11n
120
(K11n
120
)
1
Arc Sequences
5 1 8 11 2 9 10 5 1 4 7
Solving Sequence
4,11 5,7
1 2 6 10 8 3 9
c
4
c
11
c
1
c
5
c
10
c
7
c
3
c
9
c
2
, c
6
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
10
13u
8
+ 10u
7
+ 43u
6
45u
5
44u
4
+ 73u
3
24u
2
u + 1,
179541u
9
75682u
8
+ ··· + 139537b + 621157,
614158u
9
250802u
8
+ ··· + 139537a + 1323438i
I
u
2
= hu
33
5u
32
+ ··· 19u 1,
2.65214 × 10
83
u
32
+ 1.32811 × 10
84
u
31
+ ··· + 1.38940 × 10
84
b + 1.50162 × 10
84
,
2.37525 × 10
84
u
32
1.21088 × 10
85
u
31
+ ··· + 1.38940 × 10
84
a 1.82592 × 10
85
i
There are 2 irreducible components with 43 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
10
13u
8
+ · · · u + 1, 1.80 × 10
5
u
9
7.57 × 10
4
u
8
+ · · · + 1.40 ×
10
5
b +6.21 ×10
5
, 6.14×10
5
u
9
2.51× 10
5
u
8
+· · ·+ 1.40 ×10
5
a +1.32 ×10
6
i
(i) Arc colorings
a
4
=
1
0
a
11
=
4.40140u
9
+ 1.79739u
8
+ ··· 18.0877u 9.48450
1.28669u
9
+ 0.542379u
8
+ ··· 1.93038u 4.45156
a
5
=
2.43611u
9
0.966152u
8
+ ··· + 7.12908u + 9.98703
0.205809u
9
+ 0.0708916u
8
+ ··· + 8.95952u 0.734981
a
7
=
0
u
a
1
=
4.40140u
9
+ 1.79739u
8
+ ··· 18.0877u 9.48450
0.449229u
9
+ 0.0666562u
8
+ ··· + 0.673628u 2.65417
a
2
=
1.98782u
9
+ 0.714341u
8
+ ··· 21.2704u + 2.33687
0.161692u
9
+ 0.0417667u
8
+ ··· + 17.0663u 4.01855
a
6
=
3.68179u
9
1.05543u
8
+ ··· + 47.0709u + 0.712327
0.529171u
9
0.134918u
8
+ ··· 26.8296u + 5.48956
a
10
=
3.11471u
9
+ 1.25501u
8
+ ··· 16.1573u 5.03294
1.28669u
9
+ 0.542379u
8
+ ··· 1.93038u 4.45156
a
8
=
3.54763u
9
+ 1.45459u
8
+ ··· 9.24378u 10.3535
1.03704u
9
+ 0.388800u
8
+ ··· 6.49170u 2.23030
a
3
=
0.183270u
9
0.0460021u
8
+ ··· 1.35222u + 3.09936
0.205530u
9
0.182704u
8
+ ··· + 2.54548u 0.0623132
a
9
=
4.11471u
9
+ 1.25501u
8
+ ··· 40.1573u 6.03294
0.187334u
9
+ 0.359109u
8
+ ··· + 14.7173u 4.70442
a
9
=
4.11471u
9
+ 1.25501u
8
+ ··· 40.1573u 6.03294
0.187334u
9
+ 0.359109u
8
+ ··· + 14.7173u 4.70442
(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 = 3.40424
a = 0.283911
b = 0.786277
10.1434 1.94616
u = 1.57947 0.43499I
a = 0.675295 0 .018787I
b = 1.271102 + 0 .355619I
3.01759 + 3.09606I 0.30900 2.81871I
u = 1.57947 + 0 .43499I
a = 0.675295 + 0 .018787I
b = 1.271102 0 .355619I
3.01759 3.09606I 0.30900 + 2.81871I
u = 0.176080
a = 1.81541
b = 1.71168
7.30701 11.0744
u = 0.371055 0.043809I
a = 1.77099 1.96426I
b = 0.025709 0 .694144I
1.07490 2.24450I 6.05768 + 4.70336I
u = 0.371055 + 0.043809I
