11a
325
(K11a
325
)
1
Arc Sequences
7 9 1 11 8 2 10 3 6 5 4
Solving Sequence
1,4 3,8
9 2 11 5 6 10 7
c
3
c
8
c
2
c
11
c
4
c
5
c
10
c
7
c
1
, c
6
, c
9
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= ha
36
4a
35
+ ··· 15503a + 1369,
2.42707 × 10
126
u + 2.31275 × 10
127
a
35
+ ··· + 5.97181 × 10
131
a 6.43652 × 10
130
,
1.86950 × 10
127
b 1.04213 × 10
128
a
35
+ ··· 2.85418 × 10
132
a + 3.12198 × 10
131
i
I
u
2
= hu
10
u
9
+ 7u
8
6u
7
+ 17u
6
12u
5
+ 17u
4
8u
3
+ 7u
2
+ 1,
u
9
+ u
8
6u
7
+ 4u
6
11u
5
+ 4u
4
6u
3
u
2
+ a 3,
u
9
+ 2u
8
7u
7
+ 10u
6
16u
5
+ 16u
4
14u
3
+ 9u
2
+ b 4u + 1i
I
u
3
= hu
21
+ 6u
20
+ ··· + 38u + 4, u
20
4u
19
+ ··· + 2b + 7u, u
20
5u
19
+ ··· + 2a 15i
There are 3 irreducible components with 67 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
= ha
36
4a
35
+ · · · 15503a + 1369, 2.43 × 10
126
u + 2.31 × 10
127
a
35
+
· · · + 5.97 × 10
131
a 6.44 × 10
130
, 1.87 × 10
127
b 1.04 × 10
128
a
35
+ · · ·
2.85 × 10
132
a + 3.12 × 10
131
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
9.52901a
35
+ 33.3954a
34
+ ··· 246051.a + 26519.8
a
3
=
9.52901a
35
+ 33.3954a
34
+ ··· 246051.a + 26519.8
9.52901a
35
+ 33.3954a
34
+ ··· 246051.a + 26519.8
a
8
=
a
5.57439a
35
19.7586a
34
+ ··· + 152671.a 16699.6
a
9
=
0.542528a
35
1.75747a
34
+ ··· + 8238.22a 719.648
6.11691a
35
21.5161a
34
+ ··· + 160908.a 17419.2
a
2
=
1.48269a
35
4.86405a
34
+ ··· + 25242.2a 2353.60
0.186336a
35
+ 0.671553a
34
+ ··· 5556.40a + 620.591
a
11
=
1
4.45704a
35
15.8258a
34
+ ··· + 123212.a 13509.1
a
5
=
9.52901a
35
33.3954a
34
+ ··· + 246051.a 26519.8
1.17556a
35
+ 4.58169a
34
+ ··· 48420.5a + 5721.17
a
6
=
7.25548a
35
25.4992a
34
+ ··· + 190123.a 20567.6
2.56392a
35
+ 9.06187a
34
+ ··· 69212.5a + 7543.63
a
10
=
4.45704a
35
+ 15.8258a
34
+ ··· 123212.a + 13510.1
7.72291a
35
27.1751a
34
+ ··· + 203596.a 22054.5
a
7
=
3.20732a
35
11.1727a
34
+ ··· + 80074.8a 8550.71
8.26095a
35
29.0164a
34
+ ··· + 215865.a 23338.1
a
7
=
3.20732a
35
11.1727a
34
+ ··· + 80074.8a 8550.71
8.26095a
35
29.0164a
34
+ ··· + 215865.a 23338.1
(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 = 0.290170 0.487341I
a = 2.72587 0.28499I
b = 0.87751 + 1.13038I
4.89942 3.13958I 1.44626 + 9.70357I
u = 0.290170 + 0.487341I
a = 2.72587 + 0.28499I
b = 0.87751 1.13038I
4.89942 + 3.13958I 1.44626 9.70357I
u = 0.290170 + 0.487341I
a = 0.866656 1.102168I
b = 0.93260 1.90692I
4.89942 0.92019I 1.44626 2.77537I
u = 0.290170 0.487341I
a = 0.866656 + 1.102168I
