11a
194
(K11a
194
)
1
Arc Sequences
7 1 10 11 9 2 3 5 6 4 8
Solving Sequence
2,6
7 1
3,10
4 9 5 8 11
c
6
c
1
c
2
c
3
c
9
c
5
c
8
c
11
c
4
, c
7
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
\
I
v
1
I
u
1
= hu
4
+ 2u
2
+ 2, u
3
+ 2a 2u, u
3
+ u
2
+ b 2u + 1i
I
u
2
= ha
30
+ a
29
+ ··· + 4a 1, 2.21165 × 10
32
b + 8.78791 × 10
30
a
29
+ ··· + 5.71011 × 10
32
a 2.47915 × 10
32
,
2.21165 × 10
32
u + 9.63888 × 10
31
a
29
+ ··· 1.40132 × 10
32
a + 4.20701 × 10
30
i
I
u
3
= hu
23
+ 3u
22
+ ··· + 6u + 2, u
22
+ u
21
+ ··· + 2a + 2, 2u
22
7u
21
+ ··· + b 5i
I
v
1
= hv + 1, b 1, ai
There are 4 irreducible components with 58 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
4
+ 2u
2
+ 2, u
3
+ 2a 2u, u
3
+ u
2
+ b 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
2
1
2u
2
2
a
10
=
1
2
u
3
+ u
u
3
u
2
+ 2u 1
a
4
=
1
2
u
3
u
2
+ u 1
u
3
3u
2
+ 2u 3
a
9
=
1
2
u
3
+ u
u
3
u
2
+ u 1
a
5
=
1
2
u
3
+ u
u
3
u
2
+ 2u 1
a
8
=
0
u
a
11
=
u
2
+ 1
2u
2
+ 2
a
11
=
u
2
+ 1
2u
2
+ 2
(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 = 0.455090 1.098684I
a = 0.321797 0.776887I
b = 0.64359 2.55377I
0.82247 + 3.66386I 8.00000 4.00000I
u = 0.455090 + 1.098684I
a = 0.321797 + 0.776887I
b = 0.64359 + 2.55377I
0.82247 3.66386I 8.00000 + 4.00000I
u = 0.455090 1.098684I
a = 0.321797 0.776887I
b = 0.643594 0.553774I
0.82247 3.66386I 8.00000 + 4.00000I
u = 0.455090 + 1.098684I
a = 0.321797 + 0.776887I
b = 0.643594 + 0.553774I
0.82247 + 3.66386I 8.00000 4.00000I
3
II.
I
u
2
= ha
30
+a
29
+· · ·+4a1, 2.21×10
32
b+8.79×10
30
a
29
+· · ·+5.71×10
32
a
2.48 × 10
32
, 2.21 × 10
32
u + 9.64 × 10
31
a
29
+ · · · 1.40 × 10
32
a + 4.21 × 10
30
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
0.435823a
29
0.301197a
28
+ ··· + 0.633609a 0.0190220
a
7
=
0.435823a
29
0.301197a
28
+ ··· + 0.633609a 0.0190220
0.435823a
29
0.301197a
28
+ ··· + 0.633609a 0.0190220
a
1
=
0.487907a
29
0.264276a
28
+ ··· 1.51818a 0.0619032
0.487907a
29
0.264276a
28
+ ··· 1.51818a 1.06190
a
3
=
0.121839a
29
+ 0.116533a
28
+ ··· 2.75118a + 0.889051
0.609745a
29
+ 0.380809a
28
+ ··· 1.23300a + 0.950954
a
10
=
a
0.0397346a
29
+ 0.163271a
28
+ ··· 2.58183a + 1.12095
a
4
=
0.106287a
29
+ 0.130759a
28
+ ··· 2.85905a + 1.02519
1.06092a
29
+ 0.771632a
28
+ ··· + 0.102538a + 1.50581
a
9
=
a
0.183897a
29
+ 0.175280a
28
+ ··· 1.69211a + 0.633043
a
5
=
0.102877a
29
+ 0.0405082a
28
+ ··· + 0.974325a 0.134626
0.152113a
29
0.265276a
28
+ ··· + 2.03608a 0.498641
a
8
=
0.114673a
29
0.0555570a
28
+ ··· 0.0701202a + 0.211622
0.205652a
29
+ 0.133587a
28
+ ··· 2.34248a + 0.475200
a
11
=
0.226002a
29
0.271848a
28
+ ··· 0.297857a 0.523201
0.000187926a
29
0.373634a
28
+ ··· + 4.70473a 2.05540
a
11
=
0.226002a
29
0.271848a
28
+ ··· 0.297857a 0.523201
0.000187926a
29
0.373634a
28
+ ··· + 4.70473a 2.05540
(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 = 0.758945 0.422629I
a = 1.38348 0.97590I
b = 0.637765 + 0.954376I
6.30676 + 4.09199I 11.04427 3.15094I
u = 0.758945 + 0 .422629I
a = 1.38348 + 0.97590I
b = 0.637765 0.954376I
