11a
33
(K11a
33
)
1
Arc Sequences
4 1 8 2 9 11 3 5 6 7 10
Solving Sequence
3,7
8
4,11
6 10 1 2 9 5
c
7
c
3
c
6
c
10
c
11
c
2
c
9
c
5
c
1
, c
4
, c
8
Representation Ideals
I = I
u
1
\
I
v
1
I
u
1
= hu
52
+ u
51
+ ··· 232u
2
+ 32,
2.80455 × 10
71
u
51
8.84488 × 10
70
u
50
+ ··· + 1.82929 × 10
71
a 1.41514 × 10
73
,
3.59162 × 10
71
u
51
6.81177 × 10
70
u
50
+ ··· + 3.65857 × 10
71
b 1.51817 × 10
73
i
I
v
1
= hb
5
+ 2b
4
+ 3b
3
+ 2b
2
+ 2b + 1, b
4
2b
3
3b
2
b + v 1, ai
There are 2 irreducible components with 57 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
52
+u
51
+· · ·−232u
2
+32, 2.80×10
71
u
51
8.84×10
70
u
50
+· · ·+ 1.83 ×10
71
a
1.42 × 10
73
, 3.59 × 10
71
u
51
6.81 ×10
70
u
50
+ · · · +3.66 × 10
71
b 1.52 × 10
73
i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
8
=
u
u
a
4
=
u
2
+ 1
u
2
a
11
=
1.53314u
51
+ 0.483515u
50
+ ··· 115.343u + 77.3601
0.981700u
51
+ 0.186187u
50
+ ··· 59.2802u + 41.4962
a
6
=
1.19425u
51
+ 0.481246u
50
+ ··· 105.268u + 66.6624
0.198263u
51
+ 0.0892578u
50
+ ··· + 14.3724u 11.3632
a
10
=
1.53314u
51
+ 0.483515u
50
+ ··· 115.343u + 77.3601
0.291067u
51
+ 0.0291784u
50
+ ··· 10.2198u + 7.90835
a
1
=
0.196295u
51
0.00549239u
50
+ ··· 23.5061u + 20.3598
0.117453u
51
0.0692387u
50
+ ··· + 9.18679u 4.42523
a
2
=
0.154147u
51
0.0397948u
50
+ ··· 20.0268u + 17.5330
0.241668u
51
0.208983u
50
+ ··· + 11.8129u 3.67724
a
9
=
0.828488u
51
0.493482u
50
+ ··· + 70.9484u 33.7554
0.125795u
51
0.105171u
50
+ ··· 13.0041u + 13.1784
a
5
=
0.321903u
51
0.139407u
50
+ ··· + 26.4114u 18.3279
0.125608u
51
0.144899u
50
+ ··· + 2.90533u + 2.03198
a
5
=
0.321903u
51
0.139407u
50
+ ··· + 26.4114u 18.3279
0.125608u
51
0.144899u
50
+ ··· + 2.90533u + 2.03198
(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 = 1.41956 0.37842I
a = 0.592117 0.130057I
b = 0.891165 0.384837I
9.80914 + 2.73925I 5.98913 0.86649I
u = 1.41956 + 0.37842I
a = 0.592117 + 0.130057I
b = 0.891165 + 0.384837I
9.80914 2.73925I 5.98913 + 0.86649I
u = 1.38824 0.60897I
a = 0.593747 + 0.651040I
b = 0.27948 + 2.56319I
12.02741 + 4.30908I 7.47308 2.21383I
u = 1.38824 + 0.60897I
a = 0.593747 0.651040I
b = 0.27948 2.56319I
12.02741 4.30908I 7.47308 + 2.21383I
u = 1.35988 0.65311I
a = 0.058130 0.886872I
b = 0.39139 3.66290I
11.4963 + 13.8946I 6.59320 8.24119I
u = 1.35988 + 0.65311I
a = 0.058130 + 0.886872I
b = 0.39139 + 3.66290I
11.4963 13.8946I 6.59320 + 8.24119I
