11n
171
(K11n
171
)
1
Arc Sequences
5 8 1 9 1 4 11 2 4 8 7
Solving Sequence
1,4 3,7
6 5 11 8 2 10 9
c
3
c
6
c
5
c
11
c
7
c
2
c
10
c
9
c
1
, c
4
, c
8
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hu
24
+ 5u
23
+ ··· 36u + 13,
1.05613 × 10
30
u
23
3.93035 × 10
30
u
22
+ ··· + 7.53457 × 10
30
b 2.04363 × 10
31
,
5.34104 × 10
31
u
23
1.36422 × 10
32
u
22
+ ··· + 5.95231 × 10
32
a 6.40039 × 10
33
i
I
u
2
= hu
9
u
8
3u
6
+ 4u
5
u
4
+ 3u
3
3u
2
1, a + 1, u
8
+ u
7
+ 3u
5
4u
4
+ u
3
2u
2
+ b + 3ui
I
u
3
= hu
17
+ u
16
+ ··· 2u 1, a + 1, 403558u
16
174203u
15
+ ··· + 217307b + 473110i
There are 3 irreducible components with 50 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
24
+5u
23
+· · ·36u+13, 1.06×10
30
u
23
3.93×10
30
u
22
+· · ·+7.53×10
30
b
2.04× 10
31
, 5.34× 10
31
u
23
1.36 ×10
32
u
22
+· · · +5.95 ×10
32
a 6.40× 10
33
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
7
=
0.0897305u
23
+ 0.229192u
22
+ ··· 20.2640u + 10.7528
0.140171u
23
+ 0.521643u
22
+ ··· 7.26292u + 2.71234
a
6
=
0.0897305u
23
+ 0.229192u
22
+ ··· 20.2640u + 10.7528
0.0175024u
23
+ 0.0101135u
22
+ ··· + 1.80416u 0.140647
a
5
=
0.107233u
23
+ 0.239306u
22
+ ··· 18.4599u + 10.6121
0.0175024u
23
+ 0.0101135u
22
+ ··· + 1.80416u 0.140647
a
11
=
0.119813u
23
0.533793u
22
+ ··· + 19.2450u + 9.65973
0.0517260u
23
0.206565u
22
+ ··· + 4.00927u + 0.919641
a
8
=
0.139301u
23
+ 0.748045u
22
+ ··· 1.76530u + 0.157311
0.0594495u
23
0.225907u
22
+ ··· + 4.99527u 1.06290
a
2
=
0.0451506u
23
+ 0.373064u
22
+ ··· 14.1303u 8.94994
0.0175024u
23
0.0101135u
22
+ ··· 1.80416u 0.859353
a
10
=
0.246882u
23
+ 1.08130u
22
+ ··· 4.98744u + 5.07939
0.196873u
23
+ 0.778216u
22
+ ··· 6.66943u + 2.64458
a
9
=
0.246882u
23
+ 1.08130u
22
+ ··· 4.98744u + 5.07939
0.0450974u
23
+ 0.156511u
22
+ ··· + 2.05196u + 0.654170
a
9
=
0.246882u
23
+ 1.08130u
22
+ ··· 4.98744u + 5.07939
0.0450974u
23
+ 0.156511u
22
+ ··· + 2.05196u + 0.654170
(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 = 1.59548 0.20024I
a = 0.065395 0.821682I
b = 0.138835 1.234445I
7.89505 + 0.05747I 2.57572 + 0.22068I
u = 1.59548 + 0.20024I
a = 0.065395 + 0.821682I
b = 0.138835 + 1.234445I
7.89505 0.05747I 2.57572 0.22068I
u = 1.122276 0.504071I
a = 1.030348 0.298110I
b = 0.873214
2.72528 2.02988I 10.26950 + 3.46410I
u = 1.122276 + 0.504071I
a = 1.030348 + 0.298110I
b = 0.873214
2.72528 + 2.02988I 10.26950 3.46410I
u = 1.091767 0.069199I
a = 0.710026 0.436025I
b = 0.408802 1.276377I
1.23922 + 2.56224I 6.58114 + 0.25928I
u = 1.091767 + 0.069199I
a = 0.710026 + 0.436025I
b = 0.408802 + 1.276377I
1.23922 2.56224I 6.58114 0.25928I
