11a
147
(K11a
147
)
1
Arc Sequences
5 1 10 8 2 9 11 3 7 4 6
Solving Sequence
1,5
2 3
6,8
9 4 11 7 10
c
1
c
2
c
5
c
8
c
4
c
11
c
7
c
10
c
3
, c
6
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
3
+ u
2
1, a, 4u
2
+ 5b 6u 3i
I
u
2
= hu
78
2u
77
+ ··· + 2u 1, 1.56482 × 10
41
u
77
+ 5.94239 × 10
41
u
76
+ ··· + 2.06037 × 10
42
a 1.17227 × 10
42
,
4.15630 × 10
41
u
77
+ 1.42444 × 10
42
u
76
+ ··· + 2.06037 × 10
42
b 2.63953 × 10
41
i
There are 2 irreducible components with 81 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
3
+ u
2
1, a, 4u
2
+ 5b 6u 3i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
2
+ u 1
a
8
=
0
4
5
u
2
+
6
5
u +
3
5
a
9
=
1
5
u
2
+
1
5
u
2
5
2
5
u
2
+
3
5
u +
4
5
a
4
=
0
u
a
11
=
u
2u
2
u + 2
a
7
=
1
5
u
2
4
5
u
2
5
7
5
u
2
+
8
5
u
1
5
a
10
=
u
u
2
u + 1
a
10
=
u
u
2
u + 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 = 0.877439 0.744862I
a = 0
b = 0.280863 + 0.151879I
4.66906 2.82812I 8.1210 + 11.7122I
u = 0.877439 + 0.744862I
a = 0
b = 0.280863 0.151879I
4.66906 + 2.82812I 8.1210 11.7122I
u = 0.754878
a = 0
b = 1.96173
0.531480 1.88198
3
II. I
u
2
=
hu
78
2u
77
+· · · +2u 1, 1.56 × 10
41
u
77
+5.94 × 10
41
u
76
+· · · +2.06 × 10
42
a
1.17 × 10
42
, 4.16 × 10
41
u
77
+ 1.42 × 10
42
u
76
+ · · · + 2.06 × 10
42
b 2.64 × 10
41
i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
3
+ u
a
8
=
0.0759485u
77
0.288414u
76
+ ··· + 0.189784u + 0.568960
0.201726u
77
0.691350u
76
+ ··· + 2.63367u + 0.128109
a
9
=
1.90814u
77
+ 2.44809u
76
+ ··· + 1.95933u 1.41989
0.671064u
77
1.18342u
76
+ ··· + 1.02301u + 0.453741
a
4
=
1.22870u
77
2.11325u
76
+ ··· 2.05949u + 1.62321
0.213088u
77
0.465529u
76
+ ··· 0.336258u + 1.52860
a
11
=
u
4
u
2
+ 1
u
6
2u
4
+ u
2
a
7
=
1.34481u
77
+ 1.31195u
76
+ ··· + 0.279064u 0.124200
0.176490u
77
0.471217u
76
+ ··· + 2.58106u 0.254037
a
10
=
1.50047u
77
2.62066u
76
+ ··· 2.93613u + 2.80765
0.728247u
77
+ 0.780706u
76
+ ··· + 1.61654u 0.804149
a
10
=
1.50047u
77
2.62066u
76
+ ··· 2.93613u + 2.80765
0.728247u
77
+ 0.780706u
76
+ ··· + 1.61654u 0.804149
(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 = 1.214521 0.340708I
a = 0.870833 + 0.024144I
b = 0.797237 0.098529I
6.71121 6.46472I 9.58573 + 7 .25572I
u = 1.214521 + 0 .340708I
a = 0.870833 0.024144I
b = 0.797237 + 0 .098529I
6.71121 + 6.46472I 9.58573 7.25572I
u = 1.207284 0.247867I
a = 0.898110 0.845175I
b = 0.686919 + 0.239703I
5.50516 + 8.73601I 7.99409 5.01869I
u = 1.207284 + 0 .247867I
a = 0.898110 + 0 .845175I
b = 0.686919 0.239703I
5.50516 8.73601I 7.99409 + 5 .01869I
u = 1.160072 0.582250I
a = 0.970633 + 0 .223648I
b = 1.83761 + 1.33205I
0.33944 11.38210I 2.38467 + 8 .13958I
u = 1.160072 + 0 .582250I
a = 0.970633 0.223648I
b = 1.83761 1.33205I
0.33944 + 11.38210I 2.38467 8.13958I
u = 1.155641 0.314214I
a = 1.082270 + 0.885877I
b = 0.801337 0.856114I
8.20158 + 2.35498I 10.86205 1.59548I
u = 1.155641 + 0 .314214I
a = 1.082270 0.885877I
b = 0.801337 + 0 .856114I
8.20158 2.35498I 10.86205 + 1 .59548I
