11a
28
(K11a
28
)
1
Arc Sequences
5 1 10 2 9 3 11 4 6 7 8
Solving Sequence
1,5
2 3
4,8
9 11 7 6 10
c
1
c
2
c
4
c
8
c
11
c
7
c
6
c
10
c
3
, c
5
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
60
u
59
+ ··· + 2u + 1, 7.84555 × 10
60
u
59
6.43675 × 10
60
u
58
+ ··· + 7.39081 × 10
60
b 1.10746 × 10
61
,
1.38500 × 10
61
u
59
+ 4.52352 × 10
60
u
58
+ ··· + 7.39081 × 10
60
a 2.10503 × 10
61
i
There are 1 irreducible components with 60 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
60
u
59
+· · ·+2u+1, 7.85×10
60
u
59
6.44×10
60
u
58
+· · ·+7.39×10
60
b
1.11× 10
61
, 1.38× 10
61
u
59
+4.52 ×10
60
u
58
+· · · +7.39 ×10
60
a 2.11× 10
61
i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
4
=
u
u
3
+ u
a
8
=
1.87394u
59
0.612047u
58
+ ··· + 11.2165u + 2.84817
1.06153u
59
+ 0.870914u
58
+ ··· 1.16026u + 1.49843
a
9
=
1.80124u
59
0.688293u
58
+ ··· + 8.96602u + 2.18126
0.838467u
59
+ 0.794799u
58
+ ··· + 0.719619u + 2.01640
a
11
=
3.35064u
59
+ 1.59006u
58
+ ··· 9.14807u 0.107071
1.40877u
59
1.60597u
58
+ ··· 2.57774u 3.41256
a
7
=
3.73764u
59
+ 4.15854u
58
+ ··· + 4.26837u + 4.76862
0.100345u
59
0.728775u
58
+ ··· 6.83614u 3.01172
a
6
=
2.86120u
59
+ 2.94876u
58
+ ··· + 1.38730u + 2.37762
0.147559u
59
0.855835u
58
+ ··· 6.73885u 3.42491
a
10
=
1.73827u
59
0.742110u
58
+ ··· 17.5597u 5.34256
2.48038u
59
2.38623u
58
+ ··· + 1.86601u 1.73827
a
10
=
1.73827u
59
0.742110u
58
+ ··· 17.5597u 5.34256
2.48038u
59
2.38623u
58
+ ··· + 1.86601u 1.73827
(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 = 1.14561
a = 0.147831
b = 1.27084
1.61104 7.22734
u = 1.073448 0.813202I
a = 0.295810 + 0.557625I
b = 1.310499 0.080285I
0.72651 + 3.69060I 5.47549 5.38384I
u = 1.073448 + 0.813202I
a = 0.295810 0.557625I
b = 1.310499 + 0.080285I
0.72651 3.69060I 5.47549 + 5.38384I
u = 0.949109 0.482501I
a = 0.052097 0.676629I
b = 0.058164 + 0.491656I
4.80170 + 1.71569I 12.12772 3.69255I
u = 0.949109 + 0.482501I
a = 0.052097 + 0.676629I
b = 0.058164 0.491656I
4.80170 1.71569I 12.12772 + 3.69255I
u = 0.728287 1.101947I
a = 0.213717 + 0.670278I
b = 0.224433 0.448869I
2.95363 + 4.39756I 7.00202 8.96362I
u = 0.728287 + 1.101947I
a = 0.213717 0.670278I
b = 0.224433 + 0.448869I
2.95363 4.39756I 7.00202 + 8.96362I
u = 0.69338 1.30915I
a = 0.435442 1.071891I
b = 1.389382 + 0.126415I
2.17172 + 6.43280I 1.18055 8.04176I
u = 0.69338 + 1.30915I
a = 0.435442 + 1.071891I
b = 1.389382 0.126415I
2.17172 6.43280I 1.18055 + 8.04176I
u = 0.683823 0.767010I
a = 1.49727 0.71206I
b = 1.349122 + 0.039607I
3.47046 + 2.59110I 5.81433 4.79126I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.683823 + 0.767010I
a = 1.49727 + 0.71206I
b = 1.349122 0.039607I
3.47046 2.59110I 5.81433 + 4.79126I
u = 0.595998 0.876727I
a = 1.40548 0.77186I
b = 0.350200 + 0.158260I
2.11725 + 2.35876I 9.10328 + 7.61988I
u = 0.595998 + 0.876727I
a = 1.40548 + 0.77186I
b = 0.350200 0.158260I
2.11725 2.35876I 9.10328 7.61988I
u = 0.507009 0.872073I
