11n
131
(K11n
131
)
A knot diagram
1
Linearized knot diagam
7 1 11 9 8 2 10 5 3 8 9
Solving Sequence
1,7
2
3,10
8 6 5 9 11 4
c
1
c
2
c
7
c
6
c
5
c
9
c
11
c
3
c
4
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.69653 × 10
36
u
43
+ 1.93812 × 10
38
u
42
+ ··· + 1.36546 × 10
39
b + 1.44554 × 10
39
,
2.34671 × 10
40
u
43
− 2.31254 × 10
39
u
42
+ ··· + 2.59437 × 10
40
a + 1.06428 × 10
41
, u
44
+ 8u
42
+ ··· + 28u + 19i
I
u
2
= h−u
10
− 2u
9
− 3u
8
− 5u
7
− 6u
6
− 10u
5
− 9u
4
− 8u
3
− 9u
2
+ b − 4u − 4,
− u
9
− u
8
− 2u
7
− 2u
6
− 3u
5
− 5u
4
− 2u
3
− 3u
2
+ a − u − 2,
u
11
+ u
10
+ 3u
9
+ 3u
8
+ 5u
7
+ 7u
6
+ 5u
5
+ 8u
4
+ 3u
3
+ 5u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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−9.70 × 10
36
u
43
+ 1.94 × 10
38
u
42
+ · · · + 1.37 × 10
39
b + 1.45 ×
10
39
, 2.35 × 10
40
u
43
− 2.31 × 10
39
u
42
+ · · · + 2.59 × 10
40
a + 1.06 ×
10
41
, u
44
+ 8u
42
+ · · · + 28u + 19i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
10
=
−0.904540u
43
+ 0.0891368u
42
+ ··· − 28.1734u − 4.10227
0.00710130u
43
− 0.141939u
42
+ ··· − 5.47040u − 1.05865
a
8
=
0.129802u
43
− 0.616286u
42
+ ··· − 13.9864u − 18.1892
−0.112721u
43
+ 0.238849u
42
+ ··· − 2.68255u + 7.40994
a
6
=
−u
u
3
+ u
a
5
=
0.855694u
43
+ 0.294688u
42
+ ··· + 42.8937u + 18.2259
−0.198202u
43
− 0.0959296u
42
+ ··· − 8.51213u − 7.37608
a
9
=
−1.12405u
43
− 0.0401899u
42
+ ··· − 35.9422u − 8.61657
−0.406276u
43
+ 0.227899u
42
+ ··· − 10.7610u + 3.51106
a
11
=
−0.232879u
43
+ 0.618756u
42
+ ··· + 6.55564u + 18.5444
0.0121303u
43
+ 0.0705266u
42
+ ··· + 6.59355u + 5.72029
a
4
=
−0.925125u
43
+ 0.652168u
42
+ ··· − 16.2508u + 7.52727
0.107850u
43
+ 0.505554u
42
+ ··· + 18.8829u + 20.6647
a
4
=
−0.925125u
43
+ 0.652168u
42
+ ··· − 16.2508u + 7.52727
0.107850u
43
+ 0.505554u
42
+ ··· + 18.8829u + 20.6647
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.830501u
43
− 1.97049u
42
+ ··· − 84.2334u − 62.6447
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
+ 8u
42
+ ··· + 28u + 19
c
2
u
44
+ 16u
43
+ ··· + 3928u + 361
c
3
u
44
+ 4u
43
+ ··· + 13u + 1
c
4
, c
5
, c
8
u
44
+ 2u
43
+ ··· − 11u − 1
c
7
, c
10
u
44
+ u
43
+ ··· − 41u + 11
c
9
u
44
− u
43
+ ··· − 14u − 1
c
11
u
44
+ 2u
43
+ ··· + 12u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
+ 16y
43
+ ··· + 3928y + 361
c
2
y
44
+ 24y
43
+ ··· − 363932y + 130321
c
3
y
44
− 42y
43
+ ··· − 5y + 1
c
4
, c
5
, c
8
y
44
+ 12y
43
+ ··· − 37y + 1
c
7
, c
10
y
44
− 15y
43
+ ··· − 2869y + 121
c
9
y
44
+ 7y
43
+ ··· − 54y + 1
c
11
y
44
− 38y
43
