u
14
+ ··· − 6.47059u + 1.68235
2.12941u
15
+ 2.70588u
14
+ ··· + 0.352941u − 1.01176
a
2
=
3.49412u
15
+ 3.05882u
14
+ ··· − 5.47059u + 1.68235
2.34118u
15
+ 2.58824u
14
+ ··· − 1.70588u − 0.576471
a
7
=
2.27059u
15
+ 2.29412u
14
+ ··· − 7.35294u − 1.38824
3u
14
+ 3u
13
+ ··· − 4u − 4
a
10
=
1.95294u
15
− 0.529412u
14
+ ··· + 7.23529u + 6.45882
3.96471u
15
− 0.647059u
14
+ ··· + 3.17647u + 10.0941
a
6
=
1.48235u
15
+ 3.17647u
14
+ ··· − 8.41176u − 2.95294
−
16
5
u
15
+ 3u
14
+ ··· − 5u −
64
5
a
5
=
1.48235u
15
+ 3.17647u
14
+ ··· − 8.41176u − 2.95294
−2.83529u
15
+ 2.35294u
14
+ ··· − 1.82353u − 11.1059
a
5
=
1.48235u
15
+ 3.17647u
14
+ ··· − 8.41176u − 2.95294
−2.83529u
15
+ 2.35294u
14
+ ··· − 1.82353u − 11.1059
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1404
85
u
15
−
541
17
u
14
+ ··· +
1353
17
u +
3829
85
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− u
15
+ ··· + 6u
2
− 1
c
2
u
16
+ u
14
+ ··· − 3u − 1
c
3
u
16
+ 9u
15
+ ··· + 48u + 4
c
4
, c
5
u
16
− 6u
14
+ ··· − u + 1
c
6
u
16
− 3u
15
+ ··· − 3u − 1
c
7
u
16
+ 2u
14
+ ··· − 2u − 1
c
8
u
16
+ u
15
+ ··· − u − 1
c
9
u
16
− 4u
15
+ ··· + 3u + 1
c
10
u
16
− 6u
14
+ ··· + u + 1
c
11
u
16
− u
15
+ ··· + u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ y
15
+ ··· − 12y + 1
c
2
y
16
+ 2y
15
+ ··· − 15y + 1
c
3
y
16
− 13y
15
+ ··· − 1600y + 16
c
4
, c
5
, c
10
y
16
− 12y
15
+ ··· − 19y + 1
c
6
y
16
+ 5y
15
+ ··· − 11y + 1
c
7
y
16
+ 4y
15
+ ··· − 12y + 1
c
8
, c
11
y
16
+ 7y
15
+ ··· + 13y + 1
c
9
y
16
− 4y
15
+ ··· − 9y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665069 + 0.678799I
a = 0.420824 + 1.344970I
b = −0.711594 + 0.036986I
−3.33249 + 0.34499I 2.01757 + 0.37341I
u = −0.665069 − 0.678799I
a = 0.420824 − 1.344970I
b = −0.711594 − 0.036986I
−3.33249 − 0.34499I 2.01757 − 0.37341I
u = 0.343696 + 1.208130I
a = 1.53898 − 0.20131I
b = 1.098860 − 0.865659I
1.66733 + 5.08939I 7.99749 − 6.39804I
u = 0.343696 − 1.208130I
a = 1.53898 + 0.20131I
b = 1.098860 + 0.865659I
1.66733 − 5.08939I 7.99749 + 6.39804I
u = 0.083391 + 0.730027I
a = 0.297481 + 0.552196I
b = 0.53614 + 1.40238I
3.97957 − 3.37369I 2.06218 + 1.25376I
u = 0.083391 − 0.730027I
a = 0.297481 − 0.552196I
b = 0.53614 − 1.40238I
3.97957 + 3.37369I 2.06218 − 1.25376I
u = 0.306045 + 0.663071I
a = 1.27171 + 2.87741I
b = 0.792095 + 0.522312I
