11a
194
(K11a
194
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 9 2 3 5 6 4 8
Solving Sequence
2,6 7,9
10 1 3 4 5 8 11
c
6
c
9
c
1
c
2
c
3
c
5
c
8
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
22
− 2u
21
+ ··· + b + 1, 3u
22
− 7u
21
+ ··· + 2a − 8u, u
23
− 3u
22
+ ··· + 6u − 2i
I
u
2
= h−26u
14
a + 25u
14
+ ··· − 45a + 53, u
14
+ 2u
13
+ ··· − 2a + 2,
u
15
+ u
14
+ 4u
13
+ 3u
12
+ 8u
11
+ 6u
10
+ 10u
9
+ 7u
8
+ 8u
7
+ 6u
6
+ 6u
5
+ 4u
4
+ 4u
3
+ 2u
2
+ 2u + 1i
I
u
3
= hb − 1, u
3
− 2u
2
+ 2a − 2, u
4
+ 2u
2
+ 2i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 58 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hu
22
−2u
21
+· · ·+b+1, 3u
22
−7u
21
+· · ·+2a−8u, u
23
−3u
22
+· · ·+6u−2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
9
=
−
3
2
u
22
+
7
2
u
21
+ ··· − 7u
2
+ 4u
−u
22
+ 2u
21
+ ··· + 2u − 1
a
10
=
−
5
2
u
22
+
11
2
u
21
+ ··· + 6u − 1
−u
22
+ 2u
21
+ ··· + 2u − 1
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
−
1
2
u
22
+
3
2
u
21
+ ··· + 2u − 1
u
20
− u
19
+ ··· − u + 1
a
5
=
−
1
2
u
22
+
3
2
u
21
+ ··· + 4u − 1
u
20
− u
19
+ ··· − 2u + 1
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
11
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
22
− 6u
21
+ 18u
20
− 32u
19
+ 58u
18
− 84u
17
+ 122u
16
− 152u
15
+ 182u
14
− 192u
13
+
206u
12
−194u
11
+188u
10
−154u
9
+126u
8
−102u
7
+68u
6
−38u
5
+12u
4
+6u
3
+8u
2
−2u+4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
+ 3u
22
+ ··· + 6u + 2
c
2
u
23
+ 11u
22
+ ··· − 4u − 4
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
23
− u
22
+ ··· + 4u
2
− 1
c
7
u
23
− 3u
22
+ ··· − 166u + 34
c
11
u
23
+ 15u
22
+ ··· + 1790u + 314
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 11y
22
+ ··· − 4y −4
c
2
y
23
+ 3y
22
+ ··· − 208y −16
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
23
− 29y
22
+ ··· + 8y −1
c
7
y
23
− 5y
22
+ ··· + 4028y −1156
c
11
y
23
+ 7y
22
+ ··· − 489796y −98596
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768464 + 0.625797I
a = −2.35900 − 0.70924I
b = 1.59436 − 0.22254I
14.4326 − 5.1937I 13.7476 + 3.5950I
u = −0.768464 − 0.625797I
a = −2.35900 + 0.70924I
b = 1.59436 + 0.22254I
14.4326 + 5.1937I 13.7476 − 3.5950I
u = 0.835379 + 0.384998I
a = −2.06431 − 0.48967I
b = 1.55191 − 0.30830I
13.0517 − 8.4231I 12.86699 + 3.68057I
u = 0.835379 − 0.384998I
a = −2.06431 + 0.48967I
b = 1.55191 + 0.30830I
13.0517 + 8.4231I 12.86699 − 3.68057I
u = 0.305961 + 1.048060I
a = 0.143181 − 0.764944I
b = 0.168196 − 0.598689I
−3.26008 + 0.62293I −1.92583 + 0.88926I
u = 0.305961 − 1.048060I
a = 0.143181 + 0.764944I
b = 0.168196 + 0.598689I
−3.26008 − 0.62293I −1.92583 − 0.88926I
u = −0.477361 + 1.058390I
a = −0.325021 − 0.446372I
b = 0.496916 + 0.116873I
−0.90872 − 3.31162I 4.18007 + 2.04912I
u = −0.477361 − 1.058390I
a = −0.325021 + 0.446372I
b = 0.496916 − 0.116873I
−0.90872 + 3.31162I 4.18007 − 2.04912I
