11n
150
(K11n
150
)
1
Arc Sequences
9 8 1 2 3 1 11 5 4 8 7
Solving Sequence
2,9 1,5
4 10 3 6 8 11 7
c
1
c
4
c
9
c
3
c
5
c
8
c
10
c
7
c
2
, c
6
, c
11
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hu
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 10u
5
+ 3u
4
+ 2u
3
+ 2u
2
1, u
7
3u
6
4u
5
+ 2u
3
+ u
2
+ b u + 1,
u
8
+ 5u
7
+ 11u
6
+ 12u
5
+ 6u
4
+ 3u
3
+ 4u
2
+ a + 3u 1i
I
u
2
= hb
24
+ 3b
23
+ ··· + 12b + 5,
3.53630 × 10
20
b
23
9.25407 × 10
20
b
22
+ ··· + 1.64218 × 10
21
a 4.81048 × 10
21
,
2.79170 × 10
22
u + 5.00327 × 10
21
b
23
+ ··· + 1.19158 × 10
22
b + 1.40620 × 10
22
i
I
u
3
= hu
22
14u
21
+ ··· 11u + 2, 88151965u
21
+ 1158772892u
20
+ ··· + 77493574a 15339787,
37677309u
21
521416910u
20
+ ··· + 38746787b 88151965i
There are 3 irreducible components with 55 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
9
+ 5u
8
+ · · · + 2u
2
1, u
7
3u
6
4u
5
+ 2u
3
+ u
2
+ b u +
1, u
8
+ 5u
7
+ · · · + a 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
u
8
5u
7
11u
6
12u
5
6u
4
3u
3
4u
2
3u + 1
u
7
+ 3u
6
+ 4u
5
2u
3
u
2
+ u 1
a
1
=
u
7
+ 4u
6
+ 8u
5
+ 7u
4
+ 3u
3
+ 2u + 1
u
8
+ 4u
7
+ 8u
6
+ 7u
5
+ 3u
4
+ 2u
2
a
5
=
0
u
a
4
=
u
u
a
10
=
u
3
2u
2
2u
u
8
4u
7
8u
6
8u
5
6u
4
4u
3
3u
2
a
3
=
u
8
+ 5u
7
+ 12u
6
+ 15u
5
+ 10u
4
+ 3u
3
+ 2u
2
+ 2u + 1
u + 1
a
6
=
u
8
5u
7
12u
6
15u
5
10u
4
3u
3
2u
2
3u 2
u
2
u 1
a
8
=
u
8
5u
7
11u
6
12u
5
6u
4
3u
3
4u
2
3u + 1
u
8
+ 4u
7
+ 7u
6
+ 4u
5
2u
4
3u
3
1
a
11
=
2u
8
+ 8u
7
+ 16u
6
+ 15u
5
+ 9u
4
+ 4u
3
+ 4u
2
u 1
u
8
3u
7
4u
6
+ u
4
u
3
3u
2
+ u
a
7
=
u
8
+ 4u
7
+ 7u
6
+ 4u
5
2u
4
2u
3
+ 2u
2
+ u 3
2u
8
9u
7
19u
6
19u
5
8u
4
u
3
4u
2
3u + 2
a
7
=
u
8
+ 4u
7
+ 7u
6
+ 4u
5
2u
4
2u
3
+ 2u
2
+ u 3
2u
8
9u
7
19u
6
19u
5
8u
4
u
3
4u
2
3u + 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 = 1.28853 1.25362I
a = 0.486498 + 0.062040I
b = 0.549093 0.689826I
3.87432 + 3.77454I 0.80820 6.90291I
u = 1.28853 + 1.25362I
a = 0.486498 0.062040I
b = 0.549093 + 0.689826I
3.87432 3.77454I 0.80820 + 6.90291I
u = 0.911691 0.879233I
a = 0.839466 + 0.026813I
b = 0.788909 + 0.713641I
1.14384 + 3.68908I 0.51130 5.82682I
u = 0.911691 + 0.879233I
a = 0.839466 0.026813I
b = 0.788909 0.713641I
1.14384 3.68908I 0.51130 + 5.82682I
u = 0.851457 0.480952I
a = 1.43071 + 0.17460I
b = 1.134209 0.836770I
8.14041 + 4.21823I 7.07132 5.34400I
u = 0.851457 + 0.480952I
a = 1.43071 0.17460I
b = 1.134209 + 0.836770I
8.14041 4.21823I 7.07132 + 5.34400I
u = 0.331044 0.589474I
a = 0.366090 + 1.170001I
b = 0.810876 + 0.171521I
0.89563 + 5.00672I 4.18305 4.27017I
u = 0.331044 + 0.589474I
a = 0.366090 1.170001I
b = 0.810876 0.171521I
0.89563 5.00672I 4.18305 + 4.27017I
u = 0.441270
a = 1.88766
b = 0.832966
4.78668 8.18274
3
II.