a = 1.77099 + 1.96426I
b = 0.025709 + 0 .694144I
1.07490 + 2.24450I 6.05768 4.70336I
u = 1.008359 0.248536I
a = 0.829484 0 .885057I
b = 0.683925 0 .196443I
0.68101 1.88435I 5.02064 + 2.89096I
u = 1.008359 + 0.248536I
a = 0.829484 + 0 .885057I
b = 0.683925 + 0 .196443I
0.68101 + 1.88435I 5.02064 2.89096I
u = 1.99022 0.40893I
a = 0.541513 + 0 .346176I
b = 1.231759 + 0.478004I
2.52872 6.76916I 1.54858 + 6.21981I
u = 1.99022 + 0.40893I
a = 0.541513 0.346176I
b = 1.231759 0.478004I
2.52872 + 6.76916I 1.54858 6.21981I
3
II. I
u
2
=
hu
33
5u
32
+· · ·19u1, 2.65×10
83
u
32
+1.33×10
84
u
31
+· · ·+1.39×10
84
b+
1.50 × 10
84
, 2.38 × 10
84
u
32
1.21 × 10
85
u
31
+ · · · + 1.39 × 10
84
a 1.83 × 10
85
i
(i) Arc colorings
a
4
=
1
0
a
11
=
1.70955u
32
+ 8.71514u
31
+ ··· + 324.748u + 13.1418
0.190883u
32
0.955884u
31
+ ··· 26.0461u 1.08077
a
5
=
0.798984u
32
3.83575u
31
+ ··· 196.710u 26.6507
0.0921663u
32
+ 0.469164u
31
+ ··· + 8.41859u + 1.67856
a
7
=
0
u
a
1
=
1.70955u
32
+ 8.71514u
31
+ ··· + 324.748u + 13.1418
0.221124u
32
1.10293u
31
+ ··· 27.5173u 1.24817
a
2
=
2.96586u
32
+ 14.8625u
31
+ ··· + 567.293u + 58.1278
0.193644u
32
0.950037u
31
+ ··· 44.2975u 4.64469
a
6
=
3.89877u
32
+ 19.4076u
31
+ ··· + 783.687u + 83.9057
0.312147u
32
1.54651u
31
+ ··· 54.0211u 6.32109
a
10
=
1.90043u
32
+ 9.67103u
31
+ ··· + 350.794u + 14.2226
0.190883u
32
0.955884u
31
+ ··· 26.0461u 1.08077
a
8
=
1.43006u
32
7.36426u
31
+ ··· 172.434u + 14.0494
0.150832u
32
+ 0.767540u
31
+ ··· + 13.3974u 0.891150
a
3
=
4.26838u
32
21.7803u
31
+ ··· 654.631u 5.86607
0.258904u
32
+ 1.30757u
31
+ ··· + 51.2227u + 0.906668
a
9
=
2.13043u
32
10.6666u
31
+ ··· 406.356u 39.8806
0.199069u
32
+ 0.968267u
31
+ ··· + 33.4293u + 3.29812
a
9
=
2.13043u
32
10.6666u
31
+ ··· 406.356u 39.8806
0.199069u
32
+ 0.968267u
31
+ ··· + 33.4293u + 3.29812
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.32730 0.93403I
a = 0.619334 + 0 .131105I
b = 0.969438 + 0.294889I
0.20621 + 3 .24394I 3.32595 5.32169I
u = 2.32730 + 0 .93403I
a = 0.619334 0.131105I
b = 0.969438 0.294889I
0.20621 3.24394I 3.32595 + 5.32169I
u = 1.73147 0.70610I
a = 0.763258 0.294747I
b = 1.238854 0.551689I
0.59436 + 7 .58146I 4.74170 6.03486I
u = 1.73147 + 0 .70610I
a = 0.763258 + 0 .294747I
b = 1.238854 + 0 .551689I
0.59436 7.58146I 4.74170 + 6.03486I
u = 1.37832 0.86619I
a = 1.133890 0.288045I
b = 1.024181 + 0 .444622I
9.28497 3.68135I 5.78436 + 4.49683I
