11n
110
(K11n
110
)
1
Arc Sequences
7 1 11 9 10 2 10 3 5 8 9
Solving Sequence
3,11 4,8
9 5 1 2 10 6 7
c
3
c
8
c
4
c
11
c
2
c
10
c
5
c
7
c
1
, c
6
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
10
2u
8
+ u
7
+ 2u
4
5u
3
+ 4u
2
u + 1,
51u
9
+ 17u
8
+ 128u
7
62u
6
11u
5
28u
4
156u
3
+ 307u
2
+ 95b 243u + 37,
79u
9
58u
8
202u
7
+ 178u
6
+ 4u
5
33u
4
+ 169u
3
483u
2
+ 95a + 572u 143i
I
u
2
= hu
30
+ u
29
+ ··· u + 3, 7.01133 × 10
29
u
29
5.45134 × 10
29
u
28
+ ··· + 6.87676 × 10
30
b 6.16413 × 10
30
,
2.02531 × 10
31
u
29
2.06823 × 10
31
u
28
+ ··· + 2.06303 × 10
31
a + 4.75431 × 10
31
i
There are 2 irreducible components with 40 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
2u
8
+ u
7
+ 2u
4
5u
3
+ 4u
2
u + 1, 51u
9
+ 17u
8
+ · · · +
95b + 37, 79u
9
58u
8
+ · · · + 95a 143i
(i) Arc colorings
a
3
=
1
0
a
11
=
0.831579u
9
+ 0.610526u
8
+ ··· 6.02105u + 1.50526
0.536842u
9
0.178947u
8
+ ··· + 2.55789u 0.389474
a
4
=
u
9
u
8
+ 2u
7
+ u
6
u
5
2u
3
+ 3u
2
+ u 2
0.389474u
9
+ 0.536842u
8
+ ··· 1.67368u + 1.16842
a
8
=
0
u
a
9
=
u
u
a
5
=
0.821053u
9
0.726316u
8
+ ··· + 0.852632u 2.46316
0.210526u
9
+ 0.263158u
8
+ ··· 1.52632u + 1.63158
a
1
=
1.02105u
9
+ 0.673684u
8
+ ··· 6.74737u + 1.93684
0.726316u
9
0.242105u
8
+ ··· + 3.28421u 0.821053
a
2
=
1.69474u
9
0.768421u
8
+ ··· 1.66316u 3.08421
2
5
u
9
+
1
5
u
8
+ ···
4
5
u +
11
5
a
10
=
0.831579u
9
+ 0.610526u
8
+ ··· 6.02105u + 1.50526
u
9
2u
7
+ u
6
+ 2u
3
5u
2
+ 4u 1
a
6
=
1.32632u
9
0.557895u
8
+ ··· 1.08421u 3.97895
0.821053u
9
+ 0.726316u
8
+ ··· 0.852632u + 2.46316
a
7
=
1.51579u
9
0.505263u
8
+ ··· + 8.81053u 3.45263
0.831579u
9
+ 0.610526u
8
+ ··· 5.02105u + 1.50526
a
7
=
1.51579u
9
0.505263u
8
+ ··· + 8.81053u 3.45263
0.831579u
9
+ 0.610526u
8
+ ··· 5.02105u + 1.50526
(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 = 1.49757 0.34799I
a = 0.499793 0.290729I
b = 0.729854 0.051330I
3.86861 3.23765I 0.07935 + 4.10700I
u = 1.49757 + 0.34799I
a = 0.499793 + 0.290729I
b = 0.729854 + 0.051330I
3.86861 + 3.23765I 0.07935 4.10700I
u = 0.298418 1.046748I
a = 0.391518 + 0.620969I
b = 1.033941 0.503039I
0.81616 2.31326I 2.65364 + 2.24652I
u = 0.298418 + 1.046748I
a = 0.391518 0.620969I
b = 1.033941 + 0.503039I
0.81616 + 2.31326I 2.65364 2.24652I
u = 0.038142 0.505061I
a = 0.45686 + 3.00794I
b = 0.380444 1.223427I
4.70910 3.41496I 0.88361 + 1.66102I
u = 0.038142 + 0.505061I
a = 0.45686 3.00794I
b = 0.380444 + 1.223427I
4.70910 + 3.41496I 0.88361 1.66102I
u = 0.728854 0.747094I
a = 0.194612 + 0.619258I
b = 1.338216 0.457187I
0.92810 + 4.66670I 4.84081 6.38694I
u = 0.728854 + 0.747094I
a = 0.194612 0.619258I
b = 1.338216 + 0.457187I
0.92810 4.66670I 4.84081 + 6.38694I
u = 1.105276 0.236790I
a = 1.042780 0.579452I
b = 0.653686 0.055765I
2.37349 0.80372I 1.70130 + 5.71756I
u = 1.105276 + 0.236790I
a = 1.042780 + 0.579452I
b = 0.653686 + 0.055765I
2.37349 + 0.80372I 1.70130 5.71756I
3
II.
