11n
144
(K11n
144
)
1
Arc Sequences
6 1 10 7 9 2 10 5 3 5 7
Solving Sequence
2,6
7 1
3,9
10 4 5 8 11
c
6
c
1
c
2
c
9
c
3
c
5
c
8
c
11
c
4
, c
7
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= ha
24
+ 2a
23
+ ··· + 50a + 29, 1.04381 × 10
27
u 2.73743 × 10
25
a
23
+ ··· + 1.82658 × 10
27
a 3.98240 × 10
26
,
1.04381 × 10
27
b 3.69648 × 10
25
a
23
+ ··· + 7.59828 × 10
27
a + 3.70467 × 10
26
i
I
u
2
= hu
11
3u
9
+ 5u
7
4u
5
+ u
4
+ 2u
3
2u
2
+ 1, 2u
10
5u
8
u
7
+ 7u
6
+ u
5
4u
4
+ u
3
+ u
2
+ b 3u,
u
10
+ u
9
+ 3u
8
2u
7
5u
6
+ 3u
5
+ 4u
4
2u
3
u
2
+ a + 2u 1i
I
u
3
= hu
19
5u
18
+ ··· 14u + 4, u
18
4u
17
+ ··· + 2a 1, 3u
18
11u
17
+ ··· + 2b 12i
There are 3 irreducible components with 54 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I.
I
u
1
= ha
24
+ 2a
23
+ · · · + 50a + 29, 1.04 × 10
27
u 2.74 × 10
25
a
23
+ · · · + 1.83 ×
10
27
a3.98×10
26
, 1.04×10
27
b3.70×10
25
a
23
+· · ·+7.60×10
27
a+3.70×10
26
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
0.0262253a
23
+ 0.0679001a
22
+ ··· 1.74992a + 0.381525
a
7
=
0.0262253a
23
0.0679001a
22
+ ··· + 1.74992a 0.381525
0.0262253a
23
+ 0.0679001a
22
+ ··· 1.74992a + 0.381525
a
1
=
1
0.0146252a
23
+ 0.0611303a
22
+ ··· 2.53695a 1.94225
a
3
=
0.0146252a
23
+ 0.0611303a
22
+ ··· 2.53695a 0.942253
0.0236230a
23
0.103132a
22
+ ··· + 3.28934a + 1.88046
a
9
=
a
0.0354133a
23
+ 0.125562a
22
+ ··· 7.27936a 0.354917
a
10
=
0.0578513a
23
+ 0.162888a
22
+ ··· 5.08879a 1.36130
0.0677349a
23
0.186002a
22
+ ··· + 4.47121a + 2.55661
a
4
=
0.0220653a
23
+ 0.0901955a
22
+ ··· 4.82168a 1.51988
0.00455804a
23
+ 0.0230955a
22
+ ··· 0.941293a 1.04292
a
5
=
0.0107826a
23
+ 0.0435063a
22
+ ··· 1.53301a 0.448037
0.0374060a
23
0.156797a
22
+ ··· + 7.29598a + 3.01084
a
8
=
0.0389766a
23
+ 0.112175a
22
+ ··· 1.61223a 0.978872
0.0542014a
23
0.145451a
22
+ ··· + 0.481954a + 2.94449
a
11
=
0.00899781a
23
0.0420017a
22
+ ··· + 0.752387a + 0.938202
0.0236230a
23
+ 0.103132a
22
+ ··· 3.28934a 1.88046
a
11
=
0.00899781a
23
0.0420017a
22
+ ··· + 0.752387a + 0.938202
0.0236230a
23
+ 0.103132a
22
+ ··· 3.28934a 1.88046
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.428243 0.664531I
a = 1.77180 0.08003I
b = 0.946924 + 0.275652I
5.83845 + 0.92430I 4.28328 0.79423I
u = 0.428243 + 0.664531I
a = 1.77180 + 0.08003I
b = 0.946924 0.275652I
5.83845 0.92430I 4.28328 + 0.79423I
u = 1.073950 + 0.558752I
a = 1.148448 0.280772I
b = 2.57966 + 0.71790I
3.94784 + 5.69302I 8.00000 5.51057I
u = 1.073950 0.558752I
a = 1.148448 + 0.280772I
b = 2.57966 0.71790I
3.94784 5.69302I 8.00000 + 5.51057I
u = 1.002193 0.295542I
a = 1.033114 0.696551I
b = 1.319805 0.225110I
5.83845 + 0.92430I 11.71672 0.79423I
u = 1.002193 + 0.295542I
a = 1.033114 + 0.696551I
b = 1.319805 + 0.225110I
