11a
202
(K11a
202
)
1
Arc Sequences
7 1 9 8 11 2 5 3 4 6 10
Solving Sequence
4,9 10,11
1 3 2 8 5 6 7
c
9
c
11
c
3
c
2
c
8
c
4
c
5
c
7
c
1
, c
6
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hu
6
3u
4
+ 2u
2
+ 1, u
4
+ u
3
+ 2u
2
+ a u, u
5
+ u
4
+ 2u
3
2u
2
+ b ui
I
u
2
= hb
36
5b
35
+ ··· + 28312b + 272143,
7.29623 × 10
154
u 9.76176 × 10
148
b
35
+ ··· + 5.36790 × 10
154
b + 1.81429 × 10
154
,
1.16057 × 10
151
b
35
5.41827 × 10
151
b
34
+ ··· + 6.49365 × 10
156
a + 1.00449 × 10
156
i
I
u
3
= hu
25
+ 3u
24
+ ··· u + 2, 3u
24
+ 5u
23
+ ··· + b + 5, 5u
24
9u
23
+ ··· + 2a 7i
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
= hu
6
3u
4
+2u
2
+1, u
4
+u
3
+2u
2
+a u, u
5
+u
4
+2u
3
2u
2
+b ui
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
10
=
u
u
a
11
=
u
4
u
3
2u
2
+ u
u
5
u
4
2u
3
+ 2u
2
+ u
a
1
=
u
4
u
3
2u
2
+ 2u
u
5
u
4
2u
3
+ 2u
2
a
3
=
1
u
2
a
2
=
u
4
u
3
2u
2
+ 2u + 1
u
5
u
4
2u
3
+ u
2
a
8
=
u
u
3
+ u
a
5
=
u
4
+ u
2
+ 1
u
4
u
2
1
a
6
=
u
3
u
2
u + 1
u
4
u
3
u
2
+ u
a
7
=
u
5
2u
3
+ u
u
5
+ u
3
+ u
a
7
=
u
5
2u
3
+ u
u
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 = 1.307141 0.215080I
a = 0.13258 + 1.62230I
b = 0.87744 1.74486I
6.31400 2.82812I 11.50976 + 2.97945I
u = 1.307141 + 0.215080I
a = 0.13258 1.62230I
b = 0.87744 + 1.74486I
6.31400 + 2.82812I 11.50976 2.97945I
u = 0.569840I
a = 0.754878 0.754878I
b = 0.754878 1.000000I
2.17641 4.98049
u = 0.569840I
a = 0.754878 + 0.754878I
b = 0.754878 + 1.000000I
2.17641 4.98049
u = 1.307141 0.215080I
a = 1.62230 + 0.13258I
b = 0.877439 0.255138I
6.31400 + 2.82812I 11.50976 2.97945I
u = 1.307141 + 0.215080I
a = 1.62230 0.13258I
b = 0.877439 + 0.255138I
6.31400 2.82812I 11.50976 + 2.97945I
3
II. I
u
2
= hb
36
5b
35
+ · · · + 28312b + 272143, 7.30 × 10
154
u 9.76 ×
10
148
b
35
+ · · · + 5.37 × 10
154
b + 1.81 × 10
154
, 1.16 × 10
151
b
35
5.42 ×
10
151
b
34
+ · · · + 6.49 × 10
156
a + 1.00 × 10
156
i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
1.33792 × 10
6
b
35
7.59962 × 10
6
b
34
+ ··· 0.735708b 0.248661
a
10
=
1.33792 × 10
6
b
35
+ 7.59962 × 10
6
b
34
+ ··· + 0.735708b + 0.248661
1.33792 × 10
6
b
35
7.59962 × 10
6
b
34
+ ··· 0.735708b 0.248661
a
11
=
1.78724 × 10
6
b
35
+ 8.34395 × 10
6
b
34
+ ··· 2.14871b 0.154688
b
a
1
=
3.61389 × 10
7
b
35
3.42712 × 10
6
b
34
+ ··· 0.648957b + 0.706697
2.14863 × 10
6
b
35
+ 0.0000117711b
34
+ ··· 0.499753b 0.861385
a
3
=