−3.32910 + 4.68558I −1.72806 − 9.06253I
u = 0.306045 − 0.663071I
a = 1.27171 − 2.87741I
b = 0.792095 − 0.522312I
−3.32910 − 4.68558I −1.72806 + 9.06253I
u = −1.27402
a = −0.404742
b = −0.485688
2.72211 31.3500
u = −0.501271 + 1.175050I
a = −1.72984 + 0.28764I
b = −0.939350 − 0.528756I
−1.52177 − 5.31010I 3.27149 + 8.11960I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501271 − 1.175050I
a = −1.72984 − 0.28764I
b = −0.939350 + 0.528756I
−1.52177 + 5.31010I 3.27149 − 8.11960I
u = −0.096302 + 0.611710I
a = 0.48873 − 1.35280I
b = −0.319333 + 0.903954I
1.44991 + 2.46756I 14.2433 − 0.1322I
u = −0.096302 − 0.611710I
a = 0.48873 + 1.35280I
b = −0.319333 − 0.903954I
1.44991 − 2.46756I 14.2433 + 0.1322I
u = −0.135082 + 1.374290I
a = −0.554322 − 0.164051I
b = −0.43850 − 1.39183I
−7.35161 − 3.81019I 1.49699 + 3.24326I
u = −0.135082 − 1.374290I
a = −0.554322 + 0.164051I
b = −0.43850 + 1.39183I
−7.35161 + 3.81019I 1.49699 − 3.24326I
u = 1.60320
a = −0.0623831
b = 0.449044
7.57445 −38.0720
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− u
15
+ ··· + 6u
2
− 1)(u
51
+ 4u
50
+ ··· + 10304u + 1139)
c
2
(u
16
+ u
14
+ ··· − 3u − 1)(u
51
+ u
50
+ ··· + 197u + 3)
c
3
(u
16
+ 9u
15
+ ··· + 48u + 4)(u
51
+ 4u
50
+ ··· − 668u + 28)
c
4
, c
5
(u
16
− 6u
14
+ ··· − u + 1)(u
51
+ u
50
+ ··· − 15u − 1)
c
6
(u
16
− 3u
15
+ ··· − 3u − 1)(u
51
+ 14u
49
+ ··· − 3611u + 487)
c
7
(u
16
+ 2u
14
+ ··· − 2u − 1)(u
51
− u
50
+ ··· + 2734u − 367)
c
8
(u
16
+ u
15
+ ··· − u − 1)(u
51
+ 19u
49
+ ··· + 13u + 1)
c
9
(u
16
− 4u
15
+ ··· + 3u + 1)(u
51
+ 3u
50
+ ··· + 17u + 1)
c
10
(u
16
− 6u
14
+ ··· + u + 1)(u
51
+ u
50
+ ··· − 15u − 1)
c
11
(u
16
− u
15
+ ··· + u − 1)(u
51
+ 19u
49
+ ··· + 13u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ y
15
+ ··· − 12y + 1)
· (y
51
+ 48y
50
+ ··· + 51493582y −1297321)
c
2
(y
16
+ 2y
15
+ ··· − 15y + 1)(y
51
− 11y
50
+ ··· + 48673y −9)
c
3
(y
16
− 13y
15
+ ··· − 1600y + 16)(y
51
− 54y
50
+ ··· + 361104y −784)
c
4
, c
5
, c
10
(y
16
− 12y
15
+ ··· − 19y + 1)(y
51
− 13y
50
+ ··· + 69y −1)
c
6
(y
16
+ 5y
15
+ ··· − 11y + 1)
· (y
51
+ 28y
50
+ ··· − 14382675y −237169)
c
7
(y
16
+ 4y
15
+ ··· − 12y + 1)(y
51
− 13y
50
+ ··· + 4303142y −134689)
c
8
, c
11
(y
16
+ 7y
15
+ ··· + 13y + 1)(y
51
+ 38y
50
+ ··· − 63y −1)
c
9
(y
16
− 4y
15
+ ··· − 9y + 1)(y
51
+ 3y
50
+ ··· + 231y −1)
17