I
u
2
= hu
30
+u
29
+· · ·u+3, 7.01×10
29
u
29
5.45×10
29
u
28
+· · ·+6.88×10
30
b
6.16× 10
30
, 2.03×10
31
u
29
2.07 ×10
31
u
28
+· · · +2.06 ×10
31
a + 4.75× 10
31
i
(i) Arc colorings
a
3
=
1
0
a
11
=
0.981717u
29
+ 1.00252u
28
+ ··· + 6.54990u 2.30453
0.101957u
29
+ 0.0792719u
28
+ ··· + 1.58400u + 0.896371
a
4
=
0.171174u
29
0.537001u
28
+ ··· + 0.874298u 1.48983
0.920838u
29
+ 1.53111u
28
+ ··· + 8.89870u + 1.81728
a
8
=
0
u
a
9
=
u
u
a
5
=
0.0967599u
29
0.378765u
28
+ ··· + 2.87884u 0.756491
0.846424u
29
+ 1.37287u
28
+ ··· + 6.89415u + 1.08394
a
1
=
1.16177u
29
+ 1.28260u
28
+ ··· + 8.98715u 1.69844
0.282005u
29
0.200805u
28
+ ··· 0.853251u + 0.290280
a
2
=
0.479626u
29
0.560802u
28
+ ··· 3.19408u 0.293090
0.853896u
29
+ 1.21011u
28
+ ··· + 6.04638u + 0.258826
a
10
=
0.981717u
29
+ 1.00252u
28
+ ··· + 6.54990u 2.30453
0.455808u
29
0.362118u
28
+ ··· 1.34035u + 0.833966
a
6
=
0.559702u
29
1.16445u
28
+ ··· + 0.866034u + 0.256872
0.765369u
29
+ 1.71185u
28
+ ··· + 7.64914u + 4.71234
a
7
=
0.241953u
29
0.128725u
28
+ ··· 1.54903u 5.30580
0.489529u
29
0.357631u
28
+ ··· 2.75754u + 1.62556
a
7
=
0.241953u
29
0.128725u
28
+ ··· 1.54903u 5.30580
0.489529u
29
0.357631u
28
+ ··· 2.75754u + 1.62556
(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 = 1.20349 1.15802I
a = 0.837597 + 0.568132I
b = 1.47811 + 0 .10440I
10.88757 + 3.99108I 1.34517 2.29289I
u = 1.20349 + 1.15802I
a = 0.837597 0.568132I
b = 1.47811 0.10440I
10.88757 3.99108I 1.34517 + 2.29289I
u = 1.116605 0.020132I
a = 1.045224 + 0 .221858I
b = 0.560758 0.205214I
2.62675 0.08468I 4.72619 2.64005I
u = 1.116605 + 0.020132I
a = 1.045224 0.221858I
b = 0.560758 + 0.205214I
2.62675 + 0.08468I 4.72619 + 2.64005I
u = 1.07609 1.18578I
a = 0.548246 1.054381I
b = 1.65500 + 0.65507I
11.2229 12.5494I 0.76232 + 6.35479I
u = 1.07609 + 1.18578I
a = 0.548246 + 1 .054381I
b = 1.65500 0.65507I
11.2229 + 12.5494I 0.76232 6.35479I
u = 0.899919 0.738427I
a = 0.648903 0.426245I
b = 1.58129 + 0.11364I
0.32537 4.54381I 1.91240 + 4.46685I
u = 0.899919 + 0.738427I
