11a
265
(K11a
265
)
1
Arc Sequences
8 5 1 2 11 10 4 3 7 6 9
Solving Sequence
5,11 3,6
2 4 10 7 9 1 8
c
5
c
2
c
4
c
10
c
6
c
9
c
11
c
8
c
1
, c
3
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
54
u
53
+ ··· 9u + 1, 6.09255 × 10
71
u
53
1.39631 × 10
73
u
52
+ ··· + 1.77598 × 10
73
b + 1.65529 × 10
73
,
1.00796 × 10
73
u
53
1.32786 × 10
73
u
52
+ ··· + 1.77598 × 10
73
a + 2.35435 × 10
73
i
There are 1 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
= hu
54
u
53
+· · ·9u+1, 6.09×10
71
u
53
1.40×10
73
u
52
+· · ·+1.78×10
73
b+
1.66 × 10
73
, 1.01 × 10
73
u
53
1.33 × 10
73
u
52
+ · · · + 1.78 × 10
73
a + 2.35 × 10
73
i
(i) Arc colorings
a
5
=
0
u
a
11
=
0.567551u
53
+ 0.747677u
52
+ ··· 8.95397u 1.32566
0.0343052u
53
+ 0.786219u
52
+ ··· + 9.99021u 0.932039
a
3
=
1
0
a
6
=
0.682368u
53
+ 0.619917u
52
+ ··· 19.2178u + 2.17351
0.491209u
53
+ 0.0361508u
52
+ ··· + 5.62970u 0.558236
a
2
=
1
u
2
a
4
=
u
u
3
+ u
a
10
=
1.37168u
53
+ 1.16568u
52
+ ··· 23.2023u + 1.03915
0.394076u
53
+ 0.422230u
52
+ ··· + 9.13010u 0.938664
a
7
=
2.26595u
53
+ 2.33871u
52
+ ··· 53.9156u + 6.71070
0.849313u
53
0.383246u
52
+ ··· + 10.6244u 1.19224
a
9
=
2.29308u
53
+ 2.56863u
52
+ ··· 59.5783u + 7.73157
0.863733u
53
0.534066u
52
+ ··· + 10.1213u 1.37278
a
1
=
2.07405u
53
+ 0.702377u
52
+ ··· 13.1962u + 3.41796
0.573527u
53
+ 0.300928u
52
+ ··· + 4.97748u 0.702377
a
8
=
1.42935u
53
+ 2.03456u
52
+ ··· 49.4570u + 6.35880
0.863733u
53
0.534066u
52
+ ··· + 10.1213u 1.37278
a
8
=
1.42935u
53
+ 2.03456u
52
+ ··· 49.4570u + 6.35880
0.863733u
53
0.534066u
52
+ ··· + 10.1213u 1.37278
(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 = 1.61693 0.33312I
a = 0.246422 0.929244I
b = 0.969597 + 0.926926I
11.59780 2.07370I 8.52151 + 0.51627I
u = 1.61693 + 0.33312I
a = 0.246422 + 0.929244I
b = 0.969597 0.926926I
11.59780 + 2.07370I 8.52151 0.51627I
u = 1.45206 0.27843I
a = 0.275850 0.385067I
b = 0.829176 + 0.207966I
4.01735 0.63222I 7.39930 + 2.66782I
u = 1.45206 + 0.27843I
a = 0.275850 + 0.385067I
b = 0.829176 0.207966I
4.01735 + 0.63222I 7.39930 2.66782I
u = 1.37925 0.76394I
a = 0.422269 + 0.915254I
b = 2.25575 1.54751I
10.82654 + 6.06392I 6.84257 6.56103I
u = 1.37925 + 0.76394I
a = 0.422269 0.915254I
b = 2.25575 + 1.54751I
10.82654 6.06392I 6.84257 + 6.56103I
u = 1.27547 0.67924I
a = 0.043477 + 0.524015I
b = 1.52931 1.25673I
3.27194 + 4.12688I 4.58912 9.06876I
u = 1.27547 + 0.67924I
a = 0.043477 0.524015I
b = 1.52931 + 1.25673I
3.27194 4.12688I 4.58912 + 9.06876I
u = 1.115104 0.467666I
a = 0.335063 0.002117I
b = 0.770395 0.786571I
2.00449 + 1.26243I 0.21146 2.28876I
u = 1.115104 + 0.467666I
a = 0.335063 + 0.002117I
b = 0.770395 + 0.786571I