5.83845 0.92430I 11.71672 + 0.79423I
u = 1.002193 + 0.295542I
a = 0.541614 1.114369I
b = 1.65257 + 0.55500I
2.05724 0.92430I 11.71672 + 0.79423I
u = 1.002193 0.295542I
a = 0.541614 + 1.114369I
b = 1.65257 0.55500I
2.05724 + 0.92430I 11.71672 0.79423I
u = 1.002193 0.295542I
a = 0.385541 0.314901I
b = 2.37946 + 1.59006I
2.05724 + 0.92430I 11.71672 0.79423I
u = 1.002193 + 0.295542I
a = 0.385541 + 0.314901I
b = 2.37946 1.59006I
2.05724 0.92430I 11.71672 + 0.79423I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.063553 1.297187I
b = 0.072058 + 1.329797I
3.94784 5.69302I 8.00000 + 5.51057I
u = 1.073950 + 0.558752I
a = 0.063553 + 1.297187I
b = 0.072058 1.329797I
3.94784 + 5.69302I 8.00000 5.51057I
u = 0.428243 + 0.664531I
a = 0.024930 0.922281I
b = 0.626769 + 0.310715I
2.05724 0.92430I 4.28328 + 0.79423I
u = 0.428243 0.664531I
a = 0.024930 + 0.922281I
b = 0.626769 0.310715I
2.05724 + 0.92430I 4.28328 0.79423I
u = 0.428243 + 0.664531I
a = 0.15225 1.47654I
b = 0.491110 0.847702I
5.83845 0.92430I 4.28328 + 0.79423I
u = 0.428243 0.664531I
a = 0.15225 + 1.47654I
b = 0.491110 + 0.847702I
5.83845 + 0.92430I 4.28328 0.79423I
u = 0.428243 0.664531I
a = 0.64354 1.45570I
b = 0.077489 0.118368I
2.05724 + 0.92430I 4.28328 0.79423I
u = 0.428243 + 0.664531I
a = 0.64354 + 1.45570I
b = 0.077489 + 0.118368I
2.05724 0.92430I 4.28328 + 0.79423I
u = 1.073950 + 0.558752I
a = 0.793728 0.225331I
b = 1.41733 0.48227I
3.94784 + 5.69302I 8.00000 5.51057I
u = 1.073950 0.558752I
a = 0.793728 + 0.225331I
b = 1.41733 + 0.48227I
3.94784 5.69302I 8.00000 + 5.51057I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.992223 0.027806I
b = 2.97095 0.71292I
3.94784 5.69302I 8.00000 + 5.51057I
u = 1.073950 + 0.558752I
a = 0.992223 + 0.027806I
b = 2.97095 + 0.71292I
3.94784 + 5.69302I 8.00000 5.51057I
u = 1.002193 + 0.295542I
a = 1.38726 0.39118I
b = 2.85990 + 0.17025I
5.83845 0.92430I 11.71672 + 0.79423I
u = 1.002193 0.295542I
a = 1.38726 + 0.39118I
b = 2.85990 0.17025I
5.83845 + 0.92430I 11.71672 0.79423I
5
II. I
u
2
= hu
11
3u
9
+ 5u
7
4u
5
+ u
4
+ 2u
3
2u
2
+ 1, 2u
10
5u
8
+ · · · + b
3u, u
10
+ u
9
+ · · · + a 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
9
=
u
10
u
9
3u
8
+ 2u
7
+ 5u
6
3u
5
4u
4
+ 2u
3
+ u
2
2u + 1
2u
10
+ 5u
8
+ u
7
7u
6
u
5
+ 4u
4
u
3
u
2
+ 3u
a
10
=
u
10
u
9
3u
8
+ 2u
7
+ 5u
6
3u
5
3u
4
+ 2u
3
2u + 2
u
10
+ 3u
8
+ u
7
5u
6
u
5
+ 3u
4
u
2
+ 2u
a
4
=
2u
10
+ u
9
+ 5u
8
3u
7
7u
6
+ 4u
5
+ 4u
4
4u
3
u
2
+ 3u 2
u
10
u
9
3u
8
+ 3u
7
+ 4u
6
4u
5
2u
4
+ 3u
3
u
2
2u + 2
a
5
=
u
10
+ u
9
+ 3u
8
3u
7
5u
6
+ 4u
5
+ 4u
4
3u
3
u
2
+ 2u 2
u
9
u
8
+ 3u
7
+ 2u
6
4u
5
2u
4
+ 2u
3
u
2
u + 2
a
8
=
u
10
+ 2u
8
3u
6
+ u
4
u
3
u
2
+ u 1
u
10
u
9
+ 3u
8
+ 3u
7
4u
6
4u
5
+ 3u
4
+ u
3
u
2
+ 2u + 2
a
11
=
u
4
u
2
+ 1
u
4
a
11
=
u
4
u
2