u = 1.008041 0.827530I
a = 1.339481 0.278701I
b = 0.408802 + 1.276377I
1.23922 6.62201I 6.58114 + 6.66892I
u = 1.008041 + 0.827530I
a = 1.339481 + 0.278701I
b = 0.408802 1.276377I
1.23922 + 6.62201I 6.58114 6.66892I
u = 0.77382 1.99666I
a = 0.0040483 0.1124401I
b = 0.138835 + 1.234445I
7.89505 + 4.00229I 2.57572 7.14888I
u = 0.77382 + 1.99666I
a = 0.0040483 + 0.1124401I
b = 0.138835 1.234445I
7.89505 4.00229I 2.57572 + 7.14888I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.607404 0.189800I
a = 1.04128 1.88016I
b = 0.413150
4.19595 + 2.02988I 11.41678 3.46410I
u = 0.607404 + 0.189800I
a = 1.04128 + 1.88016I
b = 0.413150
4.19595 2.02988I 11.41678 + 3.46410I
u = 0.275626 1.339654I
a = 0.225421 + 0.407025I
b = 0.413150
4.19595 + 2.02988I 11.41678 3.46410I
u = 0.275626 + 1.339654I
a = 0.225421 0.407025I
b = 0.413150
4.19595 2.02988I 11.41678 + 3.46410I
u = 0.060194 1.324070I
a = 0.096249 + 1.209356I
b = 0.138835 1.234445I
7.89505 + 0.05747I 2.57572 + 0.22068I
u = 0.060194 + 1.324070I
a = 0.096249 1.209356I
b = 0.138835 + 1.234445I
7.89505 0.05747I 2.57572 0.22068I
u = 0.221372 0.095091I
a = 0.31979 + 8.88211I
b = 0.138835 + 1.234445I
7.89505 + 4.00229I 2.57572 7.14888I
u = 0.221372 + 0.095091I
a = 0.31979 8.88211I
b = 0.138835 1.234445I
7.89505 4.00229I 2.57572 + 7.14888I
u = 0.805356 0.426905I
a = 1.022716 + 0.628047I
b = 0.408802 1.276377I
1.23922 + 2.56224I 6.58114 + 0.25928I
u = 0.805356 + 0.426905I
a = 1.022716 0.628047I
b = 0.408802 + 1.276377I
1.23922 2.56224I 6.58114 0.25928I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.306603 0.184807I
a = 0.895576 0.259116I
b = 0.873214
2.72528 + 2.02988I 10.26950 3.46410I
u = 1.306603 + 0.184807I
a = 0.895576 + 0.259116I
b = 0.873214
2.72528 2.02988I 10.26950 + 3.46410I
u = 1.58089 0.82752I
a = 0.715579 0.148888I
b = 0.408802 1.276377I
1.23922 + 6.62201I 6.58114 6.66892I
u = 1.58089 + 0.82752I
a = 0.715579 + 0.148888I
b = 0.408802 + 1.276377I
1.23922 6.62201I 6.58114 + 6.66892I
5
II. I
u
2
= hu
9
u
8
3u
6
+ 4u
5
u
4
+ 3u
3
3u
2
1, a + 1, u
8
+ u
7
+
3u
5
4u
4
+ u
3
2u
2
+ b + 3ui
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
7
=
1
u
8
u
7
3u
5
+ 4u
4
u
3
+ 2u
2
3u
a
6
=
1
u
8
u
7
3u
5
+ 4u
4
u
3
+ 3u
2
3u
a
5
=
u
8
u
7
3u
5
+ 4u
4
u
3
+ 3u
2
3u 1
u
8
u
7
3u
5
+ 4u
4
u
3
+ 3u
2
3u
a
11
=
u
8
u
7
3u
5
+ 4u
4
u
3
+ 2u
2
3u + 1
u
7
+ u
6
+ 2u
4
4u
3
+ u
2
u + 3
a
8
=
u
8
+ u
6
+ 3u
5
2u
4
3u
3
u
2
+ 2u + 2
2u
8
+ 2u
7
+ 5u
5
8u
4
+ 2u
3
3u
2
+ 5u
a
2
=
u
8
+ 2u
7
u
6
+ 3u
5
7u
4
+ 5u
3
4u
2
+ 6u 2
u
7
u
6
3u
4
+ 4u
3
u
2
+ 3u 3
a
10
=
u
8
+ 2u
7
u
6
+ 2u
5
6u
4
+ 5u