u = 1.141591 0.513261I
a = 0.900867 0.281464I
b = 1.94345 1.00074I
3.10971 6.53083I 5.26619 + 5 .91055I
u = 1.141591 + 0 .513261I
a = 0.900867 + 0.281464I
b = 1.94345 + 1 .00074I
3.10971 + 6.53083I 5.26619 5.91055I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.139894 0.236298I
a = 0.961417 0.156642I
b = 0.286288 0.251325I
7.37477 1.65920I 11.50430 + 0 .44360I
u = 1.139894 + 0 .236298I
a = 0.961417 + 0 .156642I
b = 0.286288 + 0.251325I
7.37477 + 1.65920I 11.50430 0.44360I
u = 1.105227 0.476843I
a = 0.094688 0.355945I
b = 3.30119 3.16419I
2.73306 3.75480I 5.34558 2.49351I
u = 1.105227 + 0 .476843I
a = 0.094688 + 0.355945I
b = 3.30119 + 3 .16419I
2.73306 + 3.75480I 5.34558 + 2.49351I
u = 1.096643 0.524719I
a = 0.26963 1.47862I
b = 2.10794 + 0 .72036I
0.80322 8.33176I 3.43675 + 10.35591I
u = 1.096643 + 0 .524719I
a = 0.26963 + 1.47862I
b = 2.10794 0.72036I
0.80322 + 8.33176I 3.43675 10.35591I
u = 1.030611 0.412848I
a = 0.637840 + 0 .691046I
b = 1.88598 + 0.77981I
0.08665 1.81934I 1.08763 + 3.29108I
u = 1.030611 + 0 .412848I
a = 0.637840 0.691046I
b = 1.88598 0.77981I
0.08665 + 1.81934I 1.08763 3.29108I
u = 1.017104 0.476390I
a = 1.337673 + 0 .233811I
b = 2.52346 + 1.28080I
0.76206 1.48191I 1.028912 + 0 .352565I
u = 1.017104 + 0 .476390I
a = 1.337673 0.233811I
b = 2.52346 1.28080I
0.76206 + 1.48191I 1.028912 0.352565I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.934335 0.746651I
a = 0.084055 0.410900I
b = 0.573847 + 0 .390063I
4.74268 2.53637I 1.85874 12.78623I
u = 0.934335 + 0 .746651I
a = 0.084055 + 0 .410900I
b = 0.573847 0.390063I
4.74268 + 2.53637I 1.85874 + 12.78623I
u = 0.733786 0.768282I
a = 0.687574 0.030906I
b = 0.528009 0.860705I
5.29151 3.14059I 2.83969 + 9.83145I
u = 0.733786 + 0 .768282I
a = 0.687574 + 0.030906I
b = 0.528009 + 0 .860705I
5.29151 + 3.14059I 2.83969 9.83145I
u = 0.653825 0.410103I
a = 0.699015 + 0 .778492I
b = 0.999935 + 0 .918298I
1.09693 1.53880I 1.66479 + 5.08310I
u = 0.653825 + 0 .410103I
a = 0.699015 0.778492I
b = 0.999935 0.918298I
1.09693 + 1.53880I 1.66479 5.08310I
u = 0.594731
a = 0.614674
b = 4.68475
0.210538 40.2342
u = 0.536973 0.520683I
a = 0.18964 + 1 .94642I
b = 1.223757 + 0 .579060I
2.17308 2.60159I 2.40455 + 6.09883I
u = 0.536973 + 0 .520683I
a = 0.18964 1.94642I
b = 1.223757 0.579060I
2.17308 + 2.60159I 2.40455 6.09883I
u = 0.325468 0.636702I
a = 2.25988 0.27644I
b = 1.14758 0 .92447I
1.40525 + 3.78104I 0.49759 6.55380I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.325468 + 0 .636702I
a = 2.25988 + 0.27644I
b = 1.14758 + 0 .92447I
1.40525 3.78104I 0.49759 + 6 .55380I
u = 0.309437 0.842121I
a = 0.451020 + 1 .227322I
b = 1.141430 0.144632I
2.88434 + 6 .11355I 0.57263 4.98451I
u = 0.309437 + 0 .842121I
a = 0.451020 1.227322I
b = 1.141430 + 0.144632I
2.88434 6.11355I 0.57263 + 4 .98451I
u = 0.193316 0.691312I
a = 0.618269 1.191349I
b = 0.781315 0.100157I
0.42144 + 1 .94552I 2.30995 3.00822I
u = 0.193316 + 0 .691312I
a = 0.618269 + 1.191349I
b = 0.781315 + 0 .100157I