a = 5.07854 13.11452I
b = 1.407843 + 0.014691I
3.27672 + 2.05815I 44.3489 + 118.4627I
u = 0.507009 + 0.872073I
a = 5.07854 + 13.11452I
b = 1.407843 0.014691I
3.27672 2.05815I 44.3489 118.4627I
u = 0.505117 0.952086I
a = 0.698662 0.753926I
b = 0.246546 + 0.282002I
0.19554 + 2.59737I 1.80279 1.62726I
u = 0.505117 + 0.952086I
a = 0.698662 + 0.753926I
b = 0.246546 0.282002I
0.19554 2.59737I 1.80279 + 1.62726I
u = 0.503259 1.119749I
a = 0.98583 + 1.70039I
b = 1.41880 0.09036I
5.60317 + 3.97257I 5.60547 3.32374I
u = 0.503259 + 1.119749I
a = 0.98583 1.70039I
b = 1.41880 + 0.09036I
5.60317 3.97257I 5.60547 + 3.32374I
u = 0.462038
a = 1.93742
b = 0.511763
2.63603 0.0801046
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.431817 0.730337I
a = 0.497496 + 1.129928I
b = 0.026377 0.398328I
0.55804 + 1.39773I 4.97891 5.04482I
u = 0.431817 + 0.730337I
a = 0.497496 1.129928I
b = 0.026377 + 0.398328I
0.55804 1.39773I 4.97891 + 5.04482I
u = 0.287455 0.157082I
a = 1.23091 1.58196I
b = 1.325720 0.012392I
3.09648 + 0.01865I 2.15658 + 0.53019I
u = 0.287455 + 0.157082I
a = 1.23091 + 1.58196I
b = 1.325720 + 0.012392I
3.09648 0.01865I 2.15658 0.53019I
u = 0.095351 1.174259I
a = 0.116749 0.127150I
b = 0.529233 + 0.441086I
1.15016 + 4.52322I 1.58408 7.91740I
u = 0.095351 + 1.174259I
a = 0.116749 + 0.127150I
b = 0.529233 0.441086I
1.15016 4.52322I 1.58408 + 7.91740I
u = 0.002505 1.373771I
a = 0.944353 + 0.196898I
b = 1.49614 0.15819I
7.75326 + 6.77334I 3.88267 5.97766I
u = 0.002505 + 1.373771I
a = 0.944353 0.196898I
b = 1.49614 + 0.15819I
7.75326 6.77334I 3.88267 + 5.97766I
u = 0.020451 0.666218I
a = 0.922185 + 1.016624I
b = 0.019258 0.599596I
0.288784 + 1.376442I 1.36514 4.13021I
u = 0.020451 + 0.666218I
a = 0.922185 1.016624I
b = 0.019258 + 0.599596I
0.288784 1.376442I 1.36514 + 4.13021I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.158901 1.194155I
a = 0.951954 + 0.254959I
b = 1.54271 + 0.14787I
10.59539 + 2.29159I 8.03112 0.82729I
u = 0.158901 + 1.194155I
a = 0.951954 0.254959I
b = 1.54271 0.14787I
10.59539 2.29159I 8.03112 + 0.82729I
u = 0.217249 0.560610I
a = 1.16682 1.09218I
b = 1.201326 0.191717I
2.92701 + 0.02185I 2.76361 1.57896I
u = 0.217249 + 0.560610I
a = 1.16682 + 1.09218I
b = 1.201326 + 0.191717I
2.92701 0.02185I 2.76361 + 1.57896I
u = 0.234074 0.863478I
a = 0.476733 0.372342I
b = 0.911823 0.442516I
2.94476 + 0.12365I 6.35156 2.56893I
u = 0.234074 + 0.863478I
a = 0.476733 + 0.372342I
b = 0.911823 + 0.442516I
2.94476 0.12365I 6.35156 + 2.56893I
u = 0.413007 0.917472I
a = 0.216848 1.189999I
b = 1.72565 0.13500I
4.67108 1.62217I 12.48743 + 0.70918I
u = 0.413007 + 0.917472I
a = 0.216848 + 1.189999I
b = 1.72565 + 0.13500I
4.67108 + 1.62217I 12.48743 0.70918I
u = 0.421287 0.477539I
a = 0.90273 + 1.23587I
b = 0.240498 0.711477I
0.18899 + 1.45187I 1.34936 5.34755I
u = 0.421287 + 0.477539I
a = 0.90273 1.23587I
b = 0.240498 + 0.711477I