1
1.92446 × 10
7
b
35
+ 1.12751 × 10
6
b
34
+ ··· 0.0566463b 0.993388
a
2
=
3.33933 × 10
7
b
35
+ 2.72468 × 10
6
b
34
+ ··· + 2.11009b + 1.27783
1.33801 × 10
7
b
35
1.58571 × 10
6
b
34
+ ··· 1.13996b + 0.0345305
a
8
=
1.33792 × 10
6
b
35
7.59962 × 10
6
b
34
+ ··· 0.735708b 0.248661
1.78355 × 10
6
b
35
+ 9.79256 × 10
6
b
34
+ ··· + 0.176891b 0.0771826
a
5
=
7.10757 × 10
7
b
35
+ 5.44376 × 10
6
b
34
+ ··· + 1.60458b + 0.141925
1.03956 × 10
6
b
35
6.68624 × 10
6
b
34
+ ··· 1.96402b 0.341187
a
6
=
1.47070 × 10
6
b
35
+ 0.0000102005b
34
+ ··· + 1.40557b + 0.183703
3.32688 × 10
6
b
35
0.0000198202b
34
+ ··· 2.42200b 0.177914
a
7
=
1.79966 × 10
6
b
35
0.0000110889b
34
+ ··· 0.179053b + 1.41117
1.78802 × 10
6
b
35
+ 0.0000111003b
34
+ ··· + 1.95565b 0.585223
a
7
=
1.79966 × 10
6
b
35
0.0000110889b
34
+ ··· 0.179053b + 1.41117
1.78802 × 10
6
b
35
+ 0.0000111003b
34
+ ··· + 1.95565b 0.585223
(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 = 1.333562 0.360812I
a = 1.40914 + 2.47472I
b = 2.17073 1.60538I
0.60037 + 9.13509I 2.98695 5.86478I
u = 1.333562 + 0.360812I
a = 1.40914 2.47472I
b = 2.17073 + 1.60538I
0.60037 9.13509I 2.98695 + 5.86478I
u = 0.064741 0.739221I
a = 0.857216 + 0.236658I
b = 2.00838 0.88685I
0.86368 + 1.88569I 1.68331 3.99357I
u = 0.064741 + 0.739221I
a = 0.857216 0.236658I
b = 2.00838 + 0.88685I
0.86368 1.88569I 1.68331 + 3.99357I
u = 1.160032 + 0.371279I
a = 1.49054 + 1.88439I
b = 1.48494 0.71912I
1.85527 0.55896I 1.51114 0.25710I
u = 1.160032 0.371279I
a = 1.49054 1.88439I
b = 1.48494 + 0.71912I
1.85527 + 0.55896I 1.51114 + 0.25710I
u = 0.099390 + 0.822674I
a = 0.194555 0.598815I
b = 1.204716 0.060446I
5.09742 + 4.87394I 1.52680 3.60136I
u = 0.099390 0.822674I
a = 0.194555 + 0.598815I
b = 1.204716 + 0.060446I
5.09742 4.87394I 1.52680 + 3.60136I
u = 1.354281 0.099636I
a = 0.246279 + 0.653564I
b = 0.934430 0.141070I
5.44315 + 3.22673I 7.05526 3.62956I
u = 1.354281 + 0.099636I
a = 0.246279 0.653564I
b = 0.934430 + 0.141070I
5.44315 3.22673I 7.05526 + 3.62956I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.424636 0.422216I
a = 0.166359 0.244978I
b = 0.588599 0.366257I
0.06375 1.57187I 1.80878 + 4.22070I
u = 0.424636 + 0.422216I
a = 0.166359 + 0.244978I
b = 0.588599 + 0.366257I
0.06375 + 1.57187I 1.80878 4.22070I
u = 0.361873
a = 2.56614 + 1.89218I
b = 0.399690 0.777849I
3.91179 11.9800
u = 0.361873
a = 2.56614 1.89218I