a = 0.648903 + 0 .426245I
b = 1.58129 0.11364I
0.32537 + 4.54381I 1.91240 4.46685I
u = 0.605367 1.027857I
a = 0.148214 + 1 .032035I
b = 0.998159 0.324362I
1.65136 1.24421I 1.024611 0.505616I
u = 0.605367 + 1.027857I
a = 0.148214 1.032035I
b = 0.998159 + 0 .324362I
1.65136 + 1.24421I 1.024611 + 0.505616I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.333418 0.491825I
a = 0.457016 + 0 .878069I
b = 0.066357 0.474768I
0.104103 1.239119I 1.20094 + 5.47066I
u = 0.333418 + 0.491825I
a = 0.457016 0.878069I
b = 0.066357 + 0.474768I
0.104103 + 1.239119I 1.20094 5.47066I
u = 0.269585 0.962091I
a = 0.120660 + 0 .861970I
b = 1.140285 0.736299I
1.43336 3.12326I 2.11949 + 6.95210I
u = 0.269585 + 0.962091I
a = 0.120660 0.861970I
b = 1.140285 + 0 .736299I
1.43336 + 3.12326I 2.11949 6.95210I
u = 0.020674 0.772128I
a = 0.42115 + 2 .51775I
b = 0.0536954 + 0 .0853904I
5.64984 3.06569I 7.90048 + 1.52459I
u = 0.020674 + 0 .772128I
a = 0.42115 2.51775I
b = 0.0536954 0.0853904I
5.64984 + 3.06569I 7.90048 1.52459I
u = 0.173082 0.653523I
a = 0.20992 2.06536I
b = 0.15519 + 2 .17942I
5.14615 + 3.90437I 9.12338 9.65977I
u = 0.173082 + 0 .653523I
a = 0.20992 + 2.06536I
b = 0.15519 2.17942I
5.14615 3.90437I 9.12338 + 9.65977I
u = 0.187483 0.399716I
a = 2.05853 0.16469I
b = 1.049510 0.300006I
0.95851 + 2.62649I 5.25510 4.40076I
u = 0.187483 + 0 .399716I
a = 2.05853 + 0.16469I
b = 1.049510 + 0.300006I
0.95851 2.62649I 5.25510 + 4.40076I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.427524 0.839075I
a = 0.581735 0.280785I
b = 1.62693 0.17110I
3.55287 0.89069I 4.27167 + 0.33793I
u = 0.427524 + 0 .839075I
a = 0.581735 + 0.280785I
b = 1.62693 + 0 .17110I
3.55287 + 0.89069I 4.27167 0.33793I
u = 0.721305 0.682042I
a = 0.24593 + 1.66689I
b = 1.106171 0.510090I
2.53446 + 5.24872I 0.77194 8.29520I
u = 0.721305 + 0 .682042I
a = 0.24593 1.66689I
b = 1.106171 + 0.510090I
2.53446 5.24872I 0.77194 + 8.29520I
u = 1.02997 1.17794I
a = 0.685808 0.944877I
b = 1.75451 + 0 .55706I
12.05585 + 5.16332I 1.89858 2.30543I
u = 1.02997 + 1 .17794I