I
u
2
= hb
24
+ 3b
23
+ · · · + 12b + 5, 3.54 × 10
20
b
23
9.25 × 10
20
b
22
+ · · · + 1.64 ×
10
21
a4.81×10
21
, 2.79×10
22
u+5.00×10
21
b
23
+· · ·+1.19×10
22
b+1.41×10
22
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.215342b
23
+ 0.563524b
22
+ ··· + 7 .62654b + 2.92933
b
a
1
=
0.0825015b
23
0.253218b
22
+ ··· + 0 .345227b 0.0767096
b
2
a
5
=
0
0.179219b
23
0.461595b
22
+ ··· 0.426830b 0.503708
a
4
=
0.179219b
23
+ 0.461595b
22
+ ··· + 0.426830b + 0.503708
0.179219b
23
0.461595b
22
+ ··· 0.426830b 0.503708
a
10
=
0.269067b
23
+ 0.665576b
22
+ ··· + 9.13680b + 3.14888
0.0537251b
23
0.102051b
22
+ ··· 0.510264b 0.219554
a
3
=
0.261721b
23
+ 0.714813b
22
+ ··· + 0 .0816030b + 0.580418
0.134882b
23
0.399341b
22
+ ··· 0.635751b 0.605272
a
6
=
0.435517b
23
1.17100b
22
+ ··· 1.02540b 1.02216
0.0462945b
23
+ 0.232150b
22
+ ··· + 2.36988b + 0.676010
a
8
=
0.215342b
23
+ 0.563524b
22
+ ··· + 7 .62654b + 2.92933
0.0346225b
23
+ 0.0108049b
22
+ ··· 0.0662955b + 0.103181
a
11
=
0.116429b
23
+ 0.416899b
22
+ ··· + 1 .91060b + 1.14303
0.249300b
23
0.574205b
22
+ ··· 1.42171b 1.13889
a
7
=
0.267508b
23
0.765077b
22
+ ··· 0.900997b 0.524498
0.00578764b
23
+ 0.0502643b
22
+ ··· + 0.819394b 0.0559191
a
7
=
0.267508b
23
0.765077b
22
+ ··· 0.900997b 0.524498
0.00578764b
23
+ 0.0502643b
22
+ ··· + 0.819394b 0.0559191
(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 = 0.492148 0.450600I
a = 1.225554 0.099792I
b = 1.63975 0.95928I
0.39191 6.22910I 3.95991 + 11.28166I
u = 0.492148 + 0 .450600I
a = 1.225554 + 0 .099792I
b = 1.63975 + 0.95928I
0.39191 + 6.22910I 3.95991 11.28166I
u = 0.096849 0.815314I
a = 0.795764 + 0 .166864I
b = 1.33607 1.23971I
2.20294 + 4.46082I 11.64801 4.72827I
u = 0.096849 + 0.815314I
a = 0.795764 0.166864I
b = 1.33607 + 1.23971I
2.20294 4.46082I 11.64801 + 4.72827I
u = 0.897414 0.962359I
a = 0.612231 + 0 .043073I
b = 0.846489 0.848272I
0.29247 + 3.33657I 9.82297 1.92424I
u = 0.897414 + 0.962359I
a = 0.612231 0.043073I
b = 0.846489 + 0.848272I
0.29247 3.33657I 9.82297 + 1.92424I
u = 1.216864 0.709160I
a = 0.712113 + 0 .313507I
b = 0.639836 0.220339I
4.52125 + 2.53747I 2.43865 1.71275I
u = 1.216864 + 0.709160I
a = 0.712113 0.313507I
b = 0.639836 + 0.220339I
4.52125 2.53747I 2.43865 + 1.71275I
u = 0.492148 + 0 .450600I
a = 0.84166 2.71978I
b = 0.558187 0.601347I
0.39191 + 6.22910I 3.95991 11.28166I
u = 0.492148 0.450600I
a = 0.84166 + 2 .71978I
