11a
146
(K11a
146
)
1
Arc Sequences
6 1 9 11 2 10 5 3 4 7 8
Solving Sequence
1,6
2
3,8
9 5 7 11 4 10
c
1
c
2
c
8
c
5
c
7
c
11
c
4
c
10
c
3
, c
6
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
14
u
13
+ 4u
12
3u
11
+ 9u
10
6u
9
+ 13u
8
8u
7
+ 13u
6
8u
5
+ 9u
4
4u
3
+ 4u
2
u + 1,
u
13
3u
11
7u
9
9u
7
+ u
6
9u
5
+ 2u
4
5u
3
+ u
2
+ b 3u,
u
13
+ 4u
12
6u
11
+ 13u
10
14u
9
+ 27u
8
22u
7
+ 34u
6
24u
5
+ 30u
4
19u
3
+ 15u
2
+ a 6u + 5i
I
u
2
= hu
75
+ 15u
73
+ ··· 20u + 7,
1.16236 × 10
103
u
74
+ 3.74125 × 10
102
u
73
+ ··· + 1.41576 × 10
103
b 7.11244 × 10
103
,
7.14613 × 10
103
u
74
3.17559 × 10
103
u
73
+ ··· + 9.91035 × 10
103
a + 2.29421 × 10
104
i
There are 2 irreducible components with 89 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
= hu
14
u
13
+· · ·u+1, u
13
3u
11
+· · ·+b3u, u
13
+4u
12
+· · ·+a+5i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
u
13
4u
12
+ ··· + 6u 5
u
13
+ 3u
11
+ 7u
9
+ 9u
7
u
6
+ 9u
5
2u
4
+ 5u
3
u
2
+ 3u
a
9
=
2u
13
4u
12
+ ··· + 6u 4
u
12
+ 2u
10
+ u
9
+ 4u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 2u
3
+ u
2
+ 2u + 1
a
5
=
u
u
3
+ u
a
7
=
u
13
4u
12
+ ··· + 4u 4
u
13
u
12
+ ··· + 5u 1
a
11
=
4u
13
+ u
12
+ ··· 4u 3
2u
13
2u
12
+ ··· + 3u 2
a
4
=
2u
13
+ 4u
12
+ ··· 5u + 4
u
13
3u
11
6u
9
7u
7
+ u
6
5u
5
+ 2u
4
u
3
u 1
a
10
=
u
13
+ u
12
+ ··· u + 1
u
13
2u
11
2u
10
3u
9
5u
8
2u
7
8u
6
8u
4
+ 2u
3
6u
2
+ u 2
a
10
=
u
13
+ u
12
+ ··· u + 1
u
13
2u
11
2u
10
3u
9
5u
8
2u
7
8u
6
8u
4
+ 2u
3
6u
2
+ u 2
(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 = 0.734849 0.838959I
a = 1.208615 + 0.185596I
b = 0.582713 + 0.256653I
0.32678 + 2.81352I 3.82759 3.54032I
u = 0.734849 + 0.838959I
a = 1.208615 0.185596I
b = 0.582713 0.256653I
0.32678 2.81352I 3.82759 + 3.54032I
u = 0.418839 1.066630I
a = 0.291345 0.378834I
b = 0.473607 + 0.671965I
3.30861 + 3.80056I 0.83959 2.34062I
u = 0.418839 + 1.066630I
a = 0.291345 + 0.378834I
b = 0.473607 0.671965I
3.30861 3.80056I 0.83959 + 2.34062I
u = 0.330549 0.694071I
a = 1.23852 1.22506I
b = 0.019637 0.950071I
1.85356 0.60321I 0.34386 3.01291I
u = 0.330549 + 0.694071I
a = 1.23852 + 1.22506I
b = 0.019637 + 0.950071I
1.85356 + 0.60321I 0.34386 + 3.01291I
u = 0.201031 0.762183I
a = 2.79799 0.26537I
b = 0.54393 1.41064I
0.75311 + 2.85458I 1.50497 5.64699I
u = 0.201031 + 0.762183I
a = 2.79799 + 0.26537I
b = 0.54393 + 1.41064I
0.75311 2.85458I 1.50497 + 5.64699I
u = 0.316820 1.106540I
a = 0.82774 1.28027I
b = 0.896791 + 0.980193I
0.69663 5.04325I 1.15268 + 7.45720I
u = 0.316820 + 1.106540I
a = 0.82774 + 1.28027I
b = 0.896791 0.980193I
0.69663 + 5.04325I 1.15268 7.45720I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.675866 0.491616I
a = 0.482814 0.404595I
b = 1.045006 0.289500I
7.41228 0.32675I 4.63259 0.70876I
u = 0.675866 + 0.491616I
a = 0.482814 + 0.404595I