+ ··· − 96y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553611 + 0.824772I
a = 0.447859 + 1.150180I
b = −1.49583 − 0.39989I
−3.21451 − 2.15595I 1.07743 + 2.96858I
u = −0.553611 − 0.824772I
a = 0.447859 − 1.150180I
b = −1.49583 + 0.39989I
−3.21451 + 2.15595I 1.07743 − 2.96858I
u = 0.691309 + 0.811314I
a = −1.341520 + 0.125641I
b = −0.247744 + 0.790756I
4.27651 − 0.41832I 5.68762 − 0.89780I
u = 0.691309 − 0.811314I
a = −1.341520 − 0.125641I
b = −0.247744 − 0.790756I
4.27651 + 0.41832I 5.68762 + 0.89780I
u = −0.749080 + 0.765100I
a = 0.129349 − 1.222590I
b = 0.61597 + 1.72869I
5.60971 + 1.02097I 7.05881 + 0.21382I
u = −0.749080 − 0.765100I
a = 0.129349 + 1.222590I
b = 0.61597 − 1.72869I
5.60971 − 1.02097I 7.05881 − 0.21382I
u = −0.358331 + 0.841835I
a = 0.73681 + 1.63006I
b = −0.800323 − 0.656423I
−4.31132 − 1.52913I 4.89215 + 5.65142I
u = −0.358331 − 0.841835I
a = 0.73681 − 1.63006I
b = −0.800323 + 0.656423I
−4.31132 + 1.52913I 4.89215 − 5.65142I
u = 0.724746 + 0.501149I
a = 0.790041 + 0.280445I
b = 0.212674 − 0.438603I
1.31409 + 0.60593I 8.59743 − 3.14385I
u = 0.724746 − 0.501149I
a = 0.790041 − 0.280445I
b = 0.212674 + 0.438603I
1.31409 − 0.60593I 8.59743 + 3.14385I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672004 + 0.909211I
a = −0.118766 + 1.200990I
b = 0.67880 − 1.94511I
3.96994 + 5.67612I 4.70172 − 5.28440I
u = 0.672004 − 0.909211I
a = −0.118766 − 1.200990I
b = 0.67880 + 1.94511I
3.96994 − 5.67612I 4.70172 + 5.28440I
u = −0.305333 + 1.097040I
a = 0.502841 + 0.752892I
b = −0.431064 − 0.191810I
−3.64801 − 0.66413I −0.67434 − 1.82360I
u = −0.305333 − 1.097040I
a = 0.502841 − 0.752892I
b = −0.431064 + 0.191810I
−3.64801 + 0.66413I −0.67434 + 1.82360I
u = −0.724813 + 0.904533I
a = −0.048082 − 0.448492I
b = 1.168590 − 0.034882I
−4.81373 − 2.81453I 7.83387 + 2.63389I
u = −0.724813 − 0.904533I
a = −0.048082 + 0.448492I
b = 1.168590 + 0.034882I
−4.81373 + 2.81453I 7.83387 − 2.63389I
u = −0.155660 + 0.819694I
a = −0.50119 − 1.50907I
b = −0.837138 + 0.913868I
−8.09531 − 0.68903I −3.33839 − 2.14717I
u = −0.155660 − 0.819694I
a = −0.50119 + 1.50907I
b = −0.837138 − 0.913868I
−8.09531 + 0.68903I −3.33839 + 2.14717I
u = −1.035790 + 0.563745I
a = −1.135220 + 0.231350I
b = 0.457170 − 1.082790I
4.92535 + 7.92322I 5.81282 − 4.97707I
u = −1.035790 − 0.563745I
a = −1.135220 − 0.231350I
b = 0.457170 + 1.082790I
4.92535 − 7.92322I 5.81282 + 4.97707I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.702097 + 0.948685I
a = −1.230740 + 0.211924I
b = −0.165846 − 1.175810I
5.04402 − 6.54331I 5.65027 + 5.81604I