u = 1.260839 0.032726I
a = 0.218091 0.886432I
b = 0.07148 2.21557I
5.88940 2.23703I 9.81871 + 3.17171I
u = 1.260839 + 0.032726I
a = 0.218091 + 0.886432I
b = 0.07148 + 2.21557I
5.88940 + 2.23703I 9.81871 3.17171I
u = 1.153569 0.455280I
a = 0.577895 0.088468I
b = 0.123541 + 0.688937I
0.72885 + 5.40223I 0.76570 5.29849I
u = 1.153569 + 0.455280I
a = 0.577895 + 0.088468I
b = 0.123541 0.688937I
0.72885 5.40223I 0.76570 + 5.29849I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.087850 0.046512I
a = 0.376309 1.154149I
b = 0.08249 3.57499I
6.39075 + 4.67632I 6.63994 3.34452I
u = 1.087850 + 0.046512I
a = 0.376309 + 1.154149I
b = 0.08249 + 3.57499I
6.39075 4.67632I 6.63994 + 3.34452I
u = 1.086042 0.309013I
a = 0.134864 + 1.017298I
b = 0.96499 + 2.04338I
4.31532 + 4.63289I 7.37710 5.03996I
u = 1.086042 + 0.309013I
a = 0.134864 1.017298I
b = 0.96499 2.04338I
4.31532 4.63289I 7.37710 + 5.03996I
u = 1.029524 0.333804I
a = 0.273111 0.744365I
b = 1.062748 0.265689I
0.40755 + 4.20725I 0.31053 6.85372I
u = 1.029524 + 0.333804I
a = 0.273111 + 0.744365I
b = 1.062748 + 0.265689I
0.40755 4.20725I 0.31053 + 6.85372I
u = 0.628086 0.011759I
a = 0.76361 1.86660I
b = 0.511707 0.778773I
5.00504 4.26604I 11.11018 + 2.65342I
u = 0.628086 + 0.011759I
a = 0.76361 + 1.86660I
b = 0.511707 + 0.778773I
5.00504 + 4.26604I 11.11018 2.65342I
u = 0.480287 0.488293I
a = 0.864357 0.262015I
b = 1.207531 + 0.101260I
2.08809 0.78607I 3.98062 1.52380I
u = 0.480287 + 0.488293I
a = 0.864357 + 0.262015I
b = 1.207531 0.101260I
2.08809 + 0.78607I 3.98062 + 1.52380I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.347952 0.680449I
a = 0.145116 0.640559I
b = 0.550550 0.741461I
1.79468 0.95889I 4.14280 + 1.57937I
u = 0.347952 + 0.680449I
a = 0.145116 + 0.640559I
b = 0.550550 + 0.741461I
1.79468 + 0.95889I 4.14280 1.57937I
u = 0.248057 1.187933I
a = 1.080896 + 0.174432I
b = 1.48256 + 0.53189I
7.94604 7.28946I 5.85423 + 5.70080I
u = 0.248057 + 1.187933I
a = 1.080896 0.174432I
b = 1.48256 0.53189I
7.94604 + 7.28946I 5.85423 5.70080I
u = 0.169899 1.183751I
a = 0.977658 + 0.522136I
b = 1.24731 + 0.93979I
8.11586 + 2.13977I 6.28937 0.51740I
u = 0.169899 + 1.183751I
a = 0.977658 0.522136I
b = 1.24731 0.93979I
8.11586 2.13977I 6.28937 + 0.51740I
u = 0.010942 0.814358I
a = 1.204071 0.360898I
b = 0.142030 0.656396I
0.986067 0.922209I 5.57805 + 0.78370I
u = 0.010942 + 0.814358I
a = 1.204071 + 0.360898I
b = 0.142030 + 0.656396I