b = 1.045006 + 0.289500I
7.41228 + 0.32675I 4.63259 + 0.70876I
u = 0.790520 1.084836I
a = 0.666179 + 0.467389I
b = 0.524461 + 0.759534I
5.59130 5.55392I 7.03309 + 2.81100I
u = 0.790520 + 1.084836I
a = 0.666179 0.467389I
b = 0.524461 0.759534I
5.59130 + 5.55392I 7.03309 2.81100I
4
II. I
u
2
= hu
75
+ 15u
73
+ · · · 20u + 7, 1.16 × 10
103
u
74
+ 3.74 × 10
102
u
73
+
· · · + 1.42 × 10
103
b 7.11 × 10
103
, 7.15 × 10
103
u
74
3.18 × 10
103
u
73
+ · · · +
9.91 × 10
103
a + 2.29 × 10
104
i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
0.721078u
74
+ 0.320432u
73
+ ··· 5.32211u 2.31497
0.821010u
74
0.264257u
73
+ ··· 12.5249u + 5.02375
a
9
=
0.810814u
74
+ 1.04372u
73
+ ··· 19.2078u + 1.26956
1.59265u
74
0.838121u
73
+ ··· 10.7401u + 6.06974
a
5
=
u
u
3
+ u
a
7
=
0.886848u
74
+ 0.735561u
73
+ ··· 9.13546u 1.57363
1.30627u
74
0.520026u
73
+ ··· 18.1745u + 7.18831
a
11
=
1.06655u
74
1.00342u
73
+ ··· + 16.8816u + 0.960205
0.756010u
74
+ 0.0457275u
73
+ ··· + 22.8247u 7.73329
a
4
=
0.0614847u
74
+ 0.125592u
73
+ ··· + 1.89652u + 0.236355
0.0748893u
74
+ 0.280213u
73
+ ··· 0.209838u + 0.00750577
a
10
=
0.579776u
74
+ 0.227218u
73
+ ··· + 5.38557u 1.00498
0.547002u
74
0.277744u
73
+ ··· 8.65299u + 2.85168
a
10
=
0.579776u
74
+ 0.227218u
73
+ ··· + 5.38557u 1.00498
0.547002u
74
0.277744u
73
+ ··· 8.65299u + 2.85168
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.997300 0.535698I
a = 1.041711 0.863157I
b = 1.41132 + 0.74352I
6.61694 10.02953I 6.66127 + 5.15792I
u = 0.997300 + 0.535698I
a = 1.041711 + 0.863157I
b = 1.41132 0.74352I
6.61694 + 10.02953I 6.66127 5.15792I
u = 0.849508 0.542374I
a = 1.19541 + 1.04425I
b = 1.63768 0.71839I
9.48673 3.80892I 9.50577 + 2.11566I
u = 0.849508 + 0.542374I
a = 1.19541 1.04425I
b = 1.63768 + 0.71839I
9.48673 + 3.80892I 9.50577 2.11566I
u = 0.821168 0.772543I
a = 0.915115 + 0.063644I
b = 0.670177 + 0.265353I
0.90357 + 3.01315I 11.44109 8.25813I
u = 0.821168 + 0.772543I
a = 0.915115 0.063644I
b = 0.670177 0.265353I
0.90357 3.01315I 11.44109 + 8.25813I
u = 0.768859
a = 1.67495
b = 1.47011
2.41244 3.98164
u = 0.727326 1.141518I
a = 1.44570 0.77630I
b = 1.46957 1.03381I
4.7307 + 16.2882I 4.50602 8.86315I
u = 0.727326 + 1.141518I
a = 1.44570 + 0.77630I
b = 1.46957 + 1.03381I
4.7307 16.2882I 4.50602 + 8.86315I
u = 0.673658 1.087134I
a = 1.53716 + 1.02912I
b = 1.69251 + 1.06931I
7.83095 + 9.48733I 6.77732 7.16053I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.673658 + 1.087134I
a = 1.53716 1.02912I
b = 1.69251 1.06931I
7.83095 9.48733I 6.77732 + 7.16053I
u = 0.663268 0.853569I
a = 1.37734 + 0.72160I
b = 0.758278 + 0.141213I
1.06443 + 2.57629I 8.22976 3.25528I
u = 0.663268 + 0.853569I
a = 1.37734 0.72160I
b = 0.758278 0.141213I
1.06443 2.57629I 8.22976 + 3.25528I
u = 0.663115 0.870319I
a = 1.33003 + 0.51217I