b = 0.399690 + 0.777849I
3.91179 11.9800
u = 1.232890 0.279362I
a = 0.87324 + 1.22774I
b = 0.38174 1.40962I
4.41864 + 1.78695I 5.23943 + 0.02251I
u = 1.232890 + 0.279362I
a = 0.87324 1.22774I
b = 0.38174 + 1.40962I
4.41864 1.78695I 5.23943 0.02251I
u = 1.311619 0.317206I
a = 1.07366 + 1.11074I
b = 0.05295 1.74084I
5.17867 5.71427I 7.06596 + 6.05983I
u = 1.311619 + 0.317206I
a = 1.07366 1.11074I
b = 0.05295 + 1.74084I
5.17867 + 5.71427I 7.06596 6.05983I
u = 1.160032 0.371279I
a = 0.377885 + 1.210747I
b = 0.184198 0.414383I
1.85527 + 0.55896I 1.51114 + 0.25710I
u = 1.160032 + 0.371279I
a = 0.377885 1.210747I
b = 0.184198 + 0.414383I
1.85527 0.55896I 1.51114 0.25710I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.064741 0.739221I
a = 0.050120 0.809420I
b = 0.20114 1.41506I
0.86368 + 1.88569I 1.68331 3.99357I
u = 0.064741 + 0.739221I
a = 0.050120 + 0.809420I
b = 0.20114 + 1.41506I
0.86368 1.88569I 1.68331 + 3.99357I
u = 0.424636 0.422216I
a = 1.025181 + 0.809485I
b = 0.340053 0.339838I
0.06375 1.57187I 1.80878 + 4.22070I
u = 0.424636 + 0.422216I
a = 1.025181 0.809485I
b = 0.340053 + 0.339838I
0.06375 + 1.57187I 1.80878 4.22070I
u = 1.354281 0.099636I
a = 1.164527 + 0.252275I
b = 1.40470 0.41204I
5.44315 + 3.22673I 7.05526 3.62956I
u = 1.354281 + 0.099636I
a = 1.164527 0.252275I
b = 1.40470 + 0.41204I
5.44315 3.22673I 7.05526 + 3.62956I
u = 1.311619 0.317206I
a = 0.85226 + 3.18875I
b = 1.49141 2.61785I
5.17867 5.71427I 7.06596 + 6.05983I
u = 1.311619 + 0.317206I
a = 0.85226 3.18875I
b = 1.49141 + 2.61785I
5.17867 + 5.71427I 7.06596 6.05983I
u = 1.333562 + 0.360812I
a = 1.20305 + 1.27723I
b = 1.83682 0.93179I
0.60037 9.13509I 2.98695 + 5.86478I
u = 1.333562 0.360812I
a = 1.20305 1.27723I
b = 1.83682 + 0.93179I
0.60037 + 9.13509I 2.98695 5.86478I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.34147
a = 1.02663 + 1.26909I
b = 1.93594 0.69913I
9.12242 12.3720
u = 1.34147
a = 1.02663 1.26909I
b = 1.93594 + 0.69913I
9.12242 12.3720
u = 1.232890 + 0.279362I
a = 2.26153 + 1.71381I
b = 2.09907 1.16052I
4.41864 1.78695I 5.23943 0.02251I
u = 1.232890 0.279362I
a = 2.26153 1.71381I
b = 2.09907 + 1.16052I
4.41864 + 1.78695I 5.23943 + 0.02251I
u = 0.099390 0.822674I
a = 0.355080 0.062875I
b = 2.12693 0.43784I
5.09742 4.87394I 1.52680 + 3.60136I
u = 0.099390 + 0.822674I
a = 0.355080 + 0.062875I
b = 2.12693 + 0.43784I
5.09742 + 4.87394I 1.52680 3.60136I
8
III.