u = −0.666288 + 0.980877I
a = 1.51895 + 1.19962I
b = −1.60630 − 0.17413I
13.37540 − 0.20863I 12.34199 + 1.72313I
u = −0.666288 − 0.980877I
a = 1.51895 − 1.19962I
b = −1.60630 + 0.17413I
13.37540 + 0.20863I 12.34199 − 1.72313I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810177
a = 1.05047
b = −1.45269
7.53068 12.4950
u = 0.150597 + 1.188510I
a = −0.209754 + 0.504264I
b = −1.50263 + 0.26695I
7.74907 − 5.71311I 7.54100 + 2.76920I
u = 0.150597 − 1.188510I
a = −0.209754 − 0.504264I
b = −1.50263 − 0.26695I
7.74907 + 5.71311I 7.54100 − 2.76920I
u = 0.534647 + 1.084890I
a = −1.091580 + 0.807678I
b = 0.370860 + 0.589443I
−1.70058 + 6.34697I 2.48807 − 8.83395I
u = 0.534647 − 1.084890I
a = −1.091580 − 0.807678I
b = 0.370860 − 0.589443I
−1.70058 − 6.34697I 2.48807 + 8.83395I
u = 0.432454 + 1.201200I
a = 0.317778 + 1.107100I
b = 1.412020 + 0.045870I
3.91675 + 4.39214I 8.96484 − 3.62176I
u = 0.432454 − 1.201200I
a = 0.317778 − 1.107100I
b = 1.412020 − 0.045870I
3.91675 − 4.39214I 8.96484 + 3.62176I
u = 0.624484 + 0.349425I
a = 0.805631 − 0.022305I
b = −0.341398 + 0.488155I
0.39287 − 1.77603I 5.94653 + 5.32090I
u = 0.624484 − 0.349425I
a = 0.805631 + 0.022305I
b = −0.341398 − 0.488155I
0.39287 + 1.77603I 5.94653 − 5.32090I
u = 0.609932 + 1.133500I
a = 1.32397 − 2.18810I
b = −1.53955 − 0.33727I
10.8121 + 13.7968I 9.98537 − 7.70704I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609932 − 1.133500I
a = 1.32397 + 2.18810I
b = −1.53955 + 0.33727I
10.8121 − 13.7968I 9.98537 + 7.70704I
u = −0.486428 + 0.465014I
a = 0.914914 + 0.002129I
b = −0.378035 + 0.245051I
0.881089 − 0.706259I 8.61582 + 5.28098I
u = −0.486428 − 0.465014I
a = 0.914914 − 0.002129I
b = −0.378035 − 0.245051I
0.881089 + 0.706259I 8.61582 − 5.28098I
7
II. I
u
2
=
h−26u
14
a+ 25 u
14
+· · ·−45a+53, u
14
+2u
13
+· · ·−2a+2, u
15
+u
14
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
9
=
a
2.36364au
14
− 2.27273u
14
+ ··· + 4.09091a − 4.81818
a
10
=
2.36364au
14
− 2.27273u
14
+ ··· + 5.09091a − 4.81818
2.36364au
14
− 2.27273u
14
+ ··· + 4.09091a − 4.81818
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
−2.27273au
14
+ 2.45455u
14
+ ··· − 4.81818a + 4.36364
−1
a
5
=
2.27273au
14
− 2.45455u
14
+ ··· + 4.81818a − 4.36364
−1.81818au
14
+ 2.36364u
14
+ ··· − 3.45455a + 5.09091
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
11
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
13
−4u
12
−12u
11
−12u
10
−20u
9
−24u
8
−20u
7
−24u
6
−16u
5
−16u
4
−16u
3
−8u
2
−8u+2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
15
− u
14
+ ··· + 2u − 1)
2
c
2
(u
15
+ 7u
14
+ ··· + 4u
2
− 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
30
− u
29
+ ··· − 6u − 1
c
7
(u
15
+ u
14
+ ··· − 4u − 1)
2
c
11
(u
15
− 5u
14
+ ··· + 12u
3
− 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
15
+ 7y
14
+ ··· + 4y
2
− 1)
2
c
2
(y
15
+ 3y
14
