11n
154
(K11n
154
)
1
Arc Sequences
10 9 1 2 9 10 3 11 6 4 8
Solving Sequence
1,4 3,8
7 11 9 2 5 10 6
c
3
c
7
c
11
c
8
c
2
c
4
c
10
c
6
c
1
, c
5
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
11
5u
10
+ 11u
9
11u
8
+ 2u
7
+ 6u
6
u
5
10u
4
+ 13u
3
8u
2
+ 4u 1,
3u
10
13u
9
+ 22u
8
11u
7
11u
6
+ 9u
5
+ 16u
4
34u
3
+ 16u
2
+ 9a 13u + 8,
11u
10
52u
9
+ 102u
8
75u
7
28u
6
+ 70u
5
+ 25u
4
124u
3
+ 94u
2
+ 9b 30u + 16i
I
u
2
= hu
50
+ 6u
49
+ ··· 10u 1, 1.91068 × 10
122
u
49
+ 1.06950 × 10
123
u
48
+ ··· + 1.08866 × 10
122
b 4.93127 × 10
122
,
4.09914 × 10
122
u
49
+ 2.36903 × 10
123
u
48
+ ··· + 1.08866 × 10
122
a 1.10079 × 10
123
i
There are 2 irreducible components with 61 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
11
5u
10
+· · ·+4u1, 3u
10
13u
9
+· · ·+9a+8, 11u
10
52u
9
+· · ·+9b+16i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
1
3
u
10
+
13
9
u
9
+ ··· +
13
9
u
8
9
1.22222u
10
+ 5.77778u
9
+ ··· + 3.33333u 1.77778
a
7
=
u 1
8
9
u
10
+
13
3
u
9
+ ··· +
26
9
u
17
9
a
11
=
4
3
u
10
49
9
u
9
+ ···
22
9
u +
17
9
20
9
u
10
92
9
u
9
+ ···
103
9
u +
13
3
a
9
=
2.22222u
10
+ 9.88889u
9
+ ··· + 8.11111u 3.66667
2.77778u
10
+ 11.7778u
9
+ ··· + 8.55556u 5.66667
a
2
=
u
10
+ 5u
9
11u
8
+ 11u
7
2u
6
6u
5
+ u
4
+ 10u
3
13u
2
+ 8u 3
16
9
u
10
+ 8u
9
+ ··· +
28
9
u
22
9
a
5
=
u
10
5u
9
+ 11u
8
11u
7
+ 2u
6
+ 6u
5
u
4
10u
3
+ 13u
2
7u + 2
8
9
u
10
32
9
u
9
+ ··· +
23
9
u +
2
3
a
10
=
4
3
u
10
49
9
u
9
+ ···
22
9
u +
17
9
4
3
u
10
56
9
u
9
+ ···
71
9
u +
28
9
a
6
=
8
9
u
10
+
13
3
u
9
+ ··· +
26
9
u
26
9
1.88889u
10
+ 9.33333u
9
+ ··· + 10.8889u 5.88889
a
6
=
8
9
u
10
+
13
3
u
9
+ ··· +
26
9
u
26
9
1.88889u
10
+ 9.33333u
9
+ ··· + 10.8889u 5.88889
(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 = 0.907065 0.482893I
a = 1.12977 2.41843I
b = 0.020109 0.784320I
3.59148 + 3.42396I 7.58514 2.00100I
u = 0.907065 + 0.482893I
a = 1.12977 + 2.41843I
b = 0.020109 + 0.784320I
3.59148 3.42396I 7.58514 + 2.00100I
u = 0.034581 0.558517I
a = 0.653857 0.089591I
b = 0.518242 + 1.273744I
0.70704 + 4.35639I 5.54956 2.55288I
u = 0.034581 + 0.558517I
a = 0.653857 + 0.089591I
b = 0.518242 1.273744I
0.70704 4.35639I 5.54956 + 2.55288I
u = 0.462846
a = 0.315741
b = 1.34929
2.78763 26.4318
u = 0.665847 1.061959I
a = 0.161058 0.461470I