b = 0.769435 + 0.207041I
1.03816 + 2.56974I 7.04921 1.23052I
u = 0.663115 + 0.870319I
a = 1.33003 0.51217I
b = 0.769435 0.207041I
1.03816 2.56974I 7.04921 + 1.23052I
u = 0.604095 0.124629I
a = 0.520584 + 0.161680I
b = 0.562665 0.068774I
0.988802 + 0.029608I 10.70489 0.11784I
u = 0.604095 + 0.124629I
a = 0.520584 0.161680I
b = 0.562665 + 0.068774I
0.988802 0.029608I 10.70489 + 0.11784I
u = 0.594753 0.976447I
a = 1.76760 0.27801I
b = 0.992629 0.317325I
1.52512 + 5.54501I 3.31692 6.84685I
u = 0.594753 + 0.976447I
a = 1.76760 + 0.27801I
b = 0.992629 + 0.317325I
1.52512 5.54501I 3.31692 + 6.84685I
u = 0.583811 0.895077I
a = 0.752626 0.749520I
b = 0.75640 + 2.07806I
2.09042 + 6.16494I 2.83622 6.65448I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.583811 + 0.895077I
a = 0.752626 + 0.749520I
b = 0.75640 2.07806I
2.09042 6.16494I 2.83622 + 6.65448I
u = 0.583753 0.813835I
a = 1.58625 0.14110I
b = 0.21446 2.00505I
2.35458 1.52998I 4.39480 + 0.69447I
u = 0.583753 + 0.813835I
a = 1.58625 + 0.14110I
b = 0.21446 + 2.00505I
2.35458 + 1.52998I 4.39480 0.69447I
u = 0.573961 0.682020I
a = 1.38069 1.62918I
b = 0.573303 + 0.057484I
0.601433 0.843152I 6.25066 + 1.26638I
u = 0.573961 + 0.682020I
a = 1.38069 + 1.62918I
b = 0.573303 0.057484I
0.601433 + 0.843152I 6.25066 1.26638I
u = 0.558544 1.146303I
a = 0.559124 0.593863I
b = 0.774731 0.320056I
1.85708 + 4.63248I 2.65105 8.28455I
u = 0.558544 + 1.146303I
a = 0.559124 + 0.593863I
b = 0.774731 + 0.320056I
1.85708 4.63248I 2.65105 + 8.28455I
u = 0.423126 1.151837I
a = 0.063280 1.381225I
b = 1.57483 + 0.26636I
1.02193 + 4.09857I 0.694878 1.127718I
u = 0.423126 + 1.151837I
a = 0.063280 + 1.381225I
b = 1.57483 0.26636I
1.02193 4.09857I 0.694878 + 1.127718I
u = 0.329445 0.834791I
a = 2.36627 0.05733I
b = 1.18992 0.99392I
0.58773 2.04231I 0.69192 3.19638I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.329445 + 0.834791I
a = 2.36627 + 0.05733I
b = 1.18992 + 0.99392I
0.58773 + 2.04231I 0.69192 + 3.19638I
u = 0.228067 0.674546I
a = 2.29484 1.49946I
b = 0.092638 + 0.627623I
0.91162 + 4.36069I 4.50920 7.60061I
u = 0.228067 + 0.674546I
a = 2.29484 + 1.49946I
b = 0.092638 0.627623I
0.91162 4.36069I 4.50920 + 7.60061I
u = 0.219708 0.997660I
a = 0.313694 + 0.499917I
b = 0.556012 + 1.022727I
3.84788 + 0.02965I 1.99150 0.69502I
u = 0.219708 + 0.997660I
a = 0.313694 0.499917I
b = 0.556012 1.022727I
3.84788 0.02965I 1.99150 + 0.69502I
u = 0.034915 0.842594I
a = 0.508060 0.814343I
b = 0.096919 0.903738I
1.98038 + 1.28024I 1.71519 5.23822I
u = 0.034915 + 0.842594I
a = 0.508060 + 0.814343I
b = 0.096919 + 0.903738I
1.98038 1.28024I 1.71519 + 5.23822I
u = 0.005828 1.116564I
a = 0.962671 + 0.065388I
b = 0.771794 0.649501I
3.39834 2.32606I 5.01731 + 3.42052I
u = 0.005828 + 1.116564I
a = 0.962671 0.065388I
b = 0.771794 + 0.649501I