a = 0.685808 + 0.944877I
b = 1.75451 0.55706I
12.05585 5.16332I 1.89858 + 2.30543I
u = 1.18215 1.08924I
a = 0.875701 + 0 .808086I
b = 1.52906 0.04459I
11.56267 + 3.12726I 1.97467 2.33151I
u = 1.18215 + 1 .08924I
a = 0.875701 0.808086I
b = 1.52906 + 0.04459I
11.56267 3.12726I 1.97467 + 2.33151I
u = 1.262288 0.300892I
a = 0.312270 0.344335I
b = 0.158737 + 0.404400I
4.76031 + 3.13588I 9.92249 3.96046I
u = 1.262288 + 0 .300892I
a = 0.312270 + 0.344335I
b = 0.158737 0.404400I
4.76031 3.13588I 9.92249 + 3.96046I
7
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 5u
4
+ 3u
2
+ 1)
(u
30
+ 3u
28
+ ··· + 6u + 1)
c
2
(u
10
+ 5u
9
+ ··· + 6u + 1)(u
30
+ 6u
29
+ ··· + 4u + 1)
c
3
(u
10
2u
8
+ 2u
7
+ u
6
5u
5
+ 4u
4
+ 4u
3
4u
2
u + 1)
(u
30
+ u
29
+ ··· 5u + 1)
c
4
, c
5
(u
10
u
9
4u
8
+ 4u
7
+ 4u
6
5u
5
+ u
4
+ 2u
3
2u
2
+ 1)
(u
30
+ u
27
+ ··· 4u + 19)
c
6
(u
10
u
9
+ 3u
8
2u
7
+ 5u
6
2u
5
+ 5u
4
+ 3u
2
+ 1)
(u
30
+ 3u
28
+ ··· + 6u + 1)
c
7
(u
10
+ u
9
4u
8
4u
7
+ 6u
6
+ 7u
5
2u
4
6u
3
u
2
+ 2u + 1)
(u
30
20u
28
+ ··· + 702u + 143)
c
8
(u
10
2u
8
+ ··· + u + 1)(u
30
+ u
29
+ ··· u + 3)
c
9
(u
10
+ u
9
4u
8
4u
7
+ 4u
6
+ 5u
5
+ u
4
2u
3
2u
2
+ 1)
(u
30
+ u
27
+ ··· 4u + 19)
c
10
(u
10
u
9
4u
8
+ 4u
7
+ 6u
6
7u
5
2u
4
+ 6u
3
u
2
2u + 1)
(u
30
20u
28
+ ··· + 702u + 143)
c
11
(u
10
+ u
9
+ 3u
8
+ u
6
2u
5
+ 3u
4
+ u
3
+ 2u
2
+ 1)
(u
30
+ 4u
29
+ ··· + 14u + 1)
8
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
10
+ 5y
9
+ ··· + 6y + 1)(y
30
+ 6y
29
+ ··· + 4y + 1)
c
2
(y
10
+ 5y
9
+ ··· + 2y + 1)(y
30
+ 42y
29
+ ··· + 124y + 1)
c
3
(y
10
4y
9
+ 6y
8
3y
6
15y
5
+ 48y
4
56y
3
+ 32y
2
9y + 1)
(y
30
27y
29
+ ··· + 89y + 1)
c
4
, c
5
, c
9
(y
10
9y
9
+ 32y
8
56y
7
+ 48y
6
15y
5
3y
4
+ 6y
2
4y + 1)
(y
30
+ 30y
28
+ ··· + 5798y + 361)
c
7
(y
10
9y
9
+ ··· 6y + 1)(y
30
40y
29
+ ··· 169052y + 20449)
c
8
(y
10
4y
9
+ 4y
8
+ 3y
7
4y
5
+ 2y
4
9y
3
+ 10y
2
+ 7y + 1)
(y
30
+ y
29
+ ··· + 149y + 9)
c
10
(y
10
9y
9
+ ··· 6y + 1)(y
30
40y
29
+ ··· 169052y + 20449)
c
11
(y
10
+ 5y
9
+ ··· + 4y + 1)(y
30
+ 30y
29
+ ··· 30y + 1)
9