0.986067 + 0.922209I 5.57805 0.78370I
u = 0.213178 1.155909I
a = 0.113479 + 0.723602I
b = 0.063002 + 0.215299I
4.28726 + 2.50747I 2.75724 2.68671I
u = 0.213178 + 1.155909I
a = 0.113479 0.723602I
b = 0.063002 0.215299I
4.28726 2.50747I 2.75724 + 2.68671I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.301724 0.398387I
a = 0.95370 1.34817I
b = 0.290241 0.488400I
0.450033 1.234717I 4.74084 + 5.50358I
u = 0.301724 + 0.398387I
a = 0.95370 + 1.34817I
b = 0.290241 + 0.488400I
0.450033 + 1.234717I 4.74084 5.50358I
u = 0.371907 0.887604I
a = 1.124251 0.005251I
b = 0.266407 0.850009I
0.04250 + 4.54357I 1.88793 7.26372I
u = 0.371907 + 0.887604I
a = 1.124251 + 0.005251I
b = 0.266407 + 0.850009I
0.04250 4.54357I 1.88793 + 7.26372I
u = 0.611417
a = 1.15720
b = 0.0192669
1.69898 7.12316
u = 0.723834 0.276102I
a = 0.016422 + 1.324742I
b = 0.61718 + 2.91051I
0.88919 2.40502I 4.23135 + 7.49678I
u = 0.723834 + 0.276102I
a = 0.016422 1.324742I
b = 0.61718 2.91051I
0.88919 + 2.40502I 4.23135 7.49678I
u = 0.961653 0.221131I
a = 0.684968 + 0.680475I
b = 0.961581 0.230355I
0.0437779 + 0.0269953I 1.92084 0.19212I
u = 0.961653 + 0.221131I
a = 0.684968 0.680475I
b = 0.961581 + 0.230355I
0.0437779 0.0269953I 1.92084 + 0.19212I
u = 1.035659 0.105451I
a = 0.619944 0.157919I
b = 0.049581 + 0.344007I
1.98030 0.48005I 3.97181 + 0.10468I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.035659 + 0.105451I
a = 0.619944 + 0.157919I
b = 0.049581 0.344007I
1.98030 + 0.48005I 3.97181 0.10468I
u = 1.04965
a = 0.808700
b = 1.42937
2.68190 3.52272
u = 1.187855 0.537240I
a = 0.033870 + 0.877672I
b = 1.29133 + 2.25907I
2.58119 9.82991I 3.68059 + 9.74649I
u = 1.187855 + 0.537240I
a = 0.033870 0.877672I
b = 1.29133 2.25907I
2.58119 + 9.82991I 3.68059 9.74649I
u = 1.279685 0.359861I
a = 0.348404 0.778179I
b = 0.14985 2.12750I
5.10574 3.32861I 8.68775 + 2.82645I
u = 1.279685 + 0.359861I
a = 0.348404 + 0.778179I
b = 0.14985 + 2.12750I
5.10574 + 3.32861I 8.68775 2.82645I
u = 1.35677 0.62431I
a = 0.557359 0.207593I
b = 0.855811 0.619829I
7.94022 8.91057I 3.69132 + 5.27448I
u = 1.35677 + 0.62431I
a = 0.557359 + 0.207593I
b = 0.855811 + 0.619829I
7.94022 + 8.91057I 3.69132 5.27448I
u = 1.43065 0.41648I
a = 0.079812 0.898014I
b = 0.36339 3.60048I
13.4799 7.6731I 8.99342 + 3.94688I
u = 1.43065 + 0.41648I
a = 0.079812 + 0.898014I
b = 0.36339 + 3.60048I