2.00449 1.26243I 0.21146 + 2.28876I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.076367 0.115334I
a = 0.05562 1.44950I
b = 3.42619 + 3.71195I
8.80102 + 3.53795I 9.01900 + 9.64293I
u = 1.076367 + 0.115334I
a = 0.05562 + 1.44950I
b = 3.42619 3.71195I
8.80102 3.53795I 9.01900 9.64293I
u = 1.007949 0.089434I
a = 0.338133 0.584816I
b = 1.80869 + 2.51021I
1.56763 + 1.75278I 6.2825 + 17.5292I
u = 1.007949 + 0.089434I
a = 0.338133 + 0.584816I
b = 1.80869 2.51021I
1.56763 1.75278I 6.2825 17.5292I
u = 0.859276 0.037944I
a = 0.424058 + 0.465277I
b = 0.17774 + 1.53935I
1.12331 0.98698I 7.38443 + 9.46034I
u = 0.859276 + 0.037944I
a = 0.424058 0.465277I
b = 0.17774 1.53935I
1.12331 + 0.98698I 7.38443 9.46034I
u = 0.680312 0.208791I
a = 0.74403 + 2.04893I
b = 1.78311 + 1.09474I
7.92145 2.31500I 3.15419 + 5.84861I
u = 0.680312 + 0.208791I
a = 0.74403 2.04893I
b = 1.78311 1.09474I
7.92145 + 2.31500I 3.15419 5.84861I
u = 0.598688 0.933262I
a = 1.213205 0.725994I
b = 0.325036 0.901115I
8.64965 + 1.05444I 3.74303 4.22009I
u = 0.598688 + 0.933262I
a = 1.213205 + 0.725994I
b = 0.325036 + 0.901115I
8.64965 1.05444I 3.74303 + 4.22009I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.303084 0.550488I
a = 0.868388 0.477910I
b = 0.000051 0.622920I
1.31595 + 1.53064I 2.46645 4.42217I
u = 0.303084 + 0.550488I
a = 0.868388 + 0.477910I
b = 0.000051 + 0.622920I
1.31595 1.53064I 2.46645 + 4.42217I
u = 0.029668 1.223889I
a = 1.291012 + 0.087802I
b = 0.74374 1.29158I
5.94961 + 8.61448I 0.41279 7.33231I
u = 0.029668 + 1.223889I
a = 1.291012 0.087802I
b = 0.74374 + 1.29158I
5.94961 8.61448I 0.41279 + 7.33231I
u = 0.075005 0.372522I
a = 4.07694 + 0.45257I
b = 0.582432 0.249666I
6.29079 + 4.01270I 0.519880 1.012448I
u = 0.075005 + 0.372522I
a = 4.07694 0.45257I
b = 0.582432 + 0.249666I
6.29079 4.01270I 0.519880 + 1.012448I
u = 0.075767 1.121543I
a = 0.584689 + 0.412159I
b = 0.237043 1.371209I
1.47018 + 6.23173I 3.03340 8.93677I
u = 0.075767 + 1.121543I
a = 0.584689 0.412159I
b = 0.237043 + 1.371209I
1.47018 6.23173I 3.03340 + 8.93677I
u = 0.147777 0.982361I
a = 0.212428 + 0.583555I
b = 0.297164 1.256190I
2.42907 + 2.60276I 6.59954 2.27110I
u = 0.147777 + 0.982361I
a = 0.212428 0.583555I
b = 0.297164 + 1.256190I
2.42907 2.60276I 6.59954 + 2.27110I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.168286 0.172227I
a = 2.99999 + 0.03054I
b = 0.184073 + 0.000485I
0.70487 + 1.75962I 4.58587 3.17454I
u = 0.168286 + 0.172227I
a = 2.99999 0.03054I
b = 0.184073 0.000485I
0.70487 1.75962I 4.58587 + 3.17454I
u = 0.401538 0.827597I
a = 1.39145 + 0.73304I
b = 1.20206 0.82178I
2.95011 + 0.80061I 3.17303 1.15726I
u = 0.401538 + 0.827597I
a = 1.39145 0.73304I
b = 1.20206 + 0.82178I
2.95011 0.80061I 3.17303 + 1.15726I
u = 0.410909
a = 1.20855
b = 0.165396