+ 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.130651 0.376133I
a = 0.973941 + 0.585327I
b = 2.18280 0.07773I
6.99914 2.24617I 15.2425 + 3.4100I
u = 1.130651 + 0.376133I
a = 0.973941 0.585327I
b = 2.18280 + 0.07773I
6.99914 + 2.24617I 15.2425 3.4100I
u = 0.880495 0.687594I
a = 0.286856 0.446919I
b = 0.378729 + 0.769010I
5.44803 2.65181I 6.56642 + 4.06839I
u = 0.880495 + 0.687594I
a = 0.286856 + 0.446919I
b = 0.378729 0.769010I
5.44803 + 2.65181I 6.56642 4.06839I
u = 0.673568
a = 2.04401
b = 1.75002
4.44260 6.63263
u = 0.308530 0.701885I
a = 0.275741 1.375231I
b = 0.428954 0.070977I
3.30665 0.86798I 12.51115 + 0.41084I
u = 0.308530 + 0.701885I
a = 0.275741 + 1.375231I
b = 0.428954 + 0.070977I
3.30665 + 0.86798I 12.51115 0.41084I
u = 0.889831 0.305373I
a = 0.380398 + 0.840035I
b = 2.22600 + 0.34678I
3.01730 + 1.31614I 1.85963 5.09190I
u = 0.889831 + 0.305373I
a = 0.380398 0.840035I
b = 2.22600 0.34678I
3.01730 1.31614I 1.85963 + 5.09190I
u = 1.149569 0.537433I
a = 0.894929 + 0.047035I
b = 2.22611 0.55790I
5.80784 + 5.68354I 14.5040 4.4186I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.149569 + 0.537433I
a = 0.894929 0.047035I
b = 2.22611 + 0.55790I
5.80784 5.68354I 14.5040 + 4.4186I
7
III. I
u
3
=
hu
19
5u
18
+· · ·14u+4, u
18
4u
17
+· · ·+2a1, 3u
18
11u
17
+· · ·+2b12i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
9
=
1
2
u
18
+ 2u
17
+ ··· 4u +
1
2
3
2
u
18
+
11
2
u
17
+ ···
29
2
u + 6
a
10
=
u
18
7
2
u
17
+ ··· +
9
2
u
3
2
7
2
u
18
+
31
2
u
17
+ ···
77
2
u + 14
a
4
=
7
4
u
18
+
29
4
u
17
+ ···
75
4
u + 7
3
2
u
18
13
2
u
17
+ ··· +
35
2
u 7
a
5
=
3
4
u
18
17
4
u
17
+ ··· +
51
4
u 5
1
2
u
18
+
7
2
u
17
+ ···
23
2
u + 5
a
8
=
7
4
u
18
+
25
4
u
17
+ ···
39
4
u + 2
3
2
u
18
13
2
u
17
+ ··· +
25
2
u 3
a
11
=
u
4
u
2
+ 1
u
4
a
11
=
u
4
u
2
+ 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.252297 0.169624I
a = 0.903716 0.604949I
b = 2.17310 + 0.85519I
1.49409 + 5.07243I 11.25567 3.29320I
u = 1.252297 + 0.169624I
a = 0.903716 + 0.604949I
b = 2.17310 0.85519I
1.49409 5.07243I 11.25567 + 3.29320I
u = 1.213536 0.400047I
a = 0.611827 + 0.476620I
b = 1.64773 0.25131I
5.26090 2.36693I 9.94736 + 1.06990I
u = 1.213536 + 0.400047I
a = 0.611827 0.476620I
b = 1.64773 + 0.25131I
5.26090 + 2.36693I 9.94736 1.06990I
u = 0.614061
a = 0.507575
b = 0.384496
0.778408 13.4963
u = 0.096750 0.776113I
a = 0.490048 1.001747I
b = 0.285109 0.424869I
1.40681 1.74274I 5.94701 + 3.80028I
u = 0.096750 + 0.776113I
a = 0.490048 + 1.001747I
b = 0.285109 + 0.424869I
1.40681 + 1.74274I 5.94701 3.80028I
u = 0.352719 0.890647I
a = 0.33990 + 1.50834I
b = 0.091592 + 0.342070I
4.00668 8.26944I 5.84435 + 4.36564I
u = 0.352719 + 0.890647I
a = 0.33990 1.50834I
b = 0.091592 0.342070I
4.00668 + 8.26944I 5.84435 4.36564I