b = 0.93260 + 1.90692I
4.89942 + 0.92019I 1.44626 + 2.77537I
u = 0.12170 + 1.63384I
a = 0.52669 2.37123I
b = 1.19683 2.69465I
8.52641 7.53037I 5.48937 + 6.43708I
u = 0.12170 1.63384I
a = 0.52669 + 2.37123I
b = 1.19683 + 2.69465I
8.52641 + 7.53037I 5.48937 6.43708I
u = 0.429032 0.787939I
a = 0.498639 0.208516I
b = 0.112451 + 0.938176I
0.22800 + 5.44061I 3.88238 7.86053I
u = 0.429032 + 0.787939I
a = 0.498639 + 0.208516I
b = 0.112451 0.938176I
0.22800 5.44061I 3.88238 + 7.86053I
u = 0.05587 1.55975I
a = 0.48738 3.00167I
b = 1.11493 3.04955I
2.12882 0.18400I 2.24115 0.41812I
u = 0.05587 + 1.55975I
a = 0.48738 + 3.00167I
b = 1.11493 + 3.04955I
2.12882 + 0.18400I 2.24115 + 0.41812I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.12170 1.63384I
a = 0.48633 1.90111I
b = 0.57400 2.74865I
8.52641 + 7.53037I 5.48937 6.43708I
u = 0.12170 + 1.63384I
a = 0.48633 + 1.90111I
b = 0.57400 + 2.74865I
8.52641 7.53037I 5.48937 + 6.43708I
u = 0.590618
a = 0.48409 1.39762I
b = 0.223021 + 0.453223I
2.09801 + 2.02988I 0.33330 3.46410I
u = 0.590618
a = 0.48409 + 1.39762I
b = 0.223021 0.453223I
2.09801 2.02988I 0.33330 + 3.46410I
u = 0.12170 1.63384I
a = 0.14095 1.68072I
b = 0.37335 2.21295I
8.52641 + 3.47060I 5.48937 + 0.49112I
u = 0.12170 + 1.63384I
a = 0.14095 + 1.68072I
b = 0.37335 + 2.21295I
8.52641 3.47060I 5.48937 0.49112I
u = 0.429032 0.787939I
a = 0.081310 0.500133I
b = 0.84102 1.42739I
0.22800 + 5.44061I 3.88238 7.86053I
u = 0.429032 + 0.787939I
a = 0.081310 + 0.500133I
b = 0.84102 + 1.42739I
0.22800 5.44061I 3.88238 + 7.86053I
u = 0.12170 + 1.63384I
a = 0.240328 0.568351I
b = 0.558831 0.706369I
8.52641 3.47060I 5.48937 0.49112I
u = 0.12170 1.63384I
a = 0.240328 + 0.568351I
b = 0.558831 + 0.706369I
8.52641 + 3.47060I 5.48937 + 0.49112I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.429032 0.787939I
a = 0.438961 0.150202I
b = 0.303794 + 0.281335I
0.227995 + 1.380848I 3.88238 0.93232I
u = 0.429032 + 0.787939I
a = 0.438961 + 0.150202I
b = 0.303794 0.281335I
0.227995 1.380848I 3.88238 + 0.93232I
u = 0.429032 + 0.787939I
a = 0.464721 0.002276I
b = 0.250735 0.789002I
0.227995 1.380848I 3.88238 + 0.93232I
u = 0.429032 0.787939I
a = 0.464721 + 0.002276I
b = 0.250735 + 0.789002I
0.227995 + 1.380848I 3.88238 0.93232I
u = 0.290170 + 0.487341I
a = 0.527583 0.825686I
b = 0.90288 + 1.38938I
4.89942 + 3.13958I 1.44626 9.70357I
u = 0.290170 0.487341I
a = 0.527583 + 0.825686I
b = 0.90288 1.38938I
4.89942 3.13958I 1.44626 + 9.70357I