3
2u
2
+ 3u 2
u
6
+ 3u
3
u
2
2
a
9
=
u
8
+ 2u
7
u
6
+ 2u
5
6u
4
+ 5u
3
2u
2
+ 3u 2
u
7
2u
6
2u
4
+ 6u
3
2u
2
+ u 3
a
9
=
u
8
+ 2u
7
u
6
+ 2u
5
6u
4
+ 5u
3
2u
2
+ 3u 2
u
7
2u
6
2u
4
+ 6u
3
2u
2
+ u 3
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.822854 1.092227I
a = 1.00000
b = 0.075853 1.213423I
7.92625 + 2.61535I 2.34637 1.10608I
u = 0.822854 + 1.092227I
a = 1.00000
b = 0.075853 + 1.213423I
7.92625 2.61535I 2.34637 + 1.10608I
u = 0.360844 0.838663I
a = 1.00000
b = 0.140254 + 0.400864I
5.21158 + 1.80390I 1.75250 1.15156I
u = 0.360844 + 0.838663I
a = 1.00000
b = 0.140254 0.400864I
5.21158 1.80390I 1.75250 + 1.15156I
u = 0.093733 0.571308I
a = 1.00000
b = 0.03796 + 1.59738I
12.42609 + 1.12659I 0.795880 + 0.970083I
u = 0.093733 + 0.571308I
a = 1.00000
b = 0.03796 1.59738I
12.42609 1.12659I 0.795880 0.970083I
u = 1.151428 0.450468I
a = 1.00000
b = 0.369661 + 1.332036I
0.82219 + 4.09909I 8.12215 4.24227I
u = 1.151428 + 0.450468I
a = 1.00000
b = 0.369661 1.332036I
0.82219 4.09909I 8.12215 + 4.24227I
u = 1.25201
a = 1.00000
b = 0.768805
3.42422 12.1497
7
III. I
u
3
= hu
17
+ u
16
+ · · · 2u 1, a + 1, 4.04 × 10
5
u
16
1.74 × 10
5
u
15
+
· · · + 2.17 × 10
5
b + 4.73 × 10
5
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
7
=
1
1.85709u
16
+ 0.801645u
15
+ ··· 2.48425u 2.17715
a
6
=
1
1.85709u
16
+ 0.801645u
15
+ ··· 2.48425u 2.17715
a
5
=
1.85709u
16
+ 0.801645u
15
+ ··· 2.48425u 3.17715
1.85709u
16
+ 0.801645u
15
+ ··· 2.48425u 2.17715
a
11
=
1.85709u
16
+ 0.801645u
15
+ ··· 2.48425u 1.17715
0.284832u
16
0.444790u
15
+ ··· 3.35461u + 2.37336
a
8
=
2.14192u
16
1.24643u
15
+ ··· 0.870368u + 3.55051
2.77218u
16
1.24176u
15
+ ··· + 4.25300u + 5.16493
a
2
=
0.320063u
16
+ 0.481581u
15
+ ··· + 5.33126u 1.30710
1.53702u
16
+ 1.28323u
15
+ ··· + 2.84702u 4.48425
a
10
=
0.630265u
16
+ 0.00467081u
15
+ ··· + 5.12336u + 1.61442
0.270083u
16
+ 0.973006u
15
+ ··· + 1.54221u 2.01297
a
9
=
0.630265u
16
+ 0.00467081u
15
+ ··· + 5.12336u + 1.61442
0.505989u
16
+ 0.895484u
15
+ ··· + 0.902603u 2.64791
a
9
=
0.630265u
16
+ 0.00467081u
15
+ ··· + 5.12336u + 1.61442
0.505989u
16
+ 0.895484u
15
+ ··· + 0.902603u 2.64791
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.47065 0.94525I
a = 1.00000
b = 0.41260 1.41870I
5.1608 13.6066I 5.59446 + 7.46007I
u = 1.47065 + 0.94525I
a = 1.00000
b = 0.41260 + 1.41870I
5.1608 + 13.6066I 5.59446 7.46007I
u = 1.41846 0.55721I
a = 1.00000
b = 0.939675 0.221289I
0.01418 8.74564I 9.43323 + 6.21574I
u = 1.41846 + 0.55721I
a = 1.00000
b = 0.939675 + 0.221289I
0.01418 + 8.74564I 9.43323 6.21574I
u = 1.096429 0.166402I