u = 0.695357 0.843033I
a = 0.942942 + 0.204588I
b = 0.396427 + 0.035659I
6.12748 + 4.38921I 5.85287 6.32556I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.695357 + 0.843033I
a = 0.942942 0.204588I
b = 0.396427 0.035659I
6.12748 4.38921I 5.85287 + 6.32556I
u = 0.783515 0.465676I
a = 0.505777 + 0.529553I
b = 0.840056 + 0.218917I
1.11792 + 1.95845I 4.20644 5.46350I
u = 0.783515 + 0.465676I
a = 0.505777 0.529553I
b = 0.840056 0.218917I
1.11792 1.95845I 4.20644 + 5.46350I
u = 0.990938 0.758822I
a = 0.208360 0.663585I
b = 0.413297 + 0.883851I
5.25710 + 1.54392I 8.61355 + 2.51619I
u = 0.990938 + 0.758822I
a = 0.208360 + 0.663585I
b = 0.413297 0.883851I
5.25710 1.54392I 8.61355 2.51619I
u = 1.164877 0.614933I
a = 1.208296 + 0.115263I
b = 2.89222 0.17288I
1.54987 + 13.80212I 8.55217 7.85507I
u = 1.164877 + 0.614933I
a = 1.208296 0.115263I
b = 2.89222 + 0.17288I
1.54987 13.80212I 8.55217 + 7.85507I
u = 1.188708 0.496628I
a = 0.783669 0.200947I
b = 2.33800 + 0.11606I
4.57325 + 6.41400I 8.03245 7.39287I
u = 1.188708 + 0.496628I
a = 0.783669 + 0.200947I
b = 2.33800 0.11606I
4.57325 6.41400I 8.03245 + 7.39287I
10
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
6
u
5
u
4
+ 2u
3
u + 1)
4
(u
11
3u
9
+ ··· 2u
2
+ 1)(u
19
+ 5u
18
+ ··· 14u 4)
c
2
(1 + u + 2u
2
+ 4u
3
+ 5u
4
+ 3u
5
+ u
6
)
4
(u
11
+ 6u
10
+ ··· + 4u + 1)
(u
19
+ 9u
18
+ ··· + 44u + 16)
c
3
, c
8
(u
11
u
10
3u
9
+ 3u
8
+ 2u
7
u
6
+ u
5
3u
4
u
3
+ 2u
2
+ 1)
(u
19
+ u
18
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· + 94u + 29)
c
4
, c
10
(u
11
+ 2u
9
+ u
8
3u
7
u
6
u
5
2u
4
+ 3u
3
+ 3u
2
u 1)
(u
19
+ 15u
17
+ ··· + 3u 1)(u
24
+ u
23
+ ··· 166u + 79)
c
5
, c
9
(u
11
+ u
10
3u
9
3u
8
+ 2u
7
+ u
6
+ u
5
+ 3u
4
u
3
2u
2
1)
(u
19
+ u
18
+ ··· + 4u + 1)(u
24
+ u
23
+ ··· + 94u + 29)
c
6
(u
6
u
5
u
4
+ 2u
3
u + 1)
4
(u
11
3u
9
+ ··· + 2u
2
1)(u
19
+ 5u
18
+ ··· 14u 4)
c
7
(u
2
u 1)
12
(u
11
+ 4u
10
+ 4u
9
+ 2u
7
+ 3u
6
u
5
+ u
4
2u
3
4u
2
1)
(u
19
+ 15u
18
+ ··· + 544u + 64)
c
11
(u
6
3u
5
+ 5u
4
4u
3
+ 2u
2
u + 1)
4
(u
11
+ u
9
+ 4u
8
+ u
7
+ 8u
5
5u
4
+ 9u
3
3u
2
+ 1)
(u
19
+ 15u
18
+ ··· 990u 196)
11
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(1 y + 2y
2
4y
3
+ 5y
4
3y
5
+ y
6
)
4
(y
11
6y
10
+ ··· + 4y 1)
(y
19
9y
18
+ ··· + 44y 16)
c
2
(1 + 3y + 6y
2
+ 5y
4
+ y
5
+ y
6
)
4
(y
11
+ 2y
10
+ ··· + 4y 1)
(y
19
+ 3y
18
+ ··· + 2288y 256)
c
3
, c
5
, c
8
c
9
(y
11
7y
10
+ ··· 4y 1)(y
19
9y
18
+ ··· + 12y 1)
(y
24
9y
23
+ ··· 8372y + 841)
c
4
, c
10
(y
11
+ 4y
10
+ ··· + 7y 1)(y
19
+ 30y
18
+ ··· 25y 1)
(y
24
+ 15y
23
+ ··· + 63136y + 6241)
c
7
(y
2
3y + 1)
12
(y
11
8y
10
+ ··· 8y 1)
(y
19
11y
18
+ ··· + 95232y 4096)
c
11
(1 + 3y + 6y
2
+ 5y
4
+ y
5
+ y
6
)
4
(y
11
+ 2y
10
+ ··· + 6y 1)
(y
19
+ 3y
18
+ ··· + 237260y 38416)
12