3.39834 + 2.32606I 5.01731 3.42052I
u = 0.028864 1.205845I
a = 0.030043 + 0.158897I
b = 0.525695 + 0.912935I
6.15424 + 4.21404I 4.39569 5.39895I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.028864 + 1.205845I
a = 0.030043 0.158897I
b = 0.525695 0.912935I
6.15424 4.21404I 4.39569 + 5.39895I
u = 0.095706 1.407538I
a = 0.286428 0.016195I
b = 0.719842 + 0.514282I
1.04032 7.25828I 2.20278 + 7.55906I
u = 0.095706 + 1.407538I
a = 0.286428 + 0.016195I
b = 0.719842 0.514282I
1.04032 + 7.25828I 2.20278 7.55906I
u = 0.129319 0.675423I
a = 1.34198 0.85690I
b = 0.014926 1.085659I
1.94755 + 1.36953I 1.12148 5.96580I
u = 0.129319 + 0.675423I
a = 1.34198 + 0.85690I
b = 0.014926 + 1.085659I
1.94755 1.36953I 1.12148 + 5.96580I
u = 0.276964 0.055334I
a = 3.24614 + 1.82467I
b = 0.335709 0.635949I
1.70721 + 1.28972I 0.48854 2.47606I
u = 0.276964 + 0.055334I
a = 3.24614 1.82467I
b = 0.335709 + 0.635949I
1.70721 1.28972I 0.48854 + 2.47606I
u = 0.419276 0.968552I
a = 1.37090 0.96007I
b = 1.275448 0.547400I
3.84184 1.43557I 4.92095 + 1.24019I
u = 0.419276 + 0.968552I
a = 1.37090 + 0.96007I
b = 1.275448 + 0.547400I
3.84184 + 1.43557I 4.92095 1.24019I
u = 0.446827 1.030772I
a = 0.383255 0.716019I
b = 0.78263 + 1.25594I
3.66270 4.65674I 4.27743 + 9.92955I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.446827 + 1.030772I
a = 0.383255 + 0.716019I
b = 0.78263 1.25594I
3.66270 + 4.65674I 4.27743 9.92955I
u = 0.564610 0.759254I
a = 1.111496 + 0.152357I
b = 1.264581 + 0.419226I
7.40917 1.28073I 5.11860 + 6.28891I
u = 0.564610 + 0.759254I
a = 1.111496 0.152357I
b = 1.264581 0.419226I
7.40917 + 1.28073I 5.11860 6.28891I
u = 0.607031 0.944057I
a = 0.61211 1.40952I
b = 0.795124 0.593814I
6.78271 3.40013I 6.47890 + 1.43323I
u = 0.607031 + 0.944057I
a = 0.61211 + 1.40952I
b = 0.795124 + 0.593814I
6.78271 + 3.40013I 6.47890 1.43323I
u = 0.628874 0.990800I
a = 1.66426 + 0.68833I
b = 1.19979 + 0.86296I
1.46459 6.31124I 4.54139 + 8.27283I
u = 0.628874 + 0.990800I
a = 1.66426 0.68833I
b = 1.19979 0.86296I
1.46459 + 6.31124I 4.54139 8.27283I
u = 0.652679 1.083036I
a = 1.61651 0.66348I
b = 1.173455 0.781385I
2.04951 11.72602I 1.52262 + 9.27004I
u = 0.652679 + 1.083036I
a = 1.61651 + 0.66348I
b = 1.173455 + 0.781385I
2.04951 + 11.72602I 1.52262 9.27004I
u = 0.671530 0.632305I
a = 1.07681 + 1.02346I
b = 1.032103 0.508181I
2.52677 + 1.24936I 7.69965 2.52698I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.671530 + 0.632305I
a = 1.07681 1.02346I
b = 1.032103 + 0.508181I
2.52677 1.24936I 7.69965 + 2.52698I
u = 0.736446 0.947781I
a = 1.17778 + 1.13785I
b = 0.887098 + 0.641638I
6.26955 7.47029I 6.82331 + 8.59377I
u = 0.736446 + 0.947781I
a = 1.17778 1.13785I
b = 0.887098 0.641638I
6.26955 + 7.47029I 6.82331 8.59377I
u = 0.75306 1.24388I
a = 0.545367 0.387882I
b = 0.683526 0.725105I