6.30676 4.09199I 11.04427 + 3.15094I
u = 0.715401 0.518352I
a = 1.149786 0.273028I
b = 0.531487 + 0.360023I
6.82325 + 1.50523I 12.15133 2.74048I
u = 0.715401 + 0.518352I
a = 1.149786 + 0.273028I
b = 0.531487 0.360023I
6.82325 1.50523I 12.15133 + 2.74048I
u = 0.594032 + 1 .095617I
a = 0.823359 0.023140I
b = 2.45624 + 0.22119I
4.31617 + 9.21780I 7.85460 7.39135I
u = 0.594032 1.095617I
a = 0.823359 + 0.023140I
b = 2.45624 0.22119I
4.31617 9.21780I 7.85460 + 7.39135I
u = 0.594997 + 1.040825I
a = 0.627658 1.048351I
b = 2.05428 0.43390I
5.27292 3.51852I 9.71302 + 2.59027I
u = 0.594997 1.040825I
a = 0.627658 + 1.048351I
b = 2.05428 + 0.43390I
5.27292 + 3.51852I 9.71302 2.59027I
u = 0.538411
a = 0.440546
b = 0.771698
1.86559 5.43661
u = 0.426893 1.085665I
a = 0.417981 0.764905I
b = 0.97891 1.59198I
0.91830 3.60340I 1.83628 + 4.47672I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.426893 + 1.085665I
a = 0.417981 + 0.764905I
b = 0.97891 + 1.59198I
0.91830 + 3.60340I 1.83628 4.47672I
u = 0.385605 + 0.867795I
a = 0.325429 1.228674I
b = 0.302775 + 0.438441I
2.93870 1.66084I 9.51042 + 3.96405I
u = 0.385605 0.867795I
a = 0.325429 + 1.228674I
b = 0.302775 0.438441I
2.93870 + 1.66084I 9.51042 3.96405I
u = 0.594997 1.040825I
a = 0.234491 0.877517I
b = 0.97997 1.06079I
5.27292 + 3.51852I 9.71302 2.59027I
u = 0.594997 + 1.040825I
a = 0.234491 + 0.877517I
b = 0.97997 + 1.06079I
5.27292 3.51852I 9.71302 + 2.59027I
u = 0.146928 + 1.062740I
a = 0.023257 1.262890I
b = 0.855388 1.029219I
1.46912 2.07402I 4.17178 + 2.67122I
u = 0.146928 1.062740I
a = 0.023257 + 1 .262890I
b = 0.855388 + 1.029219I
1.46912 + 2.07402I 4.17178 2.67122I
u = 0.758945 + 0.422629I
a = 0.030077 1.167044I
b = 0.175735 + 0.585440I
6.30676 4.09199I 11.04427 + 3.15094I
u = 0.758945 0.422629I
a = 0.030077 + 1 .167044I
b = 0.175735 0.585440I
6.30676 + 4.09199I 11.04427 3.15094I
u = 0.426893 1.085665I
a = 0.187225 0.097865I
b = 0.361673 + 0.926531I
0.91830 3.60340I 1.83628 + 4.47672I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.426893 + 1 .085665I
a = 0.187225 + 0 .097865I
b = 0.361673 0.926531I
0.91830 + 3.60340I 1.83628 4.47672I
u = 0.146928 1.062740I
a = 0.607642 0.476690I
b = 2.04456 0.71772I
1.46912 + 2.07402I 4.17178 2.67122I
u = 0.146928 + 1 .062740I
a = 0.607642 + 0 .476690I
b = 2.04456 + 0.71772I
1.46912 2.07402I 4.17178 + 2.67122I
u = 0.594032 + 1 .095617I
a = 0.703925 0.960402I
b = 2.72496 1.13368I
4.31617 + 9.21780I 7.85460 7.39135I
u = 0.594032 1.095617I
a = 0.703925 + 0 .960402I
b = 2.72496 + 1.13368I
4.31617 9.21780I 7.85460 + 7.39135I
u = 0.385605 0.867795I
a = 0.750607 0.804208I
b = 2.14710 1.38076I
2.93870 + 1.66084I 9.51042 3.96405I
u = 0.385605 + 0.867795I
a = 0.750607 + 0 .804208I
b = 2.14710 + 1.38076I
2.93870 1.66084I 9.51042 + 3.96405I
u = 0.715401 0.518352I
a = 1.36073 0.93775I
b = 1.226859 + 0.518612I
6.82325 + 1.50523I 12.15133 2.74048I
u = 0.715401 + 0.518352I
a = 1.36073 + 0 .93775I
b = 1.226859 0.518612I
6.82325 1.50523I 12.15133 + 2.74048I
u = 0.538411
a = 2.03798
b = 0.0479905
1.86559 5.43661
7
III.