u = 0.05587 + 1.55975I
a = 0.553723 0.003748I
b = 1.66994 + 0.14661I
2.12882 + 0.18400I 2.24115 + 0.41812I
u = 0.05587 1.55975I
a = 0.553723 + 0.003748I
b = 1.66994 0.14661I
2.12882 0.18400I 2.24115 0.41812I
u = 0.05587 + 1.55975I
a = 1.04039 2.46656I
b = 1.86057 3.10678I
2.12882 + 4.24376I 2.24115 6.51008I
u = 0.05587 1.55975I
a = 1.04039 + 2.46656I
b = 1.86057 + 3.10678I
2.12882 4.24376I 2.24115 + 6.51008I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.590618
a = 1.075445 0.373366I
b = 0.269707 0.400207I
2.09801 2.02988I 0.33330 + 3.46410I
u = 0.590618
a = 1.075445 + 0.373366I
b = 0.269707 + 0.400207I
2.09801 + 2.02988I 0.33330 3.46410I
u = 0.05587 1.55975I
a = 1.52271 0.91015I
b = 0.629881 1.028051I
2.12882 4.24376I 2.24115 + 6.51008I
u = 0.05587 + 1.55975I
a = 1.52271 + 0.91015I
b = 0.629881 + 1.028051I
2.12882 + 4.24376I 2.24115 6.51008I
u = 0.290170 + 0.487341I
a = 2.43406 0.53126I
b = 0.266705 + 0.235564I
4.89942 0.92019I 1.44626 2.77537I
u = 0.290170 0.487341I
a = 2.43406 + 0.53126I
b = 0.266705 0.235564I
4.89942 + 0.92019I 1.44626 + 2.77537I
6
II.
I
u
2
= hu
10
u
9
+ · · · + 7u
2
+ 1, u
9
+ u
8
+ · · · + a 3, u
9
+ 2u
8
+ · · · + b + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
u
9
u
8
+ 6u
7
4u
6
+ 11u
5
4u
4
+ 6u
3
+ u
2
+ 3
u
9
2u
8
+ 7u
7
10u
6
+ 16u
5
16u
4
+ 14u
3
9u
2
+ 4u 1
a
9
=
u
9
+ 5u
7
+ u
6
+ 7u
5
+ 3u
4
+ 2u
3
+ 4u
2
+ 4
u
9
u
8
+ 6u
7
5u
6
+ 12u
5
9u
4
+ 10u
3
6u
2
+ 4u
a
2
=
2u
9
+ 2u
8
14u
7
+ 13u
6
34u
5
+ 27u
4
33u
3
+ 17u
2
12u
u
6
u
5
+ 4u
4
3u
3
+ 4u
2
2u + 2
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
6
=
u
8
+ 2u
7
7u
6
+ 10u
5
16u
4
+ 15u
3
14u
2
+ 6u 3
u
9
+ u
8
6u
7
+ 5u
6
12u
5
+ 8u
4
9u
3
+ 3u
2
2u 1
a
10
=
u
2
+ 1
u
4
2u
2
a
7
=
u
9
+ 5u
7
+ u
6
+ 7u
5
+ 4u
4
+ u
3
+ 6u
2
2u + 4
u
9
u
8
+ 6u
7
5u
6
+ 12u
5
8u
4
+ 10u
3
4u
2
+ 4u
a
7
=
u
9
+ 5u
7
+ u
6
+ 7u
5
+ 4u
4
+ u
3
+ 6u
2
2u + 4
u
9
u
8
+ 6u
7
5u
6
+ 12u
5
8u
4
+ 10u
3
4u
2
+ 4u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.114692 0.374125I
a = 3.02225 + 0.37249I
b = 0.05157 1.44536I
4.67120 2.22664I 2.12135 + 1.13341I
u = 0.114692 + 0.374125I
a = 3.02225 0.37249I
b = 0.05157 + 1.44536I
4.67120 + 2.22664I 2.12135 1.13341I
u = 0.106999 1.144161I
a = 0.428067 0.698551I
b = 0.578754 0.547468I
2.18773 + 1.37103I 1.096751 0.038075I
u = 0.106999 + 1.144161I
a = 0.428067 + 0.698551I
b = 0.578754 + 0.547468I
2.18773 1.37103I 1.096751 + 0.038075I
u = 0.03324 1.55527I
a = 0.05488 + 2.02307I
b = 0.86648 + 2.29337I
