11a
145
(K11a
145
)
1
Arc Sequences
6 1 10 9 2 5 11 3 4 8 7
Solving Sequence
1,6
2 3 5 7 11 8 9 4 10
c
1
c
2
c
5
c
6
c
11
c
7
c
8
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
41
+ u
40
+ ··· + u + 1i
There are 1 irreducible components with 41 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
41
+ u
40
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
3
u
5
+ u
3
+ u
a
11
=
u
8
u
6
u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
8
=
u
13
2u
11
3u
9
2u
7
+ u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
9
=
u
19
+ 4u
17
+ 10u
15
+ 16u
13
+ 19u
11
+ 18u
9
+ 14u
7
+ 10u
5
+ 5u
3
+ 2u
u
19
3u
17
6u
15
7u
13
5u
11
3u
9
+ u
3
+ u
a
4
=
u
40
+ 7u
38
+ ··· 2u
2
+ 1
u
40
u
39
+ ··· + 2u
2
1
a
10
=
u
18
3u
16
6u
14
7u
12
5u
10
3u
8
+ u
2
+ 1
u
20
+ 4u
18
+ 10u
16
+ 16u
14
+ 19u
12
+ 18u
10
+ 14u
8
+ 10u
6
+ 5u
4
+ 2u
2
a
10
=
u
18
3u
16
6u
14
7u
12
5u
10
3u
8
+ u
2
+ 1
u
20
+ 4u
18
+ 10u
16
+ 16u
14
+ 19u
12
+ 18u
10
+ 14u
8
+ 10u
6
+ 5u
4
+ 2u
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 = 0.806047 0.549030I
8.94893 6.85378I 3.02004 + 3.14653I
u = 0.806047 + 0.549030I
8.94893 + 6.85378I 3.02004 3.14653I
u = 0.755820 0.517358I
3.00487 + 0.67608I 5.83606 3.00610I
u = 0.755820 + 0.517358I
3.00487 0.67608I 5.83606 + 3.00610I
u = 0.723389 0.712701I
1.40317 2.83072I 6.43491 + 2.95500I
u = 0.723389 + 0.712701I
1.40317 + 2.83072I 6.43491 2.95500I
u = 0.693368 0.847987I
0.42753 + 2.65969I 8.24093 3.41095I
u = 0.693368 + 0.847987I
0.42753 2.65969I 8.24093 + 3.41095I
u = 0.684591 0.962511I
2.15015 + 8.22064I 4.65359 8.30848I
u = 0.684591 + 0.962511I
2.15015 8.22064I 4.65359 + 8.30848I
u = 0.668298 1.062094I
10.4751 + 12.3911I 0.95545 7.64540I
u = 0.668298 + 1.062094I
10.4751 12.3911I 0.95545 + 7.64540I
u = 0.645065 1.051396I
4.55106 + 4.63624I 3.54482 1.91862I
u = 0.645065 + 1.051396I
4.55106 4.63624I 3.54482 + 1.91862I
u = 0.621133 0.863903I
0.77518 + 2.43453I 4.67673 2.83072I
u = 0.621133 + 0.863903I
0.77518 2.43453I 4.67673 + 2.83072I
u = 0.318245
0.648370 15.5210
u = 0.115917 0.818177I
1.55862 + 1.34593I 1.69201 5.88103I
u = 0.115917 + 0.818177I
1.55862 1.34593I 1.69201 + 5.88103I
u = 0.011468 1.129054I
8.57548 + 2.18961I 0.00248 3.13615I
u = 0.011468 + 1.129054I
8.57548 2.18961I 0.00248 + 3.13615I
u = 0.023621 1.144640I
14.9420 5.4434I 3.20395 + 3.09405I
u = 0.023621 + 1.144640I
14.9420 + 5.4434I 3.20395 3.09405I
u = 0.148379 0.957091I
6.92446 3.50964I 2.41858 + 4.66080I
u = 0.148379 + 0.957091I
6.92446 + 3.50964I 2.41858 4.66080I
u = 0.480200 0.212125I
3.50591 1.71670I 5.52450 + 3.61654I
u = 0.480200 + 0.212125I
3.50591 + 1.71670I 5.52450 3.61654I
u = 0.515887 0.932646I
5.03762 1.88806I 0.24106 + 3.02995I
u = 0.515887 + 0.932646I
5.03762 + 1.88806I 0.24106 3.02995I
u = 0.634950 1.064323I
11.04332 1.60938I 0.06795 + 1.93850I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.634950 + 1.064323I
11.04332 + 1.60938I 0.06795 1.93850I
u = 0.660870 1.052988I
4.27384 8.98491I 4.35745 + 7.89511I
u = 0.660870 + 1.052988I
4.27384 + 8.98491I 4.35745 7.89511I
u = 0.674707 0.926922I
2.60925 5.20134I 10.53591 + 7.82962I
u = 0.674707 + 0.926922I
2.60925 + 5.20134I 10.53591 7.82962I
u = 0.691393 0.764064I
3.10340 0.06542I 12.57860 1.49885I
u = 0.691393 + 0.764064I
3.10340 + 0.06542I 12.57860 + 1.49885I
u = 0.774175 0.483647I
9.35158 3.69269I 2.52382 + 2.88457I
u = 0.774175 + 0.483647I
9.35158 + 3.69269I 2.52382 2.88457I
u = 0.780035 0.548337I
2.78722 + 3.54108I 6.45783 3.37439I
u = 0.780035 + 0.548337I
2.78722 3.54108I 6.45783 + 3.37439I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
41
+ u
40
+ ··· + u + 1)
c
2
, c
6
(u
41
+ 15u
40
+ ··· + 5u 1)
c
3
, c
4
, c
9
(u
41
+ u
40
+ ··· + u + 1)
c
7
, c
10
, c
11
(u
41
+ 5u
40
+ ··· 23u 3)
c
8
(u
41
+ u
40
+ ··· 53u 37)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
41
+ 15y
40
+ ··· + 5y 1)
c
2
, c
6
(y
41
+ 23y
40
+ ··· + 85y 1)
c
3
, c
4
, c
9
(y
41
+ 39y
40
+ ··· + 5y 1)
c
7
, c
10
, c
11
(y
41
+ 43y
40
+ ··· 131y 9)
c
8
(y
41
+ 19y
40
+ ··· 34931y 1369)
6