I
u
3
= hu
23
+3u
22
+· · ·+6u+2, u
22
+u
21
+· · ·+2a+2, 2u
22
7u
21
+· · ·+b5i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
10
=
1
2
u
22
1
2
u
21
+ ··· u 1
2u
22
+ 7u
21
+ ··· + 14u + 5
a
4
=
1
2
u
22
+
3
2
u
21
+ ··· + 3u + 2
u
21
+ 2u
20
+ ··· + 2u + 1
a
9
=
1
2
u
22
1
2
u
21
+ ··· u 1
u
22
+ 4u
21
+ ··· + 9u + 3
a
5
=
1
2
u
22
+
3
2
u
21
+ ··· + 3u + 1
u
20
+ u
19
+ ··· + 2u + 1
a
8
=
u
7
2u
5
2u
3
u
7
u
5
+ u
a
11
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
u
4
a
11
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
u
4
(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 = 0.835379 0.384998I
a = 1.39199 1.01057I
b = 0.120832 + 0.863877I
13.0517 8.4231I 12.86699 + 3.68057I
u = 0.835379 + 0.384998I
a = 1.39199 + 1 .01057I
b = 0.120832 0.863877I
13.0517 + 8.4231I 12.86699 3.68057I
u = 0.810177
a = 1.79305
b = 0.325869
7.53068 12.4951
u = 0.624484 0.349425I
a = 0.083237 + 0.828268I
b = 0.127127 0.453130I
0.39287 1.77603I 5.94653 + 5.32090I
u = 0.624484 + 0.349425I
a = 0.083237 0.828268I
b = 0.127127 + 0.453130I
0.39287 + 1.77603I 5.94653 5.32090I
u = 0.609932 1.133499I
a = 0.797496 + 0.929102I
b = 2.73102 + 1.78467I
10.8121 + 13.7968I 9.98537 7.70704I
u = 0.609932 + 1.133499I
a = 0.797496 0.929102I
b = 2.73102 1.78467I
10.8121 13.7968I 9.98537 + 7.70704I
u = 0.534647 1.084889I
a = 0.572697 0.059609I
b = 1.90105 + 0.03493I
1.70058 + 6.34697I 2.48807 8.83395I
u = 0.534647 + 1.084889I
a = 0.572697 + 0 .059609I
b = 1.90105 0.03493I
1.70058 6.34697I 2.48807 + 8.83395I
u = 0.432454 1.201204I
a = 0.408448 1.028453I
b = 0.63690 2.57644I
3.91675 + 4.39214I 8.96484 3.62176I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.432454 + 1.201204I
a = 0.408448 + 1 .028453I
b = 0.63690 + 2 .57644I
3.91675 4.39214I 8.96484 + 3.62176I
u = 0.305961 1.048061I
a = 0.483204 0.301545I
b = 1.52444 + 0.09088I
3.26008 + 0.62293I 1.92583 + 0.88926I
u = 0.305961 + 1.048061I
a = 0.483204 + 0.301545I
b = 1.52444 0.09088I
3.26008 0.62293I 1.92583 0.88926I
u = 0.150597 1.188510I
a = 0.063392 + 1 .272327I
b = 1.17447 + 1 .91904I
7.74907 5.71311I 7.54100 + 2.76920I
u = 0.150597 + 1.188510I
a = 0.063392 1.272327I
b = 1.17447 1.91904I
7.74907 + 5.71311I 7.54100 2.76920I
u = 0.477361 1.058388I
a = 0.084203 0.431525I
b = 0.266682 0.339221I
0.90872 3.31162I 4.18007 + 2.04912I
u = 0.477361 + 1 .058388I
a = 0.084203 + 0.431525I
b = 0.266682 + 0.339221I
0.90872 + 3.31162I 4.18007 2.04912I
u = 0.486428 0.465014I
a = 0.657699 + 0 .124968I
b = 0.376095 0.129421I
0.881089 0.706259I 8.61582 + 5.28098I
