11a
79
(K11a
79
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 3 4 11 7 5 9
Solving Sequence
1,6
2 3 7
5,9
11 8 4 10
c
1
c
2
c
6
c
5
c
11
c
8
c
4
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.23376 × 10
38
u
70
− 2.60156 × 10
38
u
69
+ ··· + 3.74973 × 10
38
b − 3.48298 × 10
38
,
6.34585 × 10
38
u
70
+ 1.49012 × 10
39
u
69
+ ··· + 3.74973 × 10
38
a − 1.05045 × 10
39
, u
71
+ 3u
70
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 71 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−1.23×10
38
u
70
−2.60×10
38
u
69
+· · ·+3.75×10
38
b−3.48×10
38
, 6.35×
10
38
u
70
+1.49×10
39
u
69
+· · ·+3.75×10
38
a−1.05×10
39
, u
71
+3u
70
+· · ·−2u−1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
9
=
−1.69235u
70
− 3.97394u
69
+ ··· + 7.85819u + 2.80141
0.329027u
70
+ 0.693799u
69
+ ··· − 0.915774u + 0.928862
a
11
=
−1.11052u
70
− 2.65167u
69
+ ··· + 6.64700u + 3.19447
0.150451u
70
+ 0.130614u
69
+ ··· − 0.554244u + 1.09861
a
8
=
−1.18217u
70
− 2.67436u
69
+ ··· + 2.39442u + 0.613804
0.532697u
70
+ 1.43786u
69
+ ··· − 0.858566u − 0.377440
a
4
=
−1.23342u
70
− 2.50666u
69
+ ··· + 1.45164u + 0.570833
0.583955u
70
+ 1.27017u
69
+ ··· + 0.0842178u − 0.334469
a
10
=
−2.85773u
70
− 7.42029u
69
+ ··· + 8.03318u + 5.13869
0.662094u
70
+ 2.56292u
69
+ ··· − 1.13925u − 1.31864
a
10
=
−2.85773u
70
− 7.42029u
69
+ ··· + 8.03318u + 5.13869
0.662094u
70
+ 2.56292u
69
+ ··· − 1.13925u − 1.31864
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.81223u
70
− 5.67213u
69
+ ··· − 3.51925u + 3.56513
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
71
− 3u
70
+ ··· − 2u + 1
c
2
u
71
+ 35u
70
+ ··· − 6u
2
− 1
c
3
u
71
+ 3u
70
+ ··· + 4u + 1
c
4
, c
7
u
71
− u
70
+ ··· − 6u
3
− 1
c
6
u
71
+ 3u
70
+ ··· + 6566u + 1721
c
8
, c
11
u
71
+ u
70
+ ··· + 20u − 1
c
9
u
71
− 5u
70
+ ··· + 2242u + 127
c
10
u
71
+ 15u
70
+ ··· + 22856u + 7097
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
71
+ 35y
70
+ ··· − 6y
2
− 1
c
2
y
71
+ 3y
70
+ ··· − 12y −1
c
3
y
71
+ 3y
70
+ ··· − 52y −1
c
4
, c
7
y
71
− 53y
70
+ ··· − 46y
2
− 1
c
6
y
71
− 29y
70
+ ··· + 37791024y −2961841
c
8
, c
11
y
71
− 49y
70
+ ··· − 76y −1
c
9
y
71
+ 43y
70
+ ··· + 525684y −16129
c
10
y
71
+ 91y
70
+ ··· − 2991356352y −50367409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951977 + 0.256619I
a = 1.43488 − 0.20483I
b = −1.126820 + 0.034203I
4.89801 − 0.93678I 19.9883 + 4.7371I
u = −0.951977 − 0.256619I
a = 1.43488 + 0.20483I
b = −1.126820 − 0.034203I
4.89801 + 0.93678I 19.9883 − 4.7371I
u = 0.366345 + 0.963903I
a = 1.251290 + 0.322417I
b = 0.962476 − 0.815520I
2.67401 − 0.67928I 0
u = 0.366345 − 0.963903I
a = 1.251290 − 0.322417I