b = 0.230973 0.394144I
1.14703 + 2.08475I 5.67789 + 0.04134I
u = 0.665847 + 1.061959I
a = 0.161058 + 0.461470I
b = 0.230973 + 0.394144I
1.14703 2.08475I 5.67789 0.04134I
u = 1.031027 0.486960I
a = 0.45525 1.64103I
b = 0.437570 1.329177I
7.66458 + 5.46030I 13.6502 4.8917I
u = 1.031027 + 0.486960I
a = 0.45525 + 1.64103I
b = 0.437570 + 1.329177I
7.66458 5.46030I 13.6502 + 4.8917I
u = 1.44419 1.05504I
a = 0.352698 + 1.161276I
b = 0.383107 + 1.187944I
3.96271 + 5.00716I 8.32130 5.65788I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.44419 + 1.05504I
a = 0.352698 1.161276I
b = 0.383107 1.187944I
3.96271 5.00716I 8.32130 + 5.65788I
3
II. I
u
2
=
hu
50
+6u
49
+· · ·10u1, 1.91×10
122
u
49
+1.07×10
123
u
48
+· · ·+1.09×10
122
b
4.93×10
122
, 4.10×10
122
u
49
+2.37×10
123
u
48
+· · ·+1.09×10
122
a1.10×10
123
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
3.76532u
49
21.7611u
48
+ ··· + 95.5470u + 10.1115
1.75509u
49
9.82402u
48
+ ··· + 30.7219u + 4.52969
a
7
=
3.70486u
49
21.5151u
48
+ ··· + 96.3137u + 9.98713
1.69463u
49
9.57803u
48
+ ··· + 31.4887u + 4.40534
a
11
=
2.87909u
49
16.6872u
48
+ ··· + 98.9816u + 15.7072
1.99588u
49
11.4515u
48
+ ··· + 45.9619u + 6.80576
a
9
=
3.92869u
49
22.7917u
48
+ ··· + 110.033u + 16.0938
2.24734u
49
12.8976u
48
+ ··· + 51.6966u + 8.52481
a
2
=
3.12403u
49
+ 17.9147u
48
+ ··· 47.6357u 5.77808
0.735701u
49
+ 4.32144u
48
+ ··· 16.9366u 3.27422
a
5
=
1.23719u
49
7.33851u
48
+ ··· 0.469102u 4.62782
0.605524u
49
+ 3.75354u
48
+ ··· 22.8919u 3.61928
a
10
=
2.87909u
49
16.6872u
48
+ ··· + 98.9816u + 15.7072
1.78476u
49
10.2503u
48
+ ··· + 42.9678u + 6.21845
a
6
=
6.02323u
49
34.3828u
48
+ ··· + 110.458u + 15.8948
2.89921u
49
16.4680u
48
+ ··· + 62.8219u + 10.1167
a
6
=
6.02323u
49
34.3828u
48
+ ··· + 110.458u + 15.8948
2.89921u
49
16.4680u
48
+ ··· + 62.8219u + 10.1167
(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 = 1.53963 0.45016I
a = 0.049432 1.398220I
b = 0.102082 0.559436I
4.40850 + 3.12436I 2.73276 0.73172I
u = 1.53963 + 0.45016I
a = 0.049432 + 1.398220I
b = 0.102082 + 0.559436I
4.40850 3.12436I 2.73276 + 0.73172I
u = 1.27204 1.13444I
a = 0.214262 0.848452I
b = 0.423936 0.983882I
2.51794 + 0.16160I 1.33532 1.94511I
u = 1.27204 + 1.13444I
a = 0.214262 + 0.848452I
b = 0.423936 + 0.983882I