a = 1.00000
b = 0.591453 + 1.005913I
2.42082 3.43267I 8.02158 + 2.98804I
u = 1.096429 + 0.166402I
a = 1.00000
b = 0.591453 1.005913I
2.42082 + 3.43267I 8.02158 2.98804I
u = 0.467507 0.199245I
a = 1.00000
b = 0.05895 + 1.66246I
11.85540 1.51678I 9.69360 + 5.86030I
u = 0.467507 + 0.199245I
a = 1.00000
b = 0.05895 1.66246I
11.85540 + 1.51678I 9.69360 5.86030I
u = 0.288253 0.365835I
a = 1.00000
b = 0.211807 0.989057I
2.01657 + 1.88656I 7.16642 4.34239I
u = 0.288253 + 0.365835I
a = 1.00000
b = 0.211807 + 0.989057I
2.01657 1.88656I 7.16642 + 4.34239I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.236542
a = 1.00000
b = 0.283727
0.582703 17.1449
u = 1.28923 0.61528I
a = 1.00000
b = 0.284641 + 1.111416I
0.64441 + 2.30767I 10.18608 0.27730I
u = 1.28923 + 0.61528I
a = 1.00000
b = 0.284641 1.111416I
0.64441 2.30767I 10.18608 + 0.27730I
u = 1.40164 0.31238I
a = 1.00000
b = 0.32482 + 1.45291I
2.38666 + 5.36037I 5.12085 4.62281I
u = 1.40164 + 0.31238I
a = 1.00000
b = 0.32482 1.45291I
2.38666 5.36037I 5.12085 + 4.62281I
u = 1.43215 0.05490I
a = 1.00000
b = 0.741532 0.257409I
3.15113 1.41738I 9.71131 + 4.88398I
u = 1.43215 + 0.05490I
a = 1.00000
b = 0.741532 + 0.257409I
3.15113 + 1.41738I 9.71131 4.88398I
10
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
2
u + 1)
12
(u
9
+ 3u
7
3u
6
+ u
5
4u
4
+ 3u
3
+ u 1)
(u
17
+ 13u
16
+ ··· + 608u + 64)
c
2
, c
9
(u
9
+ 4u
7
+ ··· u
2
+ 1)(u
17
+ 5u
15
+ ··· + 2u 1)
(u
24
+ u
23
+ ··· + 26u + 79)
c
3
, c
6
(u
9
+ u
8
+ ··· + 3u
2
+ 1)(u
17
+ u
16
+ ··· 2u 1)
(u
24
+ 5u
23
+ ··· 36u + 13)
c
4
, c
8
(u
9
+ 4u
7
+ ··· + u
2
1)(u
17
+ 5u
15
+ ··· + 2u 1)
(u
24
+ u
23
+ ··· + 26u + 79)
c
5
(u
2
u + 1)
12
(u
9
+ 3u
7
+ 3u
6
+ u
5
+ 4u
4
+ 3u
3
+ u + 1)
(u
17
+ 13u
16
+ ··· + 608u + 64)
c
7
(u
6
u
5
+ 3u
4
2u
3
+ 2u
2
u 1)
4
(u
9
u
8
+ 6u
7
5u
6
+ 12u
5
8u
4
+ 8u
3
5u
2
1)
(u
17
+ 6u
16
+ ··· 10u 4)
c
10
, c
11
(u
6
u
5
+ 3u
4
2u
3
+ 2u
2
u 1)
4
(u
9
+ u
8
+ 6u
7
+ 5u
6
+ 12u
5
+ 8u
4
+ 8u
3
+ 5u
2
+ 1)
(u
17
+ 6u
16
+ ··· 10u 4)
11
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
2
+ y + 1)
12
(y
9
+ 6y
8
+ ··· + y 1)
(y
17
+ 7y
16
+ ··· + 25600y 4096)
c
2
, c
4
, c
8
c
9
(y
9
+ 8y
8
+ 28y
7
+ 53y
6
+ 56y
5
+ 30y
4
+ 7y
3
+ 3y
2
+ 2y 1)
(y
17
+ 10y
16
+ ··· + 2y 1)(y
24
+ 15y
23
+ ··· + 53676y + 6241)
c
3
, c
6
(y
9
y
8
+ 2y
7
5y
6
+ 4y
5
+ 3y
4
3y
3
11y
2
6y 1)
(y
17
19y
16
+ ··· + 26y 1)(y
24
5y
23
+ ··· 5352y + 169)
c
7
, c
10
, c
11
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
6y
2
5y + 1)
4
(y
9
+ 11y
8
+ 50y
7
+ 119y
6
+ 150y
5
+ 76y
4
26y
3
41y
2
10y 1)
(y
17
+ 16y
16
+ ··· + 172y 16)
12