+ ··· + 8y −1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
30
− 25y
29
+ ··· + 8y + 1
c
7
(y
15
− y
14
+ ··· + 16y −1)
2
c
11
(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.385605 + 0.867795I
a = 1.48418 + 0.28748I
b = −1.191720 + 0.191378I
2.93870 + 1.66084I 9.51042 − 3.96405I
u = 0.385605 + 0.867795I
a = −0.57671 + 2.31540I
b = 0.987326 + 0.341266I
2.93870 + 1.66084I 9.51042 − 3.96405I
u = 0.385605 − 0.867795I
a = 1.48418 − 0.28748I
b = −1.191720 − 0.191378I
2.93870 − 1.66084I 9.51042 + 3.96405I
u = 0.385605 − 0.867795I
a = −0.57671 − 2.31540I
b = 0.987326 − 0.341266I
2.93870 − 1.66084I 9.51042 + 3.96405I
u = −0.146928 + 1.062740I
a = 0.506354 + 1.080350I
b = 0.417318 + 0.715805I
1.46912 + 2.07402I 4.17178 − 2.67122I
u = −0.146928 + 1.062740I
a = 0.286056 − 0.497573I
b = −1.345540 − 0.160838I
1.46912 + 2.07402I 4.17178 − 2.67122I
u = −0.146928 − 1.062740I
a = 0.506354 − 1.080350I
b = 0.417318 − 0.715805I
1.46912 − 2.07402I 4.17178 + 2.67122I
u = −0.146928 − 1.062740I
a = 0.286056 + 0.497573I
b = −1.345540 + 0.160838I
1.46912 − 2.07402I 4.17178 + 2.67122I
u = 0.715401 + 0.518352I
a = 0.929094 + 0.108337I
b = −0.681034 − 0.791319I
6.82325 + 1.50523I 12.15133 − 2.74048I
u = 0.715401 + 0.518352I
a = −2.92853 + 0.30497I
b = 1.45955 + 0.03447I
6.82325 + 1.50523I 12.15133 − 2.74048I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715401 − 0.518352I
a = 0.929094 − 0.108337I
b = −0.681034 + 0.791319I
6.82325 − 1.50523I 12.15133 + 2.74048I
u = 0.715401 − 0.518352I
a = −2.92853 − 0.30497I
b = 1.45955 − 0.03447I
6.82325 − 1.50523I 12.15133 + 2.74048I
u = −0.758945 + 0.422629I
a = 0.667191 + 0.185788I
b = −0.516053 − 0.873011I
6.30676 + 4.09199I 11.04427 − 3.15094I
u = −0.758945 + 0.422629I
a = −2.63836 + 0.44671I
b = 1.46243 + 0.15596I
6.30676 + 4.09199I 11.04427 − 3.15094I
u = −0.758945 − 0.422629I
a = 0.667191 − 0.185788I
b = −0.516053 + 0.873011I
6.30676 − 4.09199I 11.04427 + 3.15094I
u = −0.758945 − 0.422629I
a = −2.63836 − 0.44671I
b = 1.46243 − 0.15596I
6.30676 − 4.09199I 11.04427 + 3.15094I
u = −0.426893 + 1.085670I
a = −0.045925 − 1.153050I
b = 1.008860 − 0.127254I
−0.91830 − 3.60340I 1.83628 + 4.47672I
u = −0.426893 + 1.085670I
a = −0.652015 + 0.334121I
b = 0.026324 + 0.245041I
−0.91830 − 3.60340I 1.83628 + 4.47672I
u = −0.426893 − 1.085670I
a = −0.045925 + 1.153050I
b = 1.008860 + 0.127254I
−0.91830 + 3.60340I 1.83628 − 4.47672I
u = −0.426893 − 1.085670I
a = −0.652015 − 0.334121I
b = 0.026324 − 0.245041I
−0.91830 + 3.60340I 1.83628 − 4.47672I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594997 + 1.040830I
a = 0.400000 + 0.495676I
b = 0.773820 − 0.766183I
5.27292 + 3.51852I 9.71302 − 2.59027I
u = 0.594997 + 1.040830I
a = 2.00079 − 1.63767I
b = −1.46460 − 0.02952I
5.27292 + 3.51852I 9.71302 − 2.59027I
u = 0.594997 − 1.040830I
a = 0.400000 − 0.495676I
b = 0.773820 + 0.766183I