I
u
3
= hu
25
+3u
24
+· · ·−u+2, 3u
24
+5u
23
+· · ·+b+5, 5u
24
9u
23
+· · ·+2a7i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
10
=
u
u
a
11
=
5
2
u
24
+
9
2
u
23
+ ···
9
2
u +
7
2
3u
24
5u
23
+ ··· + 7u 5
a
1
=
7
2
u
24
+
13
2
u
23
+ ···
13
2
u +
11
2
4u
24
7u
23
+ ··· + 9u 7
a
3
=
1
u
2
a
2
=
5
2
u
24
9
2
u
23
+ ··· +
7
2
u
5
2
3u
24
+ 5u
23
+ ··· 6u + 5
a
8
=
u
u
3
+ u
a
5
=
u
4
+ u
2
+ 1
u
6
2u
4
+ u
2
a
6
=
3
2
u
24
+
5
2
u
23
+ ···
5
2
u +
5
2
u
24
2u
23
+ ··· + u 1
a
7
=
u
7
2u
5
+ 2u
u
9
+ 3u
7
3u
5
+ u
a
7
=
u
7
2u
5
+ 2u
u
9
+ 3u
7
3u
5
+ 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 = 1.41996 0.07613I
a = 0.692965 + 0.210949I
b = 1.38435 + 0.56025I
7.78094 7.61728I 9.88218 + 7.10707I
u = 1.41996 + 0.07613I
a = 0.692965 0.210949I
b = 1.38435 0.56025I
7.78094 + 7.61728I 9.88218 7.10707I
u = 1.383168 0.239298I
a = 1.159727 + 0.740431I
b = 0.76363 1.37726I
5.69008 0.51087I 7.53558 3.07532I
u = 1.383168 + 0.239298I
a = 1.159727 0.740431I
b = 0.76363 + 1.37726I
5.69008 + 0.51087I 7.53558 + 3.07532I
u = 1.359098 0.357240I
a = 1.73754 + 2.48812I
b = 2.67364 1.62621I
1.8285 14.8711I 5.98898 + 9.38448I
u = 1.359098 + 0.357240I
a = 1.73754 2.48812I
b = 2.67364 + 1.62621I
1.8285 + 14.8711I 5.98898 9.38448I
u = 1.293346 0.365041I
a = 1.38394 1.39554I
b = 1.87489 + 0.82706I
2.21088 3.50071I 0.821092 + 0.986963I
u = 1.293346 + 0.365041I
a = 1.38394 + 1.39554I
b = 1.87489 0.82706I
2.21088 + 3.50071I 0.821092 0.986963I
u = 1.22317
a = 0.807619
b = 1.07819
2.64205 1.56218
u = 0.200761 0.437718I
a = 0.534109 + 0.227055I
b = 0.019513 0.393038I
0.015654 1.044502I 0.46434 + 6.95411I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.200761 + 0.437718I
a = 0.534109 0.227055I
b = 0.019513 + 0.393038I
0.015654 + 1.044502I 0.46434 6.95411I
u = 0.039360 0.824168I
a = 0.240613 + 0.474652I
b = 1.48748 0.14719I
6.36489 0.77404I 3.16430 + 2.08441I
u = 0.039360 + 0.824168I
a = 0.240613 0.474652I
b = 1.48748 + 0.14719I
6.36489 + 0.77404I 3.16430 2.08441I
u = 0.143356 0.825680I
a = 0.299387 0.283522I
b = 2.24518 0.45279I
2.90521 + 10.60793I 1.48456 7.66724I
u = 0.143356 + 0.825680I
a = 0.299387 + 0.283522I
b = 2.24518 + 0.45279I
2.90521 10.60793I 1.48456 + 7.66724I
u = 0.308716 0.611993I
a = 0.185057 0.547298I
b = 0.678982 0.816105I
0.38145 2.56549I 2.38682 + 2.55463I