b = 0.558187 + 0.601347I
0.39191 6.22910I 3.95991 + 11.28166I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00664 1.21018I
a = 0.718418 0.245360I
b = 0.532206 0.861589I
3.00704 + 5.40399I 1.47702 8.56336I
u = 1.00664 + 1.21018I
a = 0.718418 + 0 .245360I
b = 0.532206 + 0.861589I
3.00704 5.40399I 1.47702 + 8.56336I
u = 0.096849 + 0.815314I
a = 1.69132 1.43781I
b = 0.058978 0.664958I
2.20294 4.46082I 11.64801 + 4.72827I
u = 0.096849 0.815314I
a = 1.69132 + 1.43781I
b = 0.058978 + 0.664958I
2.20294 + 4.46082I 11.64801 4.72827I
u = 0.225615 0.583583I
a = 0.86701 3.12152I
b = 0.313150 0.591965I
5.22591 0.91968I 15.5307 + 7.1820I
u = 0.225615 + 0 .583583I
a = 0.86701 + 3 .12152I
b = 0.313150 + 0 .591965I
5.22591 + 0.91968I 15.5307 7.1820I
u = 0.897414 + 0.962359I
a = 0.910197 0.030826I
b = 0.507973 0.627840I
0.29247 3.33657I 9.82297 + 1.92424I
u = 0.897414 0.962359I
a = 0.910197 + 0.030826I
b = 0.507973 + 0 .627840I
0.29247 + 3.33657I 9.82297 1.92424I
u = 1.216864 + 0.709160I
a = 0.471273 0.093576I
b = 0.644219 0.886498I
4.52125 2.53747I 2.43865 + 1.71275I
u = 1.216864 0.709160I
a = 0.471273 + 0.093576I
b = 0.644219 + 0 .886498I
4.52125 + 2.53747I 2.43865 1.71275I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00664 + 1.21018I
a = 0.637010 + 0.090095I
b = 1.020114 0.622426I
3.00704 5.40399I 1.47702 + 8.56336I
u = 1.00664 1.21018I
a = 0.637010 0.090095I
b = 1.020114 + 0 .622426I
3.00704 + 5.40399I 1.47702 8.56336I
u = 0.225615 + 0 .583583I
a = 1.062943 + 0.125662I
b = 1.62606 1.21023I
5.22591 + 0.91968I 15.5307 7.1820I
u = 0.225615 0.583583I
a = 1.062943 0.125662I
b = 1.62606 + 1 .21023I
5.22591 0.91968I 15.5307 + 7.1820I
7
III.
I
u
3
= hu
22
14u
21
+· · · 11u + 2, 8.82 × 10
7
u
21
+1.16 × 10
9
u
20
+· · · + 7.75 ×
10
7
a 1.53 ×10
7
, 3.77×10
7
u
21
5.21× 10
8
u
20
+· · ·+3.87 ×10
7
b 8.82 ×10
7
i
(i) Arc colorings
a
2
=
1
0
a
9
=
1.13754u
21
14.9531u
20
+ ··· + 1 .49209u + 0.197949
0.972398u
21
+ 13.4570u
20
+ ··· 12.7109u + 2.27508
a
1
=
0.195773u
21
+ 2.51037u
20
+ ··· 8.22312u + 0.854395
0.230460u
21
3.05161u
20
+ ··· + 2 .29911u 0.391547
a
5
=
0
u
a
4
=
u
u
a
10
=
0.941154u
21
11.8295u
20
+ ··· 7.15207u + 1.82967
0.776014u
21
+ 10.3334u
20
+ ··· 4.06672u + 0.643361
a
3
=
0.0346863u
21
0.541247u
20
+ ··· 5.92401u + 0.462849
0.0145948u
21
+ 0.253896u
20
+ ··· 0.525801u + 0.180651
a
6
=
0.0200915u
21
+ 0.287351u
20
+ ··· + 6.44981u 0.643500