0.18899 1.45187I 1.34936 + 5.34755I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.488226 0.968993I
a = 0.24966 2.06773I
b = 1.52138 + 0.44760I
4.06241 3.68110I 7.95874 + 9.64699I
u = 0.488226 + 0.968993I
a = 0.24966 + 2.06773I
b = 1.52138 0.44760I
4.06241 + 3.68110I 7.95874 9.64699I
u = 0.534922 0.997657I
a = 0.72112 1.37572I
b = 0.481557 + 0.943096I
1.19130 5.66306I 2.72432 + 10.76071I
u = 0.534922 + 0.997657I
a = 0.72112 + 1.37572I
b = 0.481557 0.943096I
1.19130 + 5.66306I 2.72432 10.76071I
u = 0.593897 1.112728I
a = 0.29722 + 1.95342I
b = 1.52921 0.32206I
7.70682 10.17216I 4.40393 + 7.43583I
u = 0.593897 + 1.112728I
a = 0.29722 1.95342I
b = 1.52921 + 0.32206I
7.70682 + 10.17216I 4.40393 7.43583I
u = 0.618276 0.995264I
a = 0.675732 0.527141I
b = 0.617210 + 0.869107I
3.47399 6.14744I 2.94126 + 7.00719I
u = 0.618276 + 0.995264I
a = 0.675732 + 0.527141I
b = 0.617210 0.869107I
3.47399 + 6.14744I 2.94126 7.00719I
u = 0.671385 1.084146I
a = 0.56682 + 1.31384I
b = 0.533782 0.834528I
3.66250 11.73974I 2.45717 + 9.07508I
u = 0.671385 + 1.084146I
a = 0.56682 1.31384I
b = 0.533782 + 0.834528I
3.66250 + 11.73974I 2.45717 9.07508I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.682605 1.157142I
a = 0.30554 1.88422I
b = 1.53838 + 0.29681I
3.0641 15.8799I 0.92775 + 8.64946I
u = 0.682605 + 1.157142I
a = 0.30554 + 1.88422I
b = 1.53838 0.29681I
3.0641 + 15.8799I 0.92775 8.64946I
u = 0.683723 0.624273I
a = 0.23665 + 1.63178I
b = 0.698160 0.696499I
4.58804 + 1.10123I 5.38527 0.53488I
u = 0.683723 + 0.624273I
a = 0.23665 1.63178I
b = 0.698160 + 0.696499I
4.58804 1.10123I 5.38527 + 0.53488I
u = 0.787431 0.363451I
a = 1.072749 0.554781I
b = 1.46251 + 0.26342I
5.51717 + 5.00817I 2.18154 3.53465I
u = 0.787431 + 0.363451I
a = 1.072749 + 0.554781I
b = 1.46251 0.26342I
5.51717 5.00817I 2.18154 + 3.53465I
u = 0.858242 0.533803I
a = 0.536983 1.085616I
b = 0.435894 + 0.774361I
5.33401 + 6.06206I 5.25486 4.79805I
u = 0.858242 + 0.533803I
a = 0.536983 + 1.085616I
b = 0.435894 0.774361I
5.33401 6.06206I 5.25486 + 4.79805I
u = 0.971698 0.453967I
a = 0.726756 + 0.554466I
b = 1.49031 0.27633I
0.89788 + 9.86974I 1.35103 5.07402I
u = 0.971698 + 0.453967I
a = 0.726756 0.554466I
b = 1.49031 + 0.27633I
0.89788 9.86974I 1.35103 + 5.07402I
8
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
60
+ u
59
+ ··· 2u + 1)
c
2
(u
60
+ 25u
59
+ ··· + 6u + 1)
c
3
(u
60
+ 3u
59
+ ··· + 4u + 1)
c
5
, c
9
(u
60
+ u
59
+ ··· + 5u
2
+ 1)
c
6
(u
60
+ 13u
59
+ ··· + 46u 1)
c
7
, c
10
, c
11
(u
60
+ 5u
59
+ ··· + 5u
2
+ 1)
c
8
(u
60
+ 17u
59
+ ··· + 288u + 79)
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
60
+ 25y
59
+ ··· + 6y + 1)
c
2
(y
60
+ 21y
59
+ ··· + 62y + 1)
c
3
(y
60
+ 5y
59
+ ··· + 30y + 1)
c
5
(y
60
43y
59
+ ··· + 10y + 1)
c
6
(y
60
+ 109y
59
+ ··· 2526y + 1)
c
7
(y
60
59y
59
+ ··· + 10y + 1)
c
8
(y
60
+ 73y
59
+ ··· 15478y + 6241)
c
9
(y
60
43y
59
+ ··· + 10y + 1)
c
10
(y
60
59y
59
+ ··· + 10y + 1)
c
11
(y
60
59y
59
+ ··· + 10y + 1)
10