u = −0.702097 − 0.948685I
a = −1.230740 − 0.211924I
b = −0.165846 + 1.175810I
5.04402 + 6.54331I 5.65027 − 5.81604I
u = 0.191318 + 0.786546I
a = −0.321704 + 0.371146I
b = 2.20155 − 0.83164I
1.02150 − 1.91904I −0.873774 − 0.783296I
u = 0.191318 − 0.786546I
a = −0.321704 − 0.371146I
b = 2.20155 + 0.83164I
1.02150 + 1.91904I −0.873774 + 0.783296I
u = −0.525867 + 1.092400I
a = −0.400089 + 1.030590I
b = −1.09956 − 1.76264I
−2.17094 − 6.60740I −0.69632 + 10.88929I
u = −0.525867 − 1.092400I
a = −0.400089 − 1.030590I
b = −1.09956 + 1.76264I
−2.17094 + 6.60740I −0.69632 − 10.88929I
u = 0.769126
a = 0.807876
b = 0.267033
1.54727 4.67400
u = 1.004830 + 0.721198I
a = −0.817876 − 0.261435I
b = 0.420704 + 1.060050I
5.67789 − 0.23429I 7.33450 + 1.57451I
u = 1.004830 − 0.721198I
a = −0.817876 + 0.261435I
b = 0.420704 − 1.060050I
5.67789 + 0.23429I 7.33450 − 1.57451I
u = −0.038388 + 0.751954I
a = 1.43109 + 0.27249I
b = 1.141290 + 0.618112I
0.97471 + 2.65784I −0.64848 − 4.81672I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.038388 − 0.751954I
a = 1.43109 − 0.27249I
b = 1.141290 − 0.618112I
0.97471 − 2.65784I −0.64848 + 4.81672I
u = 0.489616 + 1.163080I
a = 0.051203 − 0.505529I
b = −0.89249 + 1.30630I
−1.75776 + 4.42520I 0. − 2.66999I
u = 0.489616 − 1.163080I
a = 0.051203 + 0.505529I
b = −0.89249 − 1.30630I
−1.75776 − 4.42520I 0. + 2.66999I
u = −0.634927 + 0.276340I
a = 1.29507 − 0.74684I
b = −0.103239 + 0.918524I
0.09044 + 2.10677I 3.45567 − 5.29032I
u = −0.634927 − 0.276340I
a = 1.29507 + 0.74684I
b = −0.103239 − 0.918524I
0.09044 − 2.10677I 3.45567 + 5.29032I
u = 0.725736 + 1.115000I
a = 0.122771 − 0.880273I
b = −0.87157 + 1.15445I
−0.55823 + 5.04012I 8.95344 − 5.95960I
u = 0.725736 − 1.115000I
a = 0.122771 + 0.880273I
b = −0.87157 − 1.15445I
−0.55823 − 5.04012I 8.95344 + 5.95960I
u = 1.33218
a = 0.419650
b = −0.343484
2.55385 −14.8810
u = 0.801504 + 1.072620I
a = 0.171221 + 0.993803I
b = 1.18028 − 1.27689I
4.52542 + 6.79447I 5.00000 − 4.75364I
u = 0.801504 − 1.072620I
a = 0.171221 − 0.993803I
b = 1.18028 + 1.27689I
4.52542 − 6.79447I 5.00000 + 4.75364I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748515 + 1.151140I
a = 0.050409 − 1.131160I
b = 1.37231 + 1.59702I
3.0688 − 14.3723I 0. + 8.23244I
u = −0.748515 − 1.151140I
a = 0.050409 + 1.131160I
b = 1.37231 − 1.59702I
3.0688 + 14.3723I 0. − 8.23244I
u = 0.180695 + 1.380020I
a = −0.137763 − 0.704470I
b = 0.033690 + 0.557996I
−3.28704 + 5.28886I 0. − 7.01858I
u = 0.180695 − 1.380020I
a = −0.137763 + 0.704470I
b = 0.033690 − 0.557996I
−3.28704 − 5.28886I 0. + 7.01858I
9
II.