2.51794 0.16160I 1.33532 + 1.94511I
u = 1.22306 1.13574I
a = 0.528144 1.273648I
b = 0.60370 1.30284I
2.0157 15.3090I 4.46240 + 8.38118I
u = 1.22306 + 1.13574I
a = 0.528144 + 1.273648I
b = 0.60370 + 1.30284I
2.0157 + 15.3090I 4.46240 8.38118I
u = 1.081523 0.102902I
a = 0.15948 + 1.42065I
b = 0.283575 + 0.175769I
4.33842 3.23438I 0.09511 + 2.92284I
u = 1.081523 + 0.102902I
a = 0.15948 1.42065I
b = 0.283575 0.175769I
4.33842 + 3.23438I 0.09511 2.92284I
u = 1.04595 1.79042I
a = 0.106428 + 0.736069I
b = 0.323910 + 0.989581I
2.93158 + 5.78038I 1.50121 8.73361I
u = 1.04595 + 1.79042I
a = 0.106428 0.736069I
b = 0.323910 0.989581I
2.93158 5.78038I 1.50121 + 8.73361I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.97631 1.05986I
a = 0.64202 + 1.35591I
b = 0.59853 + 1.28483I
3.11102 8.02113I 2.81085 + 4.67335I
u = 0.97631 + 1.05986I
a = 0.64202 1.35591I
b = 0.59853 1.28483I
3.11102 + 8.02113I 2.81085 4.67335I
u = 0.863850 0.919754I
a = 0.0315060 + 0.0514867I
b = 1.129109 + 0.166305I
5.57747 9.21703I 1.51068 + 6.40591I
u = 0.863850 + 0.919754I
a = 0.0315060 0.0514867I
b = 1.129109 0.166305I
5.57747 + 9.21703I 1.51068 6.40591I
u = 0.784079 0.425120I
a = 0.58176 1.98666I
b = 0.459135 1.324361I
7.03500 5.35259I 0.40790 + 2.69920I
u = 0.784079 + 0.425120I
a = 0.58176 + 1.98666I
b = 0.459135 + 1.324361I
7.03500 + 5.35259I 0.40790 2.69920I
u = 0.721102 0.076207I
a = 0.269661 + 1.284572I
b = 0.18454 + 1.61881I
0.48592 3.61316I 11.87324 + 6.13030I
u = 0.721102 + 0.076207I
a = 0.269661 1.284572I
b = 0.18454 1.61881I
0.48592 + 3.61316I 11.87324 6.13030I
u = 0.617006 0.939363I
a = 0.0421095 + 0.0728972I
b = 1.119410 0.176516I
6.57814 2.00021I 0.63963 + 2.37590I
u = 0.617006 + 0.939363I
a = 0.0421095 0.0728972I
b = 1.119410 + 0.176516I
6.57814 + 2.00021I 0.63963 2.37590I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.431275 0.746619I
a = 2.16742 0.31781I
b = 0.325554 + 1.076705I
1.55527 5.89362I 2.34044 + 9.51760I
u = 0.431275 + 0.746619I
a = 2.16742 + 0.31781I
b = 0.325554 1.076705I
1.55527 + 5.89362I 2.34044 9.51760I
u = 0.401073 0.155532I
a = 0.42640 + 2.84358I
b = 0.294510 + 1.030321I
0.74993 1.80678I 3.40421 + 3.27437I
u = 0.401073 + 0.155532I
a = 0.42640 2.84358I
b = 0.294510 1.030321I
0.74993 + 1.80678I 3.40421 3.27437I
u = 0.261521