2.14990 2.75317I 2.40750 + 1.04370I
u = 0.03324 + 1.55527I
a = 0.05488 2.02307I
b = 0.86648 2.29337I
2.14990 + 2.75317I 2.40750 1.04370I
u = 0.15152 1.62547I
a = 0.16406 1.46477I
b = 0.14610 1.82352I
8.73669 + 4.86888I 6.80228 5.06388I
u = 0.15152 + 1.62547I
a = 0.16406 + 1.46477I
b = 0.14610 + 1.82352I
8.73669 4.86888I 6.80228 + 5.06388I
u = 0.603408 0.634582I
a = 0.268621 + 0.232892I
b = 0.014605 + 0.797763I
0.90716 + 2.13686I 9.07211 6.04607I
u = 0.603408 + 0.634582I
a = 0.268621 0.232892I
b = 0.014605 0.797763I
0.90716 2.13686I 9.07211 + 6.04607I
8
III. I
u
3
=
hu
21
+ 6 u
20
+· · ·+38u+4, u
20
4u
19
+· · ·+2b+7u, u
20
5u
19
+· · ·+2a15i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
1
2
u
20
+
5
2
u
19
+ ··· + 41u +
15
2
1
2
u
20
+ 2u
19
+ ···
29
2
u
2
7
2
u
a
9
=
1
2
u
20
+
7
2
u
19
+ ··· + 60u +
19
2
1
2
u
20
+ 3u
19
+ ··· +
31
2
u + 2
a
2
=
3
4
u
20
+ 4u
19
+ ··· +
59
4
u + 2
1
2
u
20
3u
19
+ ···
81
2
u 5
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
6
=
1
4
u
20
+ u
19
+ ···
79
4
u 4
1
2
u
20
+ 2u
19
+ ···
3
2
u 1
a
10
=
u
2
+ 1
u
4
2u
2
a
7
=
1
2
u
19
2u
18
+ ··· +
29
2
u +
7
2
1
2
u
20
3u
19
+ ···
89
2
u
2
15
2
u
a
7
=
1
2
u
19
2u
18
+ ··· +
29
2
u +
7
2
1
2
u
20
3u
19
+ ···
89
2
u
2
15
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.788990 0.182747I
a = 0.923231 0.725785I
b = 0.006021 + 0.677738I
5.88506 + 6.78578I 0.85150 5.15843I
u = 0.788990 + 0.182747I
a = 0.923231 + 0.725785I
b = 0.006021 0.677738I
5.88506 6.78578I 0.85150 + 5.15843I
u = 0.704981 0.576615I
a = 0.583257 0.205867I
b = 0.025162 1.105001I
0.41138 2.40421I 1.72315 + 4.22426I
u = 0.704981 + 0.576615I
a = 0.583257 + 0.205867I
b = 0.025162 + 1.105001I
0.41138 + 2.40421I 1.72315 4.22426I
u = 0.606698 0.777797I
a = 0.237093 + 0.252348I
b = 0.51136 + 1.54659I
4.07842 11.41590I 1.76912 + 8.47188I
u = 0.606698 + 0.777797I
a = 0.237093 0.252348I
b = 0.51136 1.54659I
4.07842 + 11.41590I 1.76912 8.47188I
u = 0.408938 1.208150I
a = 0.421359 0.139261I
b = 0.504647 0.104697I
1.62807 + 2.56050I 4.45468 5.57761I
u = 0.408938 + 1.208150I
a = 0.421359 + 0.139261I
b = 0.504647 + 0.104697I
1.62807 2.56050I 4.45468 + 5.57761I
u = 0.278989
a = 1.88660
b = 0.328214
0.983801 10.3966
u = 0.235220 0.703752I
a = 0.652456 0.376446I
b = 0.052373 1.068349I
2.86823 1.78605I 10.67672 + 1.49019I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.235220 + 0.703752I
a = 0.652456 + 0.376446I
b = 0.052373 + 1.068349I
2.86823 + 1.78605I 10.67672 1.49019I