I
u
2
= h−u
10
− 2u
9
+ · · · + b − 4, −u
9
− u
8
+ · · · + a − 2, u
11
+ u
10
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
10
=
u
9
+ u
8
+ 2u
7
+ 2u
6
+ 3u
5
+ 5u
4
+ 2u
3
+ 3u
2
+ u + 2
u
10
+ 2u
9
+ 3u
8
+ 5u
7
+ 6u
6
+ 10u
5
+ 9u
4
+ 8u
3
+ 9u
2
+ 4u + 4
a
8
=
−3u
10
− 2u
9
− 6u
8
− 5u
7
− 8u
6
− 13u
5
− 3u
4
− 11u
3
− 4u + 1
2u
9
+ u
8
+ 4u
7
+ 3u
6
+ 5u
5
+ 8u
4
+ u
3
+ 8u
2
+ 3
a
6
=
−u
u
3
+ u
a
5
=
u
9
+ u
8
+ 2u
7
+ 2u
6
+ 2u
5
+ 4u
4
+ u
3
+ 2u
2
− u − 1
−u
9
− u
8
− 2u
7
− 2u
6
− 3u
5
− 5u
4
− 2u
3
− 4u
2
− u − 2
a
9
=
−u
7
− u
6
− u
5
− u
4
− u
3
− 3u
2
u
10
+ 3u
9
+ 4u
8
+ 7u
7
+ 8u
6
+ 12u
5
+ 13u
4
+ 9u
3
+ 11u
2
+ 4u + 4
a
11
=
3u
10
+ 4u
9
+ ··· + 8u + 5
2u
10
+ u
9
+ 5u
8
+ 4u
7
+ 7u
6
+ 11u
5
+ 4u
4
+ 13u
3
+ 2u
2
+ 6u + 2
a
4
=
−2u
10
− u
9
− 5u
8
− 4u
7
− 7u
6
− 11u
5
− 4u
4
− 13u
3
− u
2
− 6u − 1
−u
10
− 2u
9
− 4u
8
− 5u
7
− 7u
6
− 10u
5
− 10u
4
− 10u
3
− 7u
2
− 6u − 3
a
4
=
−2u
10
− u
9
− 5u
8
− 4u
7
− 7u
6
− 11u
5
− 4u
4
− 13u
3
− u
2
− 6u − 1
−u
10
− 2u
9
− 4u
8
− 5u
7
− 7u
6
− 10u
5
− 10u
4
− 10u
3
− 7u
2
− 6u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
10
+ 13u
9
+ 12u
8
+ 29u
7
+ 28u
6
+ 45u
5
+ 59u
4
+ 24u
3
+ 55u
2
+ 6u + 23
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ u
10
+ 3u
9
+ 3u
8
+ 5u
7
+ 7u
6
+ 5u
5
+ 8u
4
+ 3u
3
+ 5u
2
+ u + 1
c
2
u
11
+ 5u
10
+ ··· − 9u − 1
c
3
u
11
− u
10
− 2u
9
− u
8
+ 2u
6
+ 5u
5
− 2u
4
+ 2u
3
− 4u
2
− 1
c
4
, c
5
u
11
+ u
10
+ 5u
9
+ 5u
8
+ 9u
7
+ 8u
6
+ 7u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1
c
6
u
11
− u
10
+ 3u
9
− 3u
8
+ 5u
7
− 7u
6
+ 5u
5
− 8u
4
+ 3u
3
− 5u
2
+ u − 1
c
7
u
11
− 2u
10
− 3u
9
+ 8u
8
− 10u
6
+ 7u
5
+ 3u
4
− 6u
3
+ 2u
2
+ 2u − 1
c
8
u
11
− u
10
+ 5u
9
− 5u
8
+ 9u
7
− 8u
6
+ 7u
5
− 6u
4
+ 2u
3
− 4u
2
− 1
c
9
u
11
+ 4u
9
+ 2u
8
+ 2u
7
+ 5u
6
− 2u
5
+ u
3
− 2u
2
+ u + 1
c
10
u
11
+ 2u
10
− 3u
9
− 8u
8
+ 10u
6
+ 7u
5
− 3u
4
− 6u
3
− 2u
2
+ 2u + 1
c
11
u
11
− u
10
− 4u
9
+ 6u
8
+ 4u
7
− 12u
6
+ 7u
5
+ 6u
4
− 7u
3
− u
2
+ 3u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
11
+ 5y
10
+ ··· − 9y −1
c
2
y
11
+ y
10
+ ··· + 11y −1
c
3
y
11
− 5y
10
+ ··· − 8y −1
c
4
, c
5
, c
8
y
11
+ 9y
10
+ ··· − 8y −1
c
7
, c
10
y
11
− 10y
10
+ ··· + 8y −1
c
9
y
11
+ 8y
10
+ ··· + 5y −1
c
11
y
11
− 9y
10
+ ··· + 7y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299778 + 0.927842I
a = 0.63272 + 1.53718I
b = −1.147890 − 0.441102I
−4.88598 − 1.24077I −7.95477 − 0.13168I
u = −0.299778 − 0.927842I
a = 0.63272 − 1.53718I
b = −1.147890 + 0.441102I
−4.88598 + 1.24077I −7.95477 + 0.13168I
u = 0.363187 + 0.893448I
a = 0.626586 − 1.218740I
b = 0.332981 + 0.934382I