1.13235 10.5020
u = 0.678255
a = 0.907576
b = 0.0949577
1.10777 11.9582
u = 0.821444 0.155536I
a = 0.692794 0.653739I
b = 0.669044 + 0.223900I
0.67521 2.21346I 9.82154 + 8.24478I
u = 0.821444 + 0.155536I
a = 0.692794 + 0.653739I
b = 0.669044 0.223900I
0.67521 + 2.21346I 9.82154 8.24478I
u = 0.966095 0.226943I
a = 0.358251 0.878007I
b = 0.747667 + 0.909709I
1.00016 3.95703I 2.90323 + 11.79776I
u = 0.966095 + 0.226943I
a = 0.358251 + 0.878007I
b = 0.747667 0.909709I
1.00016 + 3.95703I 2.90323 11.79776I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.010926 0.382969I
a = 0.317480 1.225270I
b = 0.784602 + 0.194260I
4.94656 5.25128I 0.05356 + 7.68308I
u = 1.010926 + 0.382969I
a = 0.317480 + 1.225270I
b = 0.784602 0.194260I
4.94656 + 5.25128I 0.05356 7.68308I
u = 1.101845 0.268114I
a = 0.19289 1.42350I
b = 1.44271 + 1.39482I
9.06286 6.69333I 3.21521 + 8.50034I
u = 1.101845 + 0.268114I
a = 0.19289 + 1.42350I
b = 1.44271 1.39482I
9.06286 + 6.69333I 3.21521 8.50034I
u = 1.215544 0.399024I
a = 0.383523 0.734839I
b = 0.031022 + 0.203305I
5.26922 5.01222I 3.06002 + 4.58452I
u = 1.215544 + 0.399024I
a = 0.383523 + 0.734839I
b = 0.031022 0.203305I
5.26922 + 5.01222I 3.06002 4.58452I
u = 1.271027 0.528070I
a = 0.507076 + 0.028077I
b = 0.694501 0.916473I
1.09662 8.00461I 2.60038 + 4.65248I
u = 1.271027 + 0.528070I
a = 0.507076 0.028077I
b = 0.694501 + 0.916473I
1.09662 + 8.00461I 2.60038 4.65248I
u = 1.32836 0.56041I
a = 0.172106 + 0.594825I
b = 1.49022 1.37188I
2.46124 12.12318I 0.08589 + 9.41589I
u = 1.32836 + 0.56041I
a = 0.172106 0.594825I
b = 1.49022 + 1.37188I
2.46124 + 12.12318I 0.08589 9.41589I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.330788 0.280176I
a = 0.261363 1.190792I
b = 0.03723 + 1.51867I
14.5155 4.5567I 6.41745 + 4.39333I
u = 1.330788 + 0.280176I
a = 0.261363 + 1.190792I
b = 0.03723 1.51867I
14.5155 + 4.5567I 6.41745 4.39333I
u = 1.37583 0.57768I
a = 0.310678 + 1.033218I
b = 2.32610 1.64046I
10.1949 14.8555I 2.74156 + 8.00870I
u = 1.37583 + 0.57768I
a = 0.310678 1.033218I
b = 2.32610 + 1.64046I
10.1949 + 14.8555I 2.74156 8.00870I
8
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
54
+ 3u
53
+ ··· + u + 1)
c
2
, c
4
(u
54
+ u
53
+ ··· + 9u + 1)
c
3
(u
54
+ 9u
53
+ ··· + u + 1)
c
5
, c
6
, c
9
c
10
(u
54
+ u
53
+ ··· + 3u + 1)
c
7
(u
54
+ 3u
53
+ ··· 15u 1)
c
8
(u
54
+ u
53
+ ··· + 39u + 7)
c
11
(u
54
+ 13u
53
+ ··· + 657u + 99)
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
54
+ 9y
53
+ ··· + 3y + 1)
c
2
, c
4
(y
54
35y
53
+ ··· 9y + 1)
c
3
(y
54
3y
53
+ ··· 9y + 1)
c
5
, c
6
, c
9
c
10
(y
54
+ 61y
53
+ ··· + 3y + 1)
c
7
(y
54
55y
53
+ ··· 413y + 1)
c
8
(y
54
43y
53
+ ··· 317y + 49)
c
11
(y
54
+ 5y
53
+ ··· + 103347y + 9801)
10