a = 1.36888
b = 1.17840
2.53971 7.57060
u = 0.082594 0.285227I
a = 9.28961 0.70843I
b = 0.149996 + 0.729770I
4.11263 + 3.83167I 4.49809 8.58455I
u = 0.082594 + 0.285227I
a = 9.28961 + 0.70843I
b = 0.149996 0.729770I
4.11263 3.83167I 4.49809 + 8.58455I
u = 0.040265 0.990110I
a = 0.916993 + 0.931185I
b = 0.323778 0.896681I
3.30459 + 1.24081I 0.684565 + 0.879327I
u = 0.040265 + 0.990110I
a = 0.916993 0.931185I
b = 0.323778 + 0.896681I
3.30459 1.24081I 0.684565 0.879327I
u = 0.192893 0.438728I
a = 0.612998 + 1.145046I
b = 0.514286 0.690679I
0.24228 + 2.13866I 2.49155 4.03852I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.192893 + 0.438728I
a = 0.612998 1.145046I
b = 0.514286 + 0.690679I
0.24228 2.13866I 2.49155 + 4.03852I
u = 0.347527 0.539174I
a = 0.436133 0.900398I
b = 0.81984 1.43888I
0.94420 + 4.84658I 1.3381 16.7858I
u = 0.347527 + 0.539174I
a = 0.436133 + 0.900398I
b = 0.81984 + 1.43888I
0.94420 4.84658I 1.3381 + 16.7858I
u = 0.390115 0.705973I
a = 0.226441 + 0.462282I
b = 0.716882 0.293195I
1.06170 + 1.95789I 2.50049 3.97543I
u = 0.390115 + 0.705973I
a = 0.226441 0.462282I
b = 0.716882 + 0.293195I
1.06170 1.95789I 2.50049 + 3.97543I
u = 0.450091 0.388693I
a = 0.592049 1.187164I
b = 0.657533 0.689664I
1.86387 + 0.30095I 9.64984 1.90143I
u = 0.450091 + 0.388693I
a = 0.592049 + 1.187164I
b = 0.657533 + 0.689664I
1.86387 0.30095I 9.64984 + 1.90143I
u = 0.58736 1.29973I
a = 0.336110 + 0.275304I
b = 0.087484 + 0.879750I
2.08438 + 2.77960I 10.17164 4.44197I
u = 0.58736 + 1.29973I
a = 0.336110 0.275304I
b = 0.087484 0.879750I
2.08438 2.77960I 10.17164 + 4.44197I
u = 0.692125 0.943636I
a = 0.303313 + 0.028753I
b = 0.418826 0.235678I
0.60147 + 2.63277I 0.64260 6.35036I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.692125 + 0.943636I
a = 0.303313 0.028753I
b = 0.418826 + 0.235678I
0.60147 2.63277I 0.64260 + 6.35036I
u = 0.696313
a = 0.662355
b = 0.625933
1.37116 7.85667
u = 1.14329 1.09191I
a = 0.68075 + 1.34500I
b = 0.400793 + 1.100981I
3.04563 + 6.16036I 5.83312 10.36352I
u = 1.14329 + 1.09191I
a = 0.68075 1.34500I
b = 0.400793 1.100981I
3.04563 6.16036I 5.83312 + 10.36352I
u = 1.25934 1.09160I
a = 0.276299 1.103953I
b = 0.387271 1.317644I
3.78607 + 5.93938I 6.42894 12.06653I
u = 1.25934 + 1.09160I
a = 0.276299 + 1.103953I