u = 0.486428 + 0 .465014I
a = 0.657699 0.124968I
b = 0.376095 + 0 .129421I
0.881089 + 0.706259I 8.61582 5.28098I
u = 0.666288 0.980877I
a = 0.639699 + 1 .203084I
b = 0.947679 + 0 .768947I
13.37537 0.20863I 12.34199 + 1.72313I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.666288 + 0 .980877I
a = 0.639699 1.203084I
b = 0.947679 0.768947I
13.37537 + 0.20863I 12.34199 1.72313I
u = 0.768464 0.625797I
a = 1.38926 0.84175I
b = 1.170700 0.237527I
14.4326 5.1937I 13.7476 + 3.5950I
u = 0.768464 + 0 .625797I
a = 1.38926 + 0.84175I
b = 1.170700 + 0.237527I
14.4326 + 5.1937I 13.7476 3.5950I
11
IV. I
v
1
= hv + 1, b 1, ai
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
7
=
1
0
a
1
=
1
0
a
3
=
1
0
a
10
=
0
1
a
4
=
1
1
a
9
=
1
1
a
5
=
0
1
a
8
=
1
0
a
11
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
3.28987 12.0000
13
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
u(u
4
+ 2u
2
+ 2)
(1 + 2u 2u
2
+ 4u
3
4u
4
+ 6u
5
6u
6
+ 8u
7
7u
8
+ 10u
9
6u
10
+ 8u
11
3u
12
+ 4u
13
u
14
+ u
15
)
2
(u
23
+ 3u
22
+ ··· + 6u + 2)
c
2
u(u
2
+ 2u + 2)
2
(1 + 4u
2
+ 12u
3
+ 26u
4
+ 52u
5
+ 86u
6
+ 118u
7
+ 143u
8
+ 156u
9
+ 146u
10
+ 110u
11
+ 63u
12
+ 26u
13
+ 7u
14
+ u
15
)
2
(u
23
+ 11u
22
+ ··· 4u 4)
c
3
, c
4
, c
8
c
9
(u + 1)
5
(u
23
+ u
22
+ ··· 4u
2
+ 1)(u
30
+ u
29
+ ··· + 6u 1)
c
5
, c
10
(u 1)
4
(u + 1)(u
23
+ u
22
+ ··· 4u
2
+ 1)(u
30
+ u
29
+ ··· + 6u 1)
c
7
u(u
4
2u
2
+ 2)
(1 4u + 8u
3
+ 10u
4
2u
5
18u
6
+ 14u
7
3u
8
+ 4u
9
6u
10
+ 8u
11
u
12
u
14
+ u
15
)
2
(u
23
+ 3u
22
+ ··· 166u 34)
c
11
u(u
4
2u
2
+ 2)
(1 + 12u
3
42u
4
+ 96u
5
158u
6
+ 206u
7
221u
8
+ 196u
9
146u
10
+ 90u
11
45u
12
+ 18u
13
5u
14
+ u
15
)
2
(u
23
+ 15u
22
+ ··· + 1790u + 314)
14
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
y(y
2
+ 2y + 2)
2
(1 + 4y
2
+ 12y
3
+ 26y
4
+ 52y
5
+ 86y
6
+ 118y
7
+ 143y
8
+ 156y
9
+ 146y
10
+ 110y
11
+ 63y
12
+ 26y
13
+ 7y
14
+ y
15
)
2
(y
23
+ 11y
22
+ ··· 4y 4)
c
2
y(y
2
+ 4)
2
(1 + 8y + 36y
2
+ 108y
3
+ 170y
4
+ 212y
5
+ 142y
6
+ 110y
7
13y
8
+ 68y
9
+ 22y
10
+ 50y
11
+ 19y
12
+ 14y
13
+ 3y
14
+ y
15
)
2
(y
23
+ 3y
22
+ ··· 208y 16)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y 1)
5
(y
23
29y
22
+ ··· + 8y 1)(y
30
25y
29
+ ··· + 8y + 1)
c
7
y(y
2
2y + 2)
2
(1 + 16y 84y
2
+ 116y
3
238y
4
+ 568y
5
318y
6
+ 322y
7
133y
8
+ 204y
9
18y
10
+ 74y
11
5y
12
+ 14y
13
y
14
+ y
15
)
2
(y
23
5y
22
+ ··· + 4028y 1156)
c
11
y(y
2
2y + 2)
2
(1 84y
2
172y
3
+ 98y
4
+ 596y
5
+ 638y
6
+ 118y
7
293y
8
196y
9
+ 102y
10
+ 218y
11
+ 147y
12
+ 54y
13
+ 11y
14
+ y
15
)
2
(y
23
+ 7y
22
+ ··· 489796y 98596)
15