0.42144 1.94552I 2.30995 + 3 .00822I
u = 0.152062 0.532162I
a = 0.717861 0.428941I
b = 1.41845 2.25892I
0.213305 0.310477I 5.75572 9.22224I
u = 0.152062 + 0 .532162I
a = 0.717861 + 0.428941I
b = 1.41845 + 2 .25892I
0.213305 + 0.310477I 5.75572 + 9.22224I
u = 0.149695 0.830340I
a = 0.415698 0.966907I
b = 0.172875 + 0.500019I
2.45171 + 2 .55877I 5.85987 5.37138I
u = 0.149695 + 0 .830340I
a = 0.415698 + 0.966907I
b = 0.172875 0.500019I
2.45171 2.55877I 5.85987 + 5 .37138I
u = 0.238423 0.742435I
a = 0.56551 2.12834I
b = 1.234285 + 0.366852I
4.07487 5.63539I 5.32059 + 5 .07237I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.238423 + 0 .742435I
a = 0.56551 + 2 .12834I
b = 1.234285 0.366852I
4.07487 + 5 .63539I 5.32059 5.07237I
u = 0.289191 0.831056I
a = 0.53748 + 1.69869I
b = 1.45738 0.16763I
0.68796 12.03560I 2.39702 + 6 .80252I
u = 0.289191 + 0 .831056I
a = 0.53748 1.69869I
b = 1.45738 + 0 .16763I
0.68796 + 12.03560I 2.39702 6.80252I
u = 0.365285 0.557959I
a = 1.48708 + 0 .73496I
b = 0.630732 0.460265I
2.76015 0.59113I 3.15854 1.26752I
u = 0.365285 + 0 .557959I
a = 1.48708 0.73496I
b = 0.630732 + 0.460265I
2.76015 + 0 .59113I 3.15854 + 1.26752I
u = 0.367142 0.771630I
a = 0.312929 + 0 .921953I
b = 0.818992 0.671671I
2.74670 1.03689I 6.52285 + 3 .02306I
u = 0.367142 + 0 .771630I
a = 0.312929 0.921953I
b = 0.818992 + 0 .671671I
2.74670 + 1 .03689I 6.52285 3.02306I
u = 0.432470 0.537624I
a = 1.04786 + 1 .46173I
b = 0.158272 0.114774I
2.94199 0.45731I 3.21783 + 1 .77421I
u = 0.432470 + 0 .537624I
a = 1.04786 1.46173I
b = 0.158272 + 0 .114774I
2.94199 + 0 .45731I 3.21783 1.77421I
u = 0.625614 0.475003I
a = 0.110854 + 0 .871219I
b = 1.25476 0.81238I
1.77605 0.65095I 5.05775 1.02917I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.625614 + 0 .475003I
a = 0.110854 0.871219I
b = 1.25476 + 0 .81238I
1.77605 + 0 .65095I 5.05775 + 1 .02917I
u = 0.739477
a = 0.436143
b = 0.356236
0.989802 10.9809
u = 0.739719 0.511752I
a = 1.42365 + 0.34254I
b = 0.48485 + 1 .56145I
1.96956 + 4 .60975I 4.54210 7.29697I
u = 0.739719 + 0 .511752I
a = 1.42365 0.34254I
b = 0.48485 1.56145I
1.96956 4.60975I 4.54210 + 7.29697I
u = 0.746844 0.705544I
a = 1.262878 + 0 .042560I
b = 0.83350 1.62278I
1.84214 + 9.51725I 1.04524 8.39740I
u = 0.746844 + 0 .705544I
a = 1.262878 0.042560I
b = 0.83350 + 1.62278I
1.84214 9.51725I 1.04524 + 8.39740I
u = 0.850399 0.683748I
a = 0.173915 1.016228I
b = 1.29837 + 0.73385I
1.54329 4.25093I 1.37927 + 3.59719I
u = 0.850399 + 0 .683748I
a = 0.173915 + 1.016228I
b = 1.29837 0.73385I
1.54329 + 4.25093I 1.37927 3.59719I
u = 1.024601 0.336794I
a = 0.430257 + 1.253522I
b = 1.56522 0.50657I
2.14618 1.33328I 6.66813 + 3.26425I
u = 1.024601 + 0 .336794I
a = 0.430257 1.253522I
b = 1.56522 + 0 .50657I
2.14618 + 1 .33328I 6.66813 3.26425I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.051897 0.501021I
a = 1.092199 0.678277I
b = 1.24189 + 1 .39945I
1.14399 + 4 .70367I 0.68489 7.01774I
u = 1.051897 + 0 .501021I
a = 1.092199 + 0.678277I