b = 0.962476 + 0.815520I
2.67401 + 0.67928I 0
u = 0.713273 + 0.766402I
a = 2.20075 − 0.64025I
b = −1.39436 − 0.36803I
8.84556 + 9.04187I 0
u = 0.713273 − 0.766402I
a = 2.20075 + 0.64025I
b = −1.39436 + 0.36803I
8.84556 − 9.04187I 0
u = −0.224116 + 1.050260I
a = 0.669798 − 0.252970I
b = −0.370664 − 0.446189I
−1.70053 − 2.56932I 0
u = −0.224116 − 1.050260I
a = 0.669798 + 0.252970I
b = −0.370664 + 0.446189I
−1.70053 + 2.56932I 0
u = 0.705586 + 0.829208I
a = 1.62621 − 1.10681I
b = −1.357000 + 0.278209I
8.66688 − 3.69608I 0
u = 0.705586 − 0.829208I
a = 1.62621 + 1.10681I
b = −1.357000 − 0.278209I
8.66688 + 3.69608I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846818 + 0.313214I
a = 1.80160 + 0.13026I
b = −1.177360 + 0.405721I
1.20494 − 6.04817I 5.22565 + 5.84091I
u = 0.846818 − 0.313214I
a = 1.80160 − 0.13026I
b = −1.177360 − 0.405721I
1.20494 + 6.04817I 5.22565 − 5.84091I
u = −0.786218 + 0.782111I
a = 1.74704 + 0.57747I
b = −1.145380 + 0.086197I
3.75200 − 2.89679I 0
u = −0.786218 − 0.782111I
a = 1.74704 − 0.57747I
b = −1.145380 − 0.086197I
3.75200 + 2.89679I 0
u = −0.841330 + 0.286074I
a = 1.92284 − 0.21858I
b = −1.40306 − 0.54314I
6.14527 + 11.63860I 7.86088 − 6.21696I
u = −0.841330 − 0.286074I
a = 1.92284 + 0.21858I
b = −1.40306 + 0.54314I
6.14527 − 11.63860I 7.86088 + 6.21696I
u = −0.396737 + 1.050830I
a = 0.611889 + 0.451445I
b = 0.763773 + 0.472136I
−1.12945 − 1.48616I 0
u = −0.396737 − 1.050830I
a = 0.611889 − 0.451445I
b = 0.763773 − 0.472136I
−1.12945 + 1.48616I 0
u = −0.504241 + 1.025470I
a = −0.61602 − 1.87132I
b = 1.75797 + 0.25690I
5.06700 − 2.91128I 0
u = −0.504241 − 1.025470I
a = −0.61602 + 1.87132I
b = 1.75797 − 0.25690I
5.06700 + 2.91128I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514985 + 0.680903I
a = −0.579773 − 0.461872I
b = 0.420336 + 1.009300I
3.23927 + 4.44956I 8.25775 − 7.58067I
u = 0.514985 − 0.680903I
a = −0.579773 + 0.461872I
b = 0.420336 − 1.009300I
3.23927 − 4.44956I 8.25775 + 7.58067I
u = 0.470433 + 1.061190I
a = −1.87151 + 0.91795I
b = 1.208490 − 0.064583I
0.50502 + 3.35540I 0
u = 0.470433 − 1.061190I
a = −1.87151 − 0.91795I
b = 1.208490 + 0.064583I
0.50502 − 3.35540I 0
u = −0.315619 + 1.134620I
a = 0.830681 + 0.958758I
b = −0.128589 + 1.134400I
−2.52331 + 2.41202I 0
u = −0.315619 − 1.134620I
a = 0.830681 − 0.958758I
b = −0.128589 − 1.134400I
−2.52331 − 2.41202I 0
u = 0.444751 + 1.090510I
a = −1.01329 − 6.86779I
b = 0.976673 − 0.016014I
0.78414 + 3.63001I 0
u = 0.444751 − 1.090510I
a = −1.01329 + 6.86779I
b = 0.976673 + 0.016014I
0.78414 − 3.63001I 0
u = −0.384067 + 0.705673I
a = 0.241639 − 0.229841I
b = 0.224870 − 0.394609I