13.4799 + 7.6731I 8.99342 3.94688I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.45538 0.35264I
a = 0.487731 + 0.750918I
b = 0.27049 + 2.93111I
13.79828 + 1.96896I 9.43817 2.22913I
u = 1.45538 + 0.35264I
a = 0.487731 0.750918I
b = 0.27049 2.93111I
13.79828 1.96896I 9.43817 + 2.22913I
7
II. I
v
1
= hb
5
+ 2b
4
+ 3b
3
+ 2b
2
+ 2b + 1, b
4
2b
3
3b
2
b + v 1, ai
(i) Arc colorings
a
3
=
1
0
a
7
=
b
4
+ 2b
3
+ 3b
2
+ b + 1
0
a
8
=
b
4
+ 2b
3
+ 3b
2
+ b + 1
0
a
4
=
1
0
a
11
=
0
b
a
6
=
b
4
+ 2b
3
+ 3b
2
+ b + 1
b
3
+ b
2
+ b
a
10
=
b
4
b
3
b
2
+ b
b
a
1
=
b
4
+ 2b
3
+ 2b
2
1
1
a
2
=
b
4
+ 2b
3
+ 2b
2
1
a
9
=
b
4
2b
3
2b
2
+ 1
b
4
2b
3
3b
2
b 1
a
5
=
b
4
2b
3
2b
2
+ 1
1
a
5
=
b
4
2b
3
2b
2
+ 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 0.309916 + 0.549911I
a = 0
b = 0.871221 1.107662I
1.31583 + 1.53058I 0.02124 2.62456I
v = 0.309916 0.549911I
a = 0
b = 0.871221 + 1.107662I
1.31583 1.53058I 0.02124 + 2.62456I
v = 1.21774
a = 0
b = 0.629714
0.756147 2.67610
v = 1.41878 0.21917I
a = 0
b = 0.186078 0.874646I
4.22763 + 4.40083I 0.31681 3.97407I
v = 1.41878 + 0.21917I
a = 0
b = 0.186078 + 0.874646I
4.22763 4.40083I 0.31681 + 3.97407I
9
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
5
(u
52
+ 6u
51
+ ··· 5u 1)
c
2
(u + 1)
5
(u
52
+ 22u
51
+ ··· 11u + 1)
c
3
, c
7
u
5
(u
52
+ u
51
+ ··· 232u
2
+ 32)
c
4
(u + 1)
5
(u
52
+ 6u
51
+ ··· 5u 1)
c
5
(u
5
u
4
+ ··· + u + 1)(u
52
+ 2u
51
+ ··· + 25u 17)
c
6
(u
5
+ u
4
+ ··· + u + 1)(u
52
+ 2u
51
+ ··· u 1)
c
8
, c
9
(u
5
+ u
4
+ ··· + u 1)(u
52
+ 2u
51
+ ··· + 25u 17)
c
10
(u
5
u
4
+ ··· + u 1)(u
52
+ 2u
51
+ ··· u 1)
c
11
(u
5
3u
4
+ ··· u + 1)(u
52
+ 30u
51
+ ··· + 5u + 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y 1)
5
(y
52
22y
51
+ ··· + 11y + 1)
c
2
(y 1)
5
(y
52
+ 22y
51
+ ··· 349y + 1)
c
3
, c
7
y
5
(y
52
33y
51
+ ··· 14848y + 1024)
c
5
1.00000000000000
(1y
5
5.00000000000000y
4
+ ··· y 1.00000000000000)
(1.00y
52
58.0y
51
+ ··· 2.29 × 10
3
y + 289.)
c
6
1.00000000000
(1y
5
+ 3.0000000000y
4
+ ··· y 1.00000000000)
(1y
52
+ 30.000000000y
51
+ ··· + 5.0000000000y + 1.00000000000)
c
8
(y
5
5y
4
+ ··· y 1)(y
52
58y
51
+ ··· 2291y + 289)
c
9
1.00000000000000
(1y
5
5.00000000000000y
4
+ ··· y 1.00000000000000)
(1.00y
52
58.0y
51
+ ··· 2.29 × 10
3
y + 289.)
c
10
(y
5
+ 3y
4
+ ··· y 1)(y
52
+ 30y
51
+ ··· + 5y + 1)
c
11
1.000000000000000
(1y
5
y
4
+ ··· + 3.000000000000000y 1.000000000000000)
(1.00y
52
14.0y
51
+ ··· + 21.0y + 1.00)
11