5.24327 6.25276I 3.11269 + 11.28852I
u = 0.75306 + 1.24388I
a = 0.545367 + 0.387882I
b = 0.683526 + 0.725105I
5.24327 + 6.25276I 3.11269 11.28852I
u = 0.791734 0.779097I
a = 0.992300 + 0.187859I
b = 1.143653 0.488302I
6.79170 + 1.71786I 6.73682 2.74411I
u = 0.791734 + 0.779097I
a = 0.992300 0.187859I
b = 1.143653 + 0.488302I
6.79170 1.71786I 6.73682 + 2.74411I
u = 0.808914 0.489775I
a = 1.29004 0.89724I
b = 0.946433 + 0.610763I
0.30295 + 6.24808I 3.92390 5.63947I
u = 0.808914 + 0.489775I
a = 1.29004 + 0.89724I
b = 0.946433 0.610763I
0.30295 6.24808I 3.92390 + 5.63947I
u = 0.853645 1.095881I
a = 0.902335 + 0.386675I
b = 0.753531 + 0.798272I
5.21306 3.57822I 6.04971 + 2.23809I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.853645 + 1.095881I
a = 0.902335 0.386675I
b = 0.753531 0.798272I
5.21306 + 3.57822I 6.04971 2.23809I
u = 0.932408 0.222383I
a = 0.471108 + 0.020661I
b = 1.033513 + 0.122082I
8.24157 0.11075I 14.1787 1.9734I
u = 0.932408 + 0.222383I
a = 0.471108 0.020661I
b = 1.033513 0.122082I
8.24157 + 0.11075I 14.1787 + 1.9734I
u = 1.110233 0.622964I
a = 0.516528 + 0.163821I
b = 0.894451 0.337332I
6.65332 3.38709I 9.68233 + 3.95237I
u = 1.110233 + 0.622964I
a = 0.516528 0.163821I
b = 0.894451 + 0.337332I
6.65332 + 3.38709I 9.68233 3.95237I
13
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
14
u
13
+ ··· u + 1)(u
75
+ 15u
73
+ ··· 20u + 7)
c
2
(u
14
+ 7u
13
+ ··· + 7u + 1)(u
75
+ 30u
74
+ ··· + 288u 49)
c
3
(u
14
8u
12
+ ··· 2u
2
+ 1)(u
75
+ u
74
+ ··· 23u 1)
c
4
(u
14
+ 5u
11
+ 2u
10
+ 3u
9
+ 9u
8
+ u
7
+ 8u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 2u
2
+ 1)
(u
75
+ 3u
74
+ ··· + 15u 1)
c
5
(u
14
+ u
13
+ ··· + u + 1)(u
75
+ 15u
73
+ ··· 20u + 7)
c
6
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
75
+ u
74
+ ··· 29u + 2)
c
7
(u
14
+ 3u
13
+ 3u
12
u
11
6u
10
6u
9
+ 2u
8
+ 6u
7
+ u
6
+ 3u
4
2u
2
+ 1)
(u
75
+ 2u
74
+ ··· 17u 1)
c
8
(u
14
8u
12
+ ··· 2u
2
+ 1)(u
75
+ u
74
+ ··· 23u 1)
c
9
(u
14
8u
12
+ ··· 2u
2
+ 1)(u
75
+ u
74
+ ··· 23u 1)
c
10
(u
14
2u
13
+ ··· 2u + 1)(u
75
+ u
74
+ ··· 29u + 2)
c
11
(u
14
+ 2u
12
+ 3u
11
+ 3u
10
+ 4u
9
+ 5u
8
+ 6u
7
+ 5u
6
+ 2u
5
+ u
4
2u
3
+ 1)
(u
75
+ 5u
74
+ ··· + 36831u + 8639)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 7y + 1)(y
75
+ 30y
74
+ ··· + 288y 49)
c
2
(y
14
+ 7y
13
+ ··· + 3y + 1)(y
75
+ 38y
74
+ ··· + 546484y 2401)
c
3
, c
8
(y
14
16y
13
+ ··· 4y + 1)(y
75
77y
74
+ ··· + 71y 1)
c
4
(y
14
+ 4y
12
+ ··· + 4y + 1)(y
75
y
74
+ ··· 29y 1)
c
6
(y
14
10y
13
+ ··· 14y + 1)(y
75
43y
74
+ ··· + 321y 4)
c
7
(y
14
3y
13
+ ··· 4y + 1)(y
75
8y
74
+ ··· 25y 1)
c
9
(y
14
16y
13
+ ··· 4y + 1)(y
75
77y
74
+ ··· + 71y 1)
c
10
(y
14
10y
13
+ ··· 14y + 1)(y
75
43y
74
+ ··· + 321y 4)
c
11
(y
14
+ 4y
13
+ ··· + 2y
2
+ 1)
(y
75
21y
74
+ ··· + 1725459695y 74632321)
15