0.01309 − 1.53015I 0.80636 + 5.17000I
u = −0.384067 − 0.705673I
a = 0.241639 + 0.229841I
b = 0.224870 + 0.394609I
0.01309 + 1.53015I 0.80636 − 5.17000I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501403 + 1.092270I
a = −1.12867 − 2.17659I
b = 1.033040 − 0.441324I
−0.32050 − 5.52962I 0
u = −0.501403 − 1.092270I
a = −1.12867 + 2.17659I
b = 1.033040 + 0.441324I
−0.32050 + 5.52962I 0
u = 0.528068 + 1.083240I
a = −1.54121 + 1.95012I
b = 1.46024 + 0.88757I
4.03427 + 7.29529I 0
u = 0.528068 − 1.083240I
a = −1.54121 − 1.95012I
b = 1.46024 − 0.88757I
4.03427 − 7.29529I 0
u = 0.346372 + 1.161380I
a = 0.593679 − 0.777762I
b = −0.392677 − 0.759378I
−5.73112 + 1.67042I 0
u = 0.346372 − 1.161380I
a = 0.593679 + 0.777762I
b = −0.392677 + 0.759378I
−5.73112 − 1.67042I 0
u = −0.473510 + 1.118310I
a = 0.782398 − 0.360085I
b = 0.0538522 − 0.0763981I
−0.74430 − 3.76429I 0
u = −0.473510 − 1.118310I
a = 0.782398 + 0.360085I
b = 0.0538522 + 0.0763981I
−0.74430 + 3.76429I 0
u = 0.335026 + 0.710399I
a = 1.72207 + 1.23343I
b = 0.657840 − 0.399802I
2.84065 − 0.69325I 7.34055 − 2.28046I
u = 0.335026 − 0.710399I
a = 1.72207 − 1.23343I
b = 0.657840 + 0.399802I
2.84065 + 0.69325I 7.34055 + 2.28046I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.211142 + 1.205460I
a = 0.162294 + 0.244515I
b = −1.013050 + 0.457090I
−3.82831 − 2.87392I 0
u = 0.211142 − 1.205460I
a = 0.162294 − 0.244515I
b = −1.013050 − 0.457090I
−3.82831 + 2.87392I 0
u = −0.719893 + 0.254367I
a = −0.115852 − 0.661368I
b = 0.073358 + 1.223210I
1.50533 + 5.54441I 6.15324 − 5.81731I
u = −0.719893 − 0.254367I
a = −0.115852 + 0.661368I
b = 0.073358 − 1.223210I
1.50533 − 5.54441I 6.15324 + 5.81731I
u = −0.247127 + 1.219380I
a = −0.116676 − 0.268220I
b = −1.31519 − 0.54925I
1.27336 + 8.27174I 0
u = −0.247127 − 1.219380I
a = −0.116676 + 0.268220I
b = −1.31519 + 0.54925I
1.27336 − 8.27174I 0
u = −0.559742 + 0.499569I
a = −2.33180 − 0.07414I
b = 1.61703 − 0.42922I
6.60638 − 1.38759I 13.61185 + 2.69699I
u = −0.559742 − 0.499569I
a = −2.33180 + 0.07414I
b = 1.61703 + 0.42922I
6.60638 + 1.38759I 13.61185 − 2.69699I
u = −0.532609 + 1.135780I
a = −1.331490 − 0.302716I
b = 0.018216 − 1.337320I
−1.03978 − 10.29640I 0
u = −0.532609 − 1.135780I
a = −1.331490 + 0.302716I
b = 0.018216 + 1.337320I
−1.03978 + 10.29640I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718324 + 0.192214I
a = 0.343599 + 0.323507I
b = −0.189188 − 0.732728I
−1.82969 − 1.80347I −0.10246 + 1.52246I
u = 0.718324 − 0.192214I
a = 0.343599 − 0.323507I
b = −0.189188 + 0.732728I
−1.82969 + 1.80347I −0.10246 − 1.52246I
u = 0.516306 + 1.147190I
a = −0.673430 + 0.126282I
b = −0.183109 + 0.870034I
−4.55999 + 6.45506I 0