0.0720342u
21
1.12230u
20
+ ··· + 1.99156u 0.0231328
a
8
=
1.13754u
21
14.9531u
20
+ ··· + 1.49209u + 0.197949
0.815858u
21
+ 11.2256u
20
+ ··· 4.28958u + 0.330282
a
11
=
0.503445u
21
7.35534u
20
+ ··· + 14.8105u 3.33457
0.624760u
21
+ 9.27278u
20
+ ··· 11.4038u + 3.07550
a
7
=
1.14264u
21
+ 15.1134u
20
+ ··· 7.55447u + 2.25416
1.10795u
21
14.5721u
20
+ ··· + 13 .4785u 2.71701
a
7
=
1.14264u
21
+ 15.1134u
20
+ ··· 7.55447u + 2.25416
1.10795u
21
14.5721u
20
+ ··· + 13 .4785u 2.71701
(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 = 0.663346 0.941102I
a = 0.377821 + 0 .233373I
b = 0.030998 + 0 .510375I
3.69794 + 2.45328I 0.65552 2.28211I
u = 0.663346 + 0.941102I
a = 0.377821 0.233373I
b = 0.030998 0.510375I
3.69794 2.45328I 0.65552 + 2.28211I
u = 0.175628 0.287507I
a = 2.50705 2.13751I
b = 0.174238 1.096202I
0.077811 + 0.121037I 6.01835 + 0.40486I
u = 0.175628 + 0.287507I
a = 2.50705 + 2.13751I
b = 0.174238 + 1 .096202I
0.077811 0.121037I 6.01835 0.40486I
u = 0.023080 0.517895I
a = 1.236479 0.147892I
b = 0.105131 0.636952I
0.808492 + 0.857573I 6.91603 4.94465I
u = 0.023080 + 0 .517895I
a = 1.236479 + 0.147892I
b = 0.105131 + 0 .636952I
0.808492 0.857573I 6.91603 + 4.94465I
u = 0.282736 0.453819I
a = 1.86718 + 0 .32775I
b = 0.676659 + 0.754694I
0.21957 2.12717I 6.07714 + 3.56253I
u = 0.282736 + 0 .453819I
a = 1.86718 0.32775I
b = 0.676659 0.754694I
0.21957 + 2.12717I 6.07714 3.56253I
u = 0.677862 0.440050I
a = 1.77956 + 0.17566I
b = 1.12900 0.90217I
7.68733 4.10610I 10.22463 + 1.15969I
u = 0.677862 + 0 .440050I
a = 1.77956 0.17566I
b = 1.12900 + 0 .90217I
7.68733 + 4.10610I 10.22463 1.15969I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.782653 1.033468I
a = 1.162672 + 0 .019568I
b = 0.93019 + 1.18627I
3.38864 4.05517I 5.85659 + 2.92403I
u = 0.782653 + 1 .033468I
a = 1.162672 0.019568I
b = 0.93019 1.18627I
3.38864 + 4.05517I 5.85659 2.92403I
u = 0.95797 1.12718I
a = 1.043585 + 0.037729I
b = 0.95719 1.21245I
6.62431 9.59009I 7.42347 + 6.05850I
u = 0.95797 + 1 .12718I
a = 1.043585 0.037729I
b = 0.95719 + 1 .21245I
6.62431 + 9.59009I 7.42347 6.05850I
u = 1.10739 1.14097I
a = 0.975052 0.092648I
b = 0.97405 + 1.21510I
1.8446 14.7873I 3.61777 + 8.09852I
u = 1.10739 + 1 .14097I
a = 0.975052 + 0 .092648I
b = 0.97405 1.21510I
1.8446 + 14.7873I 3.61777 8.09852I
u = 1.19477 1.51394I
a = 0.172481 + 0.319245I
b = 0.277244 0.642550I