b = 0.387271 + 1.317644I
3.78607 5.93938I 6.42894 + 12.06653I
u = 1.34578 0.61803I
a = 0.05256 1.55463I
b = 0.226733 1.148504I
4.23706 + 3.34809I 10.42134 1.19861I
u = 1.34578 + 0.61803I
a = 0.05256 + 1.55463I
b = 0.226733 + 1.148504I
4.23706 3.34809I 10.42134 + 1.19861I
u = 1.45385 0.77080I
a = 0.460759 + 1.081022I
b = 0.467468 + 1.179723I
4.51765 + 4.23526I 12.34564 0.73227I
u = 1.45385 + 0.77080I
a = 0.460759 1.081022I
b = 0.467468 1.179723I
4.51765 4.23526I 12.34564 + 0.73227I
9
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
11
+ u
10
u
9
4u
8
+ u
6
2u
5
3u
4
+ 3u
3
+ 2u
2
u 1)
(u
50
+ 8u
49
+ ··· 87u + 71)
c
2
(u
11
+ u
10
+ 2u
9
+ 4u
8
2u
7
+ u
6
2u
5
9u
4
+ 9u
3
+ 2u
2
4u + 1)
(u
50
+ 2u
49
+ ··· + 314u + 193)
c
3
(u
11
+ 5u
10
+ ··· + 4u + 1)(u
50
+ 6u
49
+ ··· 10u 1)
c
4
(u
11
6u
10
+ ··· + 4u 1)(u
50
+ 5u
49
+ ··· 304u + 403)
c
5
(u
11
+ u
10
3u
9
3u
8
+ 4u
7
+ 4u
6
7u
5
6u
4
+ 7u
3
+ 4u
2
2u 1)
(u
50
+ 4u
49
+ ··· 6u + 1)
c
6
(u
11
+ u
10
3u
9
3u
8
+ 4u
7
+ 4u
6
7u
5
6u
4
+ 7u
3
+ 4u
2
2u 1)
(u
50
+ 4u
49
+ ··· 6u + 1)
c
7
(u
11
+ 2u
10
+ 5u
9
+ 9u
8
+ 9u
7
+ 2u
6
+ 5u
5
+ 12u
4
+ 10u
3
2u 1)
(u
50
+ u
49
+ ··· + 512u + 29)
c
8
(u
11
+ 4u
9
2u
8
+ 6u
7
8u
6
+ u
5
13u
4
4u
3
7u
2
2u 1)
(u
50
+ u
49
+ ··· + 3u
2
+ 1)
c
9
(u
11
u
10
3u
9
+ 3u
8
+ 4u
7
4u
6
7u
5
+ 6u
4
+ 7u
3
4u
2
2u + 1)
(u
50
+ 4u
49
+ ··· 6u + 1)
c
10
(u
11
+ u
10
2u
9
3u
8
+ 3u
7
+ 2u
6
u
5
+ 4u
3
+ u
2
u 1)
(u
50
+ 2u
49
+ ··· + 13u 1)
c
11
(u
11
+ 4u
9
+ 2u
8
+ 6u
7
+ 8u
6
+ u
5
+ 13u
4
4u
3
+ 7u
2
2u + 1)
(u
50
+ u
49
+ ··· + 3u
2
+ 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
11
3y
10
+ ··· + 5y 1)(y
50
20y
49
+ ··· 590053y + 5041)
c
2
(y
11
+ 3y
10
+ ··· + 12y 1)(y
50
+ 46y
49
+ ··· + 780712y + 37249)
c
3
(y
11
3y
10
+ ··· + 20y
2
1)(y
50
4y
49
+ ··· 154y
2
+ 1)
c
4
(y
11
4y
10
+ 18y
8
+ 40y
7
+ 28y
6
+ 45y
5
+ 75y
4
+ 70y
3
+ 5y
2
6y 1)
(y
50
45y
49
+ ··· 1305446y + 162409)
c
5
(y
11
7y
10
+ ··· + 12y 1)(y
50
12y
49
+ ··· 48y + 1)
c
6
(y
11
7y
10
+ ··· + 12y 1)(y
50
12y
49
+ ··· 48y + 1)
c
7
(y
11
+ 6y
10
+ ··· + 4y 1)(y
50
+ 13y
49
+ ··· 327684y + 841)
c
8
, c
11
(y
11
+ 8y
10
+ ··· 10y 1)(y
50
+ 31y
49
+ ··· + 6y + 1)
c
9
(y
11
7y
10
+ ··· + 12y 1)(y
50
12y
49
+ ··· 48y + 1)
c
10
(y
11
5y
10
+ ··· + 3y 1)(y
50
2y
49
+ ··· 35y + 1)
11