u = 1.37832 + 0 .86619I
a = 1.133890 + 0 .288045I
b = 1.024181 0.444622I
9.28497 + 3 .68135I 5.78436 4.49683I
u = 1.173124 0.374770I
a = 0.437666 + 0 .245880I
b = 1.29329 + 0.58740I
1.69477 + 3 .95490I 4.65099 5.53433I
u = 1.173124 + 0 .374770I
a = 0.437666 0.245880I
b = 1.29329 0.58740I
1.69477 3.95490I 4.65099 + 5.53433I
u = 0.954937 0.484835I
a = 0.020032 0.256360I
b = 0.581482 0.277100I
1.46450 0.11042I 7.61890 0.69071I
u = 0.954937 + 0 .484835I
a = 0.020032 + 0 .256360I
b = 0.581482 + 0 .277100I
1.46450 + 0 .11042I 7.61890 + 0.69071I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.412855 0.469269I
a = 0.91714 + 1 .29576I
b = 0.842720 + 0 .296682I
0.92676 3.03549I 5.42554 + 8.81658I
u = 0.412855 + 0 .469269I
a = 0.91714 1 .29576I
b = 0.842720 0.296682I
0.92676 + 3.03549I 5.42554 8.81658I
u = 0.306953 0.613517I
a = 0.825429 + 0 .154285I
b = 1.78465 + 0 .49161I
7.19656 + 0.44528I 9.6672 13.0657I
u = 0.306953 + 0 .613517I
a = 0.825429 0.154285I
b = 1.78465 0.49161I
7.19656 0.44528I 9.6672 + 13.0657I
u = 0.0560931 0.0591473I
a = 3.0229 15.9562I
b = 0.175040 + 1 .144642I
13.1119 6.5830I 7.26190 + 3 .76102I
u = 0.0560931 + 0 .0591473I
a = 3.0229 + 15 .9562I
b = 0.175040 1 .144642I
13.1119 + 6 .5830I 7.26190 3.76102I
u = 0.008400 0.317446I
a = 2.21628 + 1 .02309I
b = 0.144587 0.528173I
0.08685 1.51365I 1.21011 + 3.17114I
u = 0.008400 + 0 .317446I
a = 2.21628 1 .02309I
b = 0.144587 + 0.528173I
0.08685 + 1.51365I 1.21011 3.17114I
u = 0.035519 0.290026I
a = 2.75946 1.26209I
b = 0.151070 1.035001I
2.74722 2.04706I 9.49316 + 3.23628I
u = 0.035519 + 0.290026I
a = 2.75946 + 1 .26209I
b = 0.151070 + 1 .035001I
2.74722 + 2.04706I 9.49316 3.23628I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.306100 0.581557I
a = 2.29801 0.10820I
b = 0.735686 + 0.204903 I
0.659531 0.792248I 4.14798 2.75904I
u = 0.306100 + 0. 581557I
a = 2.29801 + 0.10820I
b = 0.735686 0.204903 I
0.659531 + 0.792248I 4.14798 + 2 .75904I
u = 1.40077 0.28452I
a = 0.776881 0.221843I
b = 1.159344 0.332137 I
2.50185 1.42660I 0.894808 0.237180I
u = 1.40077 + 0 .28452I
a = 0.776881 + 0.221843I
b = 1.159344 + 0.332137 I
2.50185 + 1.42660I 0.894808 + 0 .237180I
u = 1.53281 1.18148I
a = 0.131722 + 0 .501517I
b = 1.048955 + 0.366373 I
8.66188 + 2.58631I 6.35568 5.14908I
u = 1.53281 + 1 .18148I
a = 0.131722 0.501517I
b = 1.048955 0.366373 I
8.66188 2.58631I 6.35568 + 5 .14908I
u = 1.91488 0.37791I