1.94956 + 5.83716I 9.57717 8.35225I
u = 1.19477 + 1 .51394I
a = 0.172481 0.319245I
b = 0.277244 + 0.642550I
1.94956 5.83716I 9.57717 + 8.35225I
u = 1.34747 1.07987I
a = 0.127865 0.441757I
b = 0.304748 + 0 .733332I
5.71309 + 1.52838I 12.61169 4.44312I
u = 1.34747 + 1 .07987I
a = 0.127865 + 0 .441757I
b = 0.304748 0.733332I
5.71309 1.52838I 12.61169 + 4.44312I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.46505 0.64978I
a = 0.021431 + 0.576437I
b = 0.343162 0.858436I
1.45123 2.66218I 7.52164 0.32161I
u = 1.46505 + 0 .64978I
a = 0.021431 0.576437I
b = 0.343162 + 0.858436I
1.45123 + 2.66218I 7.52164 + 0.32161I
10
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
(u
9
+ u
8
+ ··· 2u
2
+ 1)(u
22
+ u
21
+ ··· + u + 1)
(u
24
+ 3u
23
+ ··· + 12 u + 5)
c
2
, c
9
(u
9
2u
7
u
6
+ 2u
5
+ 2u
4
2u
3
u
2
+ u + 1)
(u
22
4u
20
+ ··· 14u + 5)(u
24
+ u
23
+ ··· 14u + 11)
c
3
, c
5
(u
9
+ 4u
8
+ 8u
7
+ 13u
6
+ 18u
5
+ 18u
4
+ 14u
3
+ 9u
2
+ 3u + 1)
(u
22
+ 2u
21
+ ··· 2u + 1)(u
24
+ u
23
+ ··· 188u + 145)
c
4
(u
9
5u
8
+ 12u
7
15u
6
+ 10u
5
3u
4
+ 2u
3
2u
2
+ 1)
(1 + 3u
2
3u
3
+ 6u
4
8u
5
+ 12u
6
16u
7
+ 21u
8
20u
9
+ 13u
10
5u
11
+ u
12
)
2
(u
22
+ 14u
21
+ ··· + 11u + 2)
c
6
, c
7
(u
9
2u
8
+ 7u
7
10u
6
+ 16u
5
16u
4
+ 13u
3
9u
2
+ 2u 1)
(1 2u u
2
+ 3u
3
+ 10u
4
+ 22u
5
+ 28u
6
+ 30u
7
+ 25u
8
+ 16u
9
+ 9u
10
+ 3u
11
+ u
12
)
2
(u
22
5u
21
+ ··· 3u + 4)
c
10
, c
11
(u
9
+ 2u
8
+ 7u
7
+ 10u
6
+ 16u
5
+ 16u
4
+ 13u
3
+ 9u
2
+ 2u + 1)
(1 2u u
2
+ 3u
3
+ 10u
4
+ 22u
5
+ 28u
6
+ 30u
7
+ 25u
8
+ 16u
9
+ 9u
10
+ 3u
11
+ u
12
)
2
(u
22
5u
21
+ ··· 3u + 4)
11
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
8
(y
9
3y
8
+ 9y
7
14y
6
+ 18y
5
18y
4
+ 13y
3
8y
2
+ 4y 1)
(y
22
+ 9y
21
+ ··· + 21y + 1)(y
24
5y
23
+ ··· + 116 y + 25)
c
2
, c
9
(y
9
4y
8
+ 8y
7
13y
6
+ 18y
5
18y
4
+ 14y
3
9y
2
+ 3y 1)
(y
22
8y
21
+ ··· 246y + 25)(y
24
9y
23
+ ··· + 7812y + 121)
c
3
, c
5
(y
9
4y
7
+ 3y
6
+ 14y
5
14y
4
46y
3
33y
2
9y 1)
(y
22
28y
21
+ ··· 10y + 1)(y
24
9y
23
+ ··· 29544y + 21025)
c
4
(y
9
y
8
+ 14y
7
11y
6
+ 38y
5
19y
4
+ 22y
3
+ 2y
2
+ 4y 1)
(1 + 6y + 21y
2
+ 51y
3
+ 102y
4
+ 136y
5
+ 100y
6
+ 60y
7
+ 45y
8
+ 10y
9
+ 11y
10
+ y
11
+ y
12
)
2
(y
22
+ 36y
20
+ ··· + 71 y + 4)
c
6
, c
7
, c
10
c
11
(y
9
+ 10y
8
+ 41y
7
+ 86y
6
+ 86y
5
+ 4y
4
75y
3
61y
2
14y 1)
(1 6y + 33y
2
+ 115y
3
+ 82y
4
72y
5
136y
6
44y
7
+ 57y
8
+ 70y
9
+ 35y
10
+ 9y
11
+ y
12
)
2
(y
22
+ 19y
21
+ ··· + 7 y + 16)
12