u = 0.516306 − 1.147190I
a = −0.673430 − 0.126282I
b = −0.183109 − 0.870034I
−4.55999 − 6.45506I 0
u = 0.628529 + 0.365318I
a = −1.89811 + 0.16062I
b = 1.46936 − 0.72031I
6.10269 − 2.74373I 12.45226 + 3.77694I
u = 0.628529 − 0.365318I
a = −1.89811 − 0.16062I
b = 1.46936 + 0.72031I
6.10269 + 2.74373I 12.45226 − 3.77694I
u = 0.584181 + 1.160180I
a = 1.41110 − 1.54314I
b = −1.217140 − 0.473437I
−1.33313 + 11.33620I 0
u = 0.584181 − 1.160180I
a = 1.41110 + 1.54314I
b = −1.217140 + 0.473437I
−1.33313 − 11.33620I 0
u = −0.575118 + 1.166630I
a = 1.44257 + 1.87148I
b = −1.41933 + 0.58854I
3.5170 − 16.8714I 0
u = −0.575118 − 1.166630I
a = 1.44257 − 1.87148I
b = −1.41933 − 0.58854I
3.5170 + 16.8714I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350099 + 1.280170I
a = 0.231862 + 0.485291I
b = −1.013310 + 0.202385I
−0.03586 − 5.23290I 0
u = −0.350099 − 1.280170I
a = 0.231862 − 0.485291I
b = −1.013310 − 0.202385I
−0.03586 + 5.23290I 0
u = −0.625953 + 1.188270I
a = 0.96793 + 1.10206I
b = −1.106350 + 0.106102I
2.12005 − 4.76886I 0
u = −0.625953 − 1.188270I
a = 0.96793 − 1.10206I
b = −1.106350 − 0.106102I
2.12005 + 4.76886I 0
u = −0.557121 + 0.298889I
a = −1.74606 + 1.17248I
b = 1.009520 + 0.310743I
1.90959 + 1.23782I 5.72103 − 1.19948I
u = −0.557121 − 0.298889I
a = −1.74606 − 1.17248I
b = 1.009520 − 0.310743I
1.90959 − 1.23782I 5.72103 + 1.19948I
u = 0.436090 + 0.450755I
a = −3.04281 + 1.18729I
b = 1.112600 + 0.136483I
2.35203 + 0.54203I 3.52424 + 2.42131I
u = 0.436090 − 0.450755I
a = −3.04281 − 1.18729I
b = 1.112600 − 0.136483I
2.35203 − 0.54203I 3.52424 − 2.42131I
u = −0.563914 + 0.238552I
a = 1.178280 + 0.450091I
b = 0.112264 − 0.124633I
1.74562 − 0.37740I 6.30964 + 0.12141I
u = −0.563914 − 0.238552I
a = 1.178280 − 0.450091I
b = 0.112264 + 0.124633I
1.74562 + 0.37740I 6.30964 − 0.12141I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489141
a = 7.66462
b = 1.04131
3.44799 −43.6260
12
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
71
− 3u
70
+ ··· − 2u + 1
c
2
u
71
+ 35u
70
+ ··· − 6u
2
− 1
c
3
u
71
+ 3u
70
+ ··· + 4u + 1
c
4
, c
7
u
71
− u
70
+ ··· − 6u
3
− 1
c
6
u
71
+ 3u
70
+ ··· + 6566u + 1721
c
8
, c
11
u
71
+ u
70
+ ··· + 20u − 1
c
9
u
71
− 5u
70
+ ··· + 2242u + 127
c
10
u
71
+ 15u
70
+ ··· + 22856u + 7097
13
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
71
+ 35y
70
+ ··· − 6y
2
− 1
c
2
y
71
+ 3y
70
+ ··· − 12y −1
c
3
y
71
+ 3y
70
+ ··· − 52y −1
c
4
, c
7
y
71
− 53y
70
+ ··· − 46y
2
− 1
c
6
y
71
− 29y
70
+ ··· + 37791024y −2961841
c
8
, c
11
y
71
− 49y
70
+ ··· − 76y −1
c
9
y
71
+ 43y
70
+ ··· + 525684y −16129
c
10
y
71
+ 91y
70
+ ··· − 2991356352y −50367409
14
