11a
341
(K11a
341
)
1
Arc Sequences
8 7 1 11 10 9 2 3 6 4 5
Solving Sequence
4,10
11 5 6 1 3 9 7 2 8
c
10
c
4
c
5
c
11
c
3
c
9
c
6
c
2
c
8
c
1
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
30
+ u
29
+ ··· u 1i
There are 1 irreducible components with 30 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
30
+ u
29
+ · · · u 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
11
=
u
u
a
5
=
u
2
+ 1
u
2
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
3
2u
u
3
+ u
a
3
=
u
6
3u
4
+ 2u
2
+ 1
u
6
+ 2u
4
u
2
a
9
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
7
=
u
8
+ 3u
6
3u
4
+ 1
u
10
+ 4u
8
5u
6
+ 3u
2
a
2
=
u
24
+ 9u
22
+ ··· 2u
2
+ 1
u
26
+ 10u
24
+ ··· 10u
4
u
2
a
8
=
u
19
8u
17
+ 26u
15
40u
13
+ 19u
11
+ 24u
9
30u
7
+ 2u
5
+ 5u
3
+ 2u
u
19
+ 7u
17
20u
15
+ 27u
13
11u
11
13u
9
+ 16u
7
6u
5
+ u
3
+ u
a
8
=
u
19
8u
17
+ 26u
15
40u
13
+ 19u
11
+ 24u
9
30u
7
+ 2u
5
+ 5u
3
+ 2u
u
19
+ 7u
17
20u
15
+ 27u
13
11u
11
13u
9
+ 16u
7
6u
5
+ u
3
+ u
(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 = 1.306326 0.437358I
12.2507 10.4619I 5.88987 + 5.77440I
u = 1.306326 + 0.437358I
12.2507 + 10.4619I 5.88987 5.77440I
u = 1.291241 0.080442I
1.40610 2.59166I 13.13861 + 3.85906I
u = 1.291241 + 0.080442I
1.40610 + 2.59166I 13.13861 3.85906I
u = 1.289934 0.269184I
2.71542 7.35959I 8.50810 + 6.87083I
u = 1.289934 + 0.269184I
2.71542 + 7.35959I 8.50810 6.87083I
u = 1.274058 0.435895I
6.01443 2.51871I 8.78607 + 0.11545I
u = 1.274058 + 0.435895I
6.01443 + 2.51871I 8.78607 0.11545I
u = 1.170377 0.182149I
1.55681 1.24454I 9.57026 + 0.01940I
u = 1.170377 + 0.182149I
1.55681 + 1.24454I 9.57026 0.01940I
u = 0.289035
0.539047 18.6187
u = 0.085803 0.574843I
1.55006 1.51308I 5.97054 + 5.56899I
u = 0.085803 + 0.574843I
1.55006 + 1.51308I 5.97054 5.56899I
u = 0.011432 0.903800I
9.93135 2.26722I 5.50678 + 2.95936I
u = 0.011432 + 0.903800I
9.93135 + 2.26722I 5.50678 2.95936I
u = 0.025624 0.918937I
16.4000 + 5.6172I 2.30571 2.94796I
u = 0.025624 + 0.918937I
16.4000 5.6172I 2.30571 + 2.94796I
u = 0.133435 0.677542I
7.12139 + 3.97751I 2.60373 4.61085I
u = 0.133435 + 0.677542I
7.12139 3.97751I 2.60373 + 4.61085I
u = 0.384081 0.329837I
3.55481 + 1.33307I 6.99438 4.68394I
u = 0.384081 + 0.329837I
3.55481 1.33307I 6.99438 + 4.68394I
u = 1.077259 0.280883I
4.37079 0.39876I 5.65256 0.33151I
u = 1.077259 + 0.280883I
4.37079 + 0.39876I 5.65256 + 0.33151I
u = 1.259718 0.224875I
2.55759 + 4.40021I 13.4404 7.3156I
u = 1.259718 + 0.224875I
2.55759 4.40021I 13.4404 + 7.3156I
u = 1.266670 0.453503I
12.55708 0.72268I 5.44447 0.15080I
u = 1.266670 + 0.453503I
12.55708 + 0.72268I 5.44447 + 0.15080I
u = 1.26925
5.06052 19.4193
u = 1.292276 0.430300I
5.87624 + 7.03616I 9.16949 5.90820I
u = 1.292276 + 0.430300I
5.87624 7.03616I 9.16949 + 5.90820I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
(u
30
+ u
29
+ ··· + u 1)
c
3
, c
5
, c
6
c
9
(u
30
+ 3u
29
+ ··· + 7u + 3)
c
4
, c
10
, c
11
(u
30
+ u
29
+ ··· u 1)
c
8
(u
30
+ u
29
+ ··· 135u 53)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
(y
30
+ 29y
29
+ ··· 9y + 1)
c
3
, c
5
, c
6
c
9
(y
30
+ 37y
29
+ ··· 49y + 9)
c
4
, c
10
, c
11
(y
30
23y
29
+ ··· 9y + 1)
c
8
(y
30
+ 17y
29
+ ··· + 12939y + 2809)
5