u = 0.21396 1.58648I
a = 0.51451 + 1.49458I
b = 0.12412 + 1.73304I
6.84048 5.76907I 4.07518 + 4.56239I
u = 0.21396 + 1.58648I
a = 0.51451 1.49458I
b = 0.12412 1.73304I
6.84048 + 5.76907I 4.07518 4.56239I
u = 0.18174 1.63465I
a = 0.08922 2.24092I
b = 0.91061 2.71331I
4.0861 14.4126I 4.28661 + 7.20471I
u = 0.18174 + 1.63465I
a = 0.08922 + 2.24092I
b = 0.91061 + 2.71331I
4.0861 + 14.4126I 4.28661 7.20471I
u = 0.06375 1.61581I
a = 0.30868 + 2.03963I
b = 0.56963 + 2.53669I
10.89630 2.89300I 9.55027 + 0.75508I
u = 0.06375 + 1.61581I
a = 0.30868 2.03963I
b = 0.56963 2.53669I
10.89630 + 2.89300I 9.55027 0.75508I
u = 0.00544 1.65590I
a = 0.298531 1.158784I
b = 0.73909 1.58571I
8.83155 + 2.25669I 7.66847 3.47538I
u = 0.00544 + 1.65590I
a = 0.298531 + 1.158784I
b = 0.73909 + 1.58571I
8.83155 2.25669I 7.66847 + 3.47538I
u = 0.349217 0.697364I
a = 0.478741 0.125041I
b = 0.017720 + 0.499730I
0.19501 + 1.45011I 2.94900 3.15728I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.349217 + 0.697364I
a = 0.478741 + 0.125041I
b = 0.017720 0.499730I
0.19501 1.45011I 2.94900 + 3.15728I
11
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
(u
10
+ 5u
8
u
7
+ 10u
6
3u
5
+ 9u
4
3u
3
+ 4u
2
+ 1)
(u
21
+ 7u
19
+ ··· + 2u 1)(u
36
+ u
35
+ ··· 88u + 121)
c
2
, c
6
(u
10
+ 5u
8
+ u
7
+ 10u
6
+ 3u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ 1)
(u
21
+ 7u
19
+ ··· + 2u 1)(u
36
+ u
35
+ ··· 88u + 121)
c
3
, c
4
(u
9
u
8
+ 6u
7
5u
6
+ 11u
5
7u
4
+ 6u
3
2u
2
+ u 1)
4
(u
10
+ u
9
+ 7u
8
+ 6u
7
+ 17u
6
+ 12u
5
+ 17u
4
+ 8u
3
+ 7u
2
+ 1)
(u
21
+ 6u
20
+ ··· + 38u + 4)
c
5
, c
7
(u
10
+ 3u
7
+ ··· + u + 1)(u
21
6u
19
+ ··· 7u 1)
(u
36
+ 9u
35
+ ··· 8u + 1)
c
9
(u
2
u + 1)
18
(u
10
u
9
+ u
8
4u
7
+ 3u
6
+ 3u
4
3u
3
+ 1)
(u
21
+ 18u
20
+ ··· + 4352u + 512)
c
10
, c
11
(u
9
u
8
+ 6u
7
5u
6
+ 11u
5
7u
4
+ 6u
3
2u
2
+ u 1)
4
(u
10
u
9
+ 7u
8
6u
7
+ 17u
6
12u
5
+ 17u
4
8u
3
+ 7u
2
+ 1)
(u
21
+ 6u
20
+ ··· + 38u + 4)
12
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
c
8
(y
10
+ 10y
9
+ ··· + 8y + 1)(y
21
+ 14y
20
+ ··· + 12y
2
1)
(y
36
+ 27y
35
+ ··· + 187308y + 14641)
c
3
, c
4
, c
10
c
11
(y
9
+ 11y
8
+ 48y
7
+ 105y
6
+ 121y
5
+ 73y
4
+ 20y
3
6y
2
3y 1)
4
(y
10
+ 13y
9
+ ··· + 14y + 1)(y
21
+ 24y
20
+ ··· + 108y 16)
c
5
, c
7
(y
10
+ 6y
8
3y
7
+ 11y
6
4y
5
+ 9y
4
4y
3
y
2
+ y + 1)
(y
21
12y
20
+ ··· + 27y 1)(y
36
+ 3y
35
+ ··· 44y + 1)
c
9
(y
2
+ y + 1)
18
(y
10
+ y
9
+ ··· + 6y
2
+ 1)
(y
21
+ 2y
20
+ ··· + 65536y 262144)
13