b = 1.24189 1.39945I
1.14399 4.70367I 0.68489 + 7 .01774I
u = 1.078790 0.507036I
a = 0.411374 1.021214I
b = 0.369719 + 0.580320I
0.70811 + 4 .91347I 0.65713 3.64036I
u = 1.078790 + 0 .507036I
a = 0.411374 + 1.021214I
b = 0.369719 0.580320I
0.70811 4.91347I 0.65713 + 3 .64036I
u = 1.088043 0.413183I
a = 0.182256 + 0.482380I
b = 0.53163 + 2.17015I
3.19952 + 3 .59888I 4.94774 4.49419I
u = 1.088043 + 0 .413183I
a = 0.182256 0.482380I
b = 0.53163 2.17015I
3.19952 3.59888I 4.94774 + 4 .49419I
u = 1.129542 0.584934I
a = 0.723226 0.143814I
b = 0.68180 + 1 .66967I
5.00368 + 6 .17548I 8.15389 7.39445I
u = 1.129542 + 0 .584934I
a = 0.723226 + 0.143814I
b = 0.68180 1.66967I
5.00368 6.17548I 8.15389 + 7 .39445I
u = 1.145482 0.533343I
a = 1.47474 0.17364I
b = 2.39131 1.80228I
6.70525 + 10.43610I 8.24868 8.49271I
u = 1.145482 + 0 .533343I
a = 1.47474 + 0 .17364I
b = 2.39131 + 1.80228I
6.70525 10.43610I 8.24868 + 8 .49271I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.155384 0.357963I
a = 0.630466 + 0 .546648I
b = 0.552372 0.377984I
4.19189 + 1.50549I 8.00053 1.44295I
u = 1.155384 + 0 .357963I
a = 0.630466 0.546648I
b = 0.552372 + 0.377984I
4.19189 1.50549I 8.00053 + 1.44295I
u = 1.162449 0.573065I
a = 1.252111 + 0.222576I
b = 2.40851 + 1 .75097I
3.2894 + 17 .2353I 5.40359 10.20114I
u = 1.162449 + 0 .573065I
a = 1.252111 0.222576I
b = 2.40851 1.75097I
3.2894 17.2353I 5.40359 + 10 .20114I
u = 1.187197 0.508151I
a = 0.629217 + 0 .297798I
b = 0.722338 1.143058I
5.56201 + 2.30321I 9.57625 + 1.06030I
u = 1.187197 + 0 .508151I
a = 0.629217 0.297798I
b = 0.722338 + 1.143058I
5.56201 2.30321I 9.57625 1.06030I
u = 1.207249 0.220796I
a = 0.696150 0.577856I
b = 0.414726 + 0 .146360I
2.09592 2.91398I 5.84484 + 3.38261I
u = 1.207249 + 0 .220796I
a = 0.696150 + 0.577856I
b = 0.414726 0.146360I
2.09592 + 2.91398I 5.84484 3.38261I
12
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
+ u
2
1)(u
78
+ 2u
77
+ ··· 2u 1)
c
2
(u
3
+ u
2
+ 2u + 1)(u
78
+ 38u
77
+ ··· + 4u + 1)
c
3
(u
3
+ u
2
+ 2u + 1)(u
78
+ 2u
77
+ ··· + 4u + 1)
c
4
u
3
(u
78
+ 3u
77
+ ··· + 1620u + 200)
c
5
(u
3
u
2
+ 1)(u
78
+ 2u
77
+ ··· 2u 1)
c
6
(u + 1)
3
(u
78
+ 4u
77
+ ··· 349u 25)
c
7
(5u
3
+ 11u
2
+ 6u + 1)(20u
78
+ 88u
77
+ ··· 8295u 1316)
c
8
(5u
3
+ 4u
2
+ u + 1)(5u
78
+ 57u
77
+ ··· + 1179u 1431)
c
9
(u 1)
3
(u
78
+ 4u
77
+ ··· 349u 25)
c
10
(u
3
u
2
+ 2u 1)(u
78
+ 2u
77
+ ··· + 4u + 1)
c
11
(u
3
+ 3u
2
+ 2u 1)(u
78
+ 6u
77
+ ··· 20170u 4025)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
3
y
2
+ 2y 1)(y
78
38y
77
+ ··· 4y + 1)
c
2
(y
3
+ 3y
2
+ 2y 1)(y
78
+ 6y
77
+ ··· + 8y + 1)
c
3
, c
10
(y
3
+ 3y
2
+ 2y 1)(y
78
42y
77
+ ··· 4y + 1)
c
4
y
3
(y
78
21y
77
+ ··· 354000y + 40000)
c
6
, c
9
(y 1)
3
(y
78
44y
77
+ ··· 59401y + 625)
c
7
(25y
3
61y
2
+ 14y 1)
(1801800y
78
+ 13405392y
77
+ ··· + 52393461120y + 7801145352)
c
8
(25y
3
6y
2
7y 1)
(12600y
78
251496y
77
+ ··· 10164481992y + 1032071544)
c
11
(y
3
5y
2
+ 10y 1)(y
78
+ 26y
77
+ ··· 3.91693 × 10
7
y + 1.62006 × 10
7
)
14