a = 0.713612 + 0 .046137I
b = 0.325848 + 0.301516I
11.16572 + 0 .07120I 8.48040 + 1 .16675I
u = 1.91488 + 0 .37791I
a = 0.713612 0.046137I
b = 0.325848 0.301516I
11.16572 0.07120I 8.48040 1.16675I
u = 2.02346 0.67132I
a = 0.471883 + 0 .146646I
b = 1.192389 + 0.377520I
3.57986 4.96677I 0.77431 + 5.63197I
u = 2.02346 + 0 .67132I
a = 0.471883 0.146646I
b = 1.192389 0.377520I
3.57986 + 4.96677I 0.77431 5.63197I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.14398 0.94653I
a = 0.633825 0.281551I
b = 1.30010 0.62038I
9.6038 12.7751I 4.29331 + 6.17524I
u = 2.14398 + 0.94653I
a = 0.633825 + 0.281551I
b = 1.30010 + 0. 62038I
9.6038 + 12 .7751I 4.29331 6.17524I
u = 2.98387
a = 0.113927
b = 0.629512
10.7048 13.8447
8
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
10
u
9
5u
8
+ 6u
7
+ 6u
6
9u
5
4u
4
+ 6u
3
+ 2u
2
2u 1)
(u
33
+ 4u
32
+ ··· + 20u 1)
c
2
(u
10
+ 11u
9
+ ··· + 8u + 1)(u
33
+ 48u
32
+ ··· + 88u + 1)
c
3
(u
10
2u
8
3u
7
u
5
6u
4
9u
3
6u
2
2u 1)
(u
33
+ u
32
+ ··· + 864u + 691)
c
4
, c
10
(u
10
+ u
9
4u
8
3u
7
+ 6u
6
+ 3u
5
3u
4
+ u
3
u
2
u + 1)
(u
33
11u
31
+ ··· u 1)
c
6
(u
10
+ 7u
9
+ 20u
8
+ 33u
7
+ 37u
6
+ 31u
5
+ 21u
4
+ 12u
3
+ 7u
2
+ 3u + 1)
(u
33
6u
32
+ ··· 2315u 1751)
c
7
(u
10
3u
9
+ 2u
8
+ 5u
7
12u
6
+ 12u
5
6u
4
+ u
3
+ 2u
2
2u + 1)
(u
33
+ 10u
32
+ ··· + 108u + 11)
c
8
(u
10
+ u
9
5u
8
+ 6u
7
+ 4u
6
21u
5
+ 31u
4
28u
3
+ 17u
2
6u + 1)
(u
33
32u
31
+ ··· + 138u 193)
c
9
(u
10
+ 3u
9
u
8
u
7
+ 3u
6
3u
4
u
3
u 1)
(u
33
+ 8u
32
+ ··· + 8781u + 1799)
c
11
(u
10
u
9
+ ··· + 3u 1)(u
33
+ 2u
32
+ ··· + 5u 1)
9
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
10
11y
9
+ ··· 8y + 1)(y
33
48y
32
+ ··· + 88y 1)
c
2
(y
10
23y
9
+ ··· + 8y + 1)(y
33
124y
32
+ ··· 3924y 1)
c
3
(y
10
4y
9
+ 4y
8
21y
7
+ 6y
6
33y
5
+ 10y
4
13y
3
+ 12y
2
+ 8y + 1)
(y
33
21y
32
+ ··· + 2800148y 477481)
c
4
, c
10
(y
10
9y
9
+ 34y
8
69y
7
+ 74y
6
27y
5
23y
4
+ 23y
3
3y
2
3y + 1)
(y
33
22y
32
+ ··· + 11y 1)
c
6
(y
10
9y
9
+ 12y
8
y
7
+ 9y
6
+ 41y
5
+ 57y
4
+ 38y
3
+ 19y
2
+ 5y + 1)
(y
33
58y
32
+ ··· + 8486511y 3066001)
c
7
(y
10
5y
9
+ 10y
8
13y
7
+ 10y
6
12y
5
12y
4
y
3
4y
2
+ 1)
(y
33
+ 2y
32
+ ··· + 48y 121)
c
8
(y
10
11y
9
+ ··· 2y + 1)(y
33
64y
32
+ ··· 45418y 37249)
c
9
(y
10
11y
9
+ 13y
8
13y
7
+ 21y
6
16y
5
+ 9y
4
7y
3
+ 4y
2
y + 1)
(y
33
36y
32
+ ··· + 44853489y 3236401)
c
11
(y
10
y
9
+ 4y
8
7y
7
+ 9y
6
16y
5
+ 21y
4
13y
3
+ 13y
2
11y + 1)
(y
33
+ 2y
32
+ ··· 17y 1)
10