u = 0.308716 + 0.611993I
a = 0.185057 + 0.547298I
b = 0.678982 + 0.816105I
0.38145 + 2.56549I 2.38682 2.55463I
u = 0.607665 0.412689I
a = 1.03539 + 1.20606I
b = 0.641715 0.418679I
1.35523 + 6.21788I 4.83403 8.18700I
u = 0.607665 + 0.412689I
a = 1.03539 1.20606I
b = 0.641715 + 0.418679I
1.35523 6.21788I 4.83403 + 8.18700I
u = 1.093165 0.381251I
a = 1.38711 1.97234I
b = 1.169580 + 0.560138I
0.00199 6.23078I 4.13739 + 4.00981I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.093165 + 0.381251I
a = 1.38711 + 1.97234I
b = 1.169580 0.560138I
0.00199 + 6.23078I 4.13739 4.00981I
u = 1.226681 0.374932I
a = 0.54037 + 1.67032I
b = 0.651612 0.795102I
2.70416 + 5.08779I 0.84739 5.77549I
u = 1.226681 + 0.374932I
a = 0.54037 1.67032I
b = 0.651612 + 0.795102I
2.70416 5.08779I 0.84739 + 5.77549I
u = 1.348971 0.191132I
a = 0.662774 + 0.364138I
b = 0.341623 0.269136I
4.86135 + 3.43962I 5.00084 5.92088I
u = 1.348971 + 0.191132I
a = 0.662774 0.364138I
b = 0.341623 + 0.269136I
4.86135 3.43962I 5.00084 + 5.92088I
12
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
, c
6
c
10
(u
2
+ 1)
3
(u
25
+ 5u
23
+ ··· + 5u
2
+ 1)(u
36
+ u
35
+ ··· + 2u + 5)
c
2
, c
11
(u + 1)
6
(u
25
+ 10u
24
+ ··· 10u 1)(u
36
+ 19u
35
+ ··· + 136u + 25)
c
3
, c
8
, c
9
(u
6
3u
4
+ 2u
2
+ 1)
(1 + u + 3u
2
+ 6u
3
14u
6
16u
7
+ 13u
8
+ 11u
9
+ 11u
10
+ 8u
11
27u
12
13u
13
+ 20u
14
+ 6u
15
7u
16
u
17
+ u
18
)
2
(u
25
+ 3u
24
+ ··· u + 2)
c
4
, c
7
(u
6
+ u
4
+ 2u
2
+ 1)
(3 3u 11u
2
+ 44u
3
90u
4
+ 138u
5
144u
6
+ 126u
7
59u
8
5u
9
+ 61u
10
86u
11
+ 85u
12
65u
13
+ 44u
14
22u
15
+ 11u
16
3u
17
+ u
18
)
2
(u
25
+ 9u
24
+ ··· + 151u + 22)
13
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
, c
6
c
10
(y + 1)
6
(y
25
+ 10y
24
+ ··· 10y 1)(y
36
+ 19y
35
+ ··· + 136y + 25)
c
2
, c
11
(y 1)
6
(y
25
+ 18y
24
+ ··· + 6y 1)(y
36
5y
35
+ ··· + 4204y + 625)
c
3
, c
8
, c
9
(y
3
3y
2
+ 2y + 1)
2
(1 7y 3y
2
8y
3
78y
4
+ 226y
5
+ 168y
6
892y
7
+ 491y
8
+ 1063y
9
1715y
10
+ 536y
11
+ 1003y
12
1451y
13
+ 972y
14
396y
15
+ 101y
16
15y
17
+ y
18
)
2
(y
25
21y
24
+ ··· 19y 4)
c
4
, c
7
(y
3
+ y
2
+ 2y + 1)
2
(9 75y 155y
2
+ 8y
3
474y
4
2578y
5
4328y
6
2912y
7
+ 295y
8
+ 1671y
9
+ 873y
10
+ 156y
11
+ 363y
12
+ 665y
13
+ 552y
14
+ 264y
15
+ 77y
16
+ 13y
17
+ y
18
)
2
(y
25
+ 15y
24
+ ··· 563y 484)
14