−7.76852 + 1.52130I 0.55594 − 5.61462I
u = 0.363187 − 0.893448I
a = 0.626586 + 1.218740I
b = 0.332981 − 0.934382I
−7.76852 − 1.52130I 0.55594 + 5.61462I
u = 0.735549 + 0.971108I
a = 0.249319 − 0.595629I
b = −1.286840 + 0.135867I
−5.46767 + 2.92476I −5.12520 − 4.54367I
u = 0.735549 − 0.971108I
a = 0.249319 + 0.595629I
b = −1.286840 − 0.135867I
−5.46767 − 2.92476I −5.12520 + 4.54367I
u = −1.27239
a = 0.381829
b = −0.0451978
2.76650 23.9440
u = −0.535222 + 1.201170I
a = −0.093193 + 0.766402I
b = −0.63928 − 1.45867I
−1.44280 − 5.48967I 2.58502 + 8.73904I
u = −0.535222 − 1.201170I
a = −0.093193 − 0.766402I
b = −0.63928 + 1.45867I
−1.44280 + 5.48967I 2.58502 − 8.73904I
u = −0.127541 + 0.574472I
a = 1.39365 + 0.29759I
b = 1.76363 + 0.62512I
1.73238 + 2.30988I 9.96723 − 2.64055I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.127541 − 0.574472I
a = 1.39365 − 0.29759I
b = 1.76363 − 0.62512I
1.73238 − 2.30988I 9.96723 + 2.64055I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ u
10
+ 3u
9
+ 3u
8
+ 5u
7
+ 7u
6
+ 5u
5
+ 8u
4
+ 3u
3
+ 5u
2
+ u + 1)
· (u
44
+ 8u
42
+ ··· + 28u + 19)
c
2
(u
11
+ 5u
10
+ ··· − 9u − 1)(u
44
+ 16u
43
+ ··· + 3928u + 361)
c
3
(u
11
− u
10
− 2u
9
− u
8
+ 2u
6
+ 5u
5
− 2u
4
+ 2u
3
− 4u
2
− 1)
· (u
44
+ 4u
43
+ ··· + 13u + 1)
c
4
, c
5
(u
11
+ u
10
+ 5u
9
+ 5u
8
+ 9u
7
+ 8u
6
+ 7u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
44
+ 2u
43
+ ··· − 11u − 1)
c
6
(u
11
− u
10
+ 3u
9
− 3u
8
+ 5u
7
− 7u
6
+ 5u
5
− 8u
4
+ 3u
3
− 5u
2
+ u − 1)
· (u
44
+ 8u
42
+ ··· + 28u + 19)
c
7
(u
11
− 2u
10
− 3u
9
+ 8u
8
− 10u
6
+ 7u
5
+ 3u
4
− 6u
3
+ 2u
2
+ 2u − 1)
· (u
44
+ u
43
+ ··· − 41u + 11)
c
8
(u
11
− u
10
+ 5u
9
− 5u
8
+ 9u
7
− 8u
6
+ 7u
5
− 6u
4
+ 2u
3
− 4u
2
− 1)
· (u
44
+ 2u
43
+ ··· − 11u − 1)
c
9
(u
11
+ 4u
9
+ 2u
8
+ 2u
7
+ 5u
6
− 2u
5
+ u
3
− 2u
2
+ u + 1)
· (u
44
− u
43
+ ··· − 14u − 1)
c
10
(u
11
+ 2u
10
− 3u
9
− 8u
8
+ 10u
6
+ 7u
5
− 3u
4
− 6u
3
− 2u
2
+ 2u + 1)
· (u
44
+ u
43
+ ··· − 41u + 11)
c
11
(u
11
− u
10
− 4u
9
+ 6u
8
+ 4u
7
− 12u
6
+ 7u
5
+ 6u
4
− 7u
3
− u
2
+ 3u − 1)
· (u
44
+ 2u
43
+ ··· + 12u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
11
+ 5y
10
+ ··· − 9y −1)(y
44
+ 16y
43
+ ··· + 3928y + 361)
c
2
(y
11
+ y
10
+ ··· + 11y −1)(y
44
+ 24y
43
+ ··· − 363932y + 130321)
c
3
(y
11
− 5y
10
+ ··· − 8y −1)(y
44
− 42y
43
+ ··· − 5y + 1)
c
4
, c
5
, c
8
(y
11
+ 9y
10
+ ··· − 8y −1)(y
44
+ 12y
43
+ ··· − 37y + 1)
c
7
, c
10
(y
11
− 10y
10
+ ··· + 8y −1)(y
44
− 15y
43
+ ··· − 2869y + 121)
c
9
(y
11
+ 8y
10
+ ··· + 5y −1)(y
44
+ 7y
43
+ ··· − 54y + 1)
c
11
(y
11
− 9y
10
+ ··· + 7y −1)(y
44
− 38y
43
+ ··· − 96y + 1)
16