5.27292 − 3.51852I 9.71302 + 2.59027I
u = 0.594997 − 1.040830I
a = 2.00079 + 1.63767I
b = −1.46460 + 0.02952I
5.27292 − 3.51852I 9.71302 + 2.59027I
u = −0.594032 + 1.095620I
a = −1.24711 − 0.90132I
b = 0.463749 − 0.915832I
4.31617 − 9.21780I 7.85460 + 7.39135I
u = −0.594032 + 1.095620I
a = 1.71287 + 2.15495I
b = −1.47039 + 0.20072I
4.31617 − 9.21780I 7.85460 + 7.39135I
u = −0.594032 − 1.095620I
a = −1.24711 + 0.90132I
b = 0.463749 + 0.915832I
4.31617 + 9.21780I 7.85460 − 7.39135I
u = −0.594032 − 1.095620I
a = 1.71287 − 2.15495I
b = −1.47039 − 0.20072I
4.31617 + 9.21780I 7.85460 − 7.39135I
u = −0.538411
a = 1.00814
b = −1.09727
1.86559 5.43660
u = −0.538411
a = 1.19609
b = 0.237195
1.86559 5.43660
13
III. I
u
3
= hb − 1, u
3
− 2u
2
+ 2a − 2, u
4
+ 2u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
9
=
−
1
2
u
3
+ u
2
+ 1
1
a
10
=
−
1
2
u
3
+ u
2
+ 2
1
a
1
=
−u
u
3
+ u
a
3
=
−u
3
−u
3
− u
a
4
=
−
3
2
u
3
+ u
2
+ 2
−u
3
− u + 1
a
5
=
−
1
2
u
3
+ u
2
+ 2
1
a
8
=
−1
0
a
11
=
u
3
u
3
+ u
a
11
=
u
3
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
+ 2u
2
+ 2
c
2
(u
2
+ 2u + 2)
2
c
3
, c
4
, c
8
c
9
(u + 1)
4
c
5
, c
10
(u − 1)
4
c
7
, c
11
u
4
− 2u
2
+ 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
2
+ 2y + 2)
2
c
2
(y
2
+ 4)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y −1)
4
c
7
, c
11
(y
2
− 2y + 2)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455090 + 1.098680I
a = 0.77689 + 1.32180I
b = 1.00000
0.82247 + 3.66386I 8.00000 − 4.00000I
u = 0.455090 − 1.098680I
a = 0.77689 − 1.32180I
b = 1.00000
0.82247 − 3.66386I 8.00000 + 4.00000I
u = −0.455090 + 1.098680I
a = −0.776887 − 0.678203I
b = 1.00000
0.82247 − 3.66386I 8.00000 + 4.00000I
u = −0.455090 − 1.098680I
a = −0.776887 + 0.678203I
b = 1.00000
0.82247 + 3.66386I 8.00000 − 4.00000I
17
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
6
=
1
0
a
7
=
1
0
a
9
=
0
−1
a
10
=
−1
−1
a
1
=
−1
0
a
3
=
−1
0
a
4
=
0
1
a
5
=
1
1
a
8
=
1
0
a
11
=
−1
0
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
u
c
3
, c
4
, c
8
c
9
u − 1
c
5
, c
10
u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
y
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y − 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
3.28987 12.0000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u
4
+ 2u
2
+ 2)(u
15
− u
14
+ ··· + 2u − 1)
2
(u
23
+ 3u
22
+ ··· + 6u + 2)
c
2
u(u
2
+ 2u + 2)
2
(u
15
+ 7u
14
+ ··· + 4u
2
− 1)
2
· (u
23
+ 11u
22
+ ··· − 4u − 4)
c
3
, c
4
, c
8
c
9
(u − 1)(u + 1)
4
(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)(u
15
+ u
14
+ ··· − 4u − 1)
2
· (u
23
− 3u
22
+ ··· − 166u + 34)
c
11
u(u
4
− 2u
2
+ 2)(u
15
− 5u
14
+ ··· + 12u
3
− 1)
2
· (u
23
+ 15u
22
+ ··· + 1790u + 314)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y(y
2
+ 2y + 2)
2
(y
15
+ 7y
14
+ ··· + 4y
2
− 1)
2
· (y
23
+ 11y
22
+ ··· − 4y − 4)
c
2
y(y
2
+ 4)
2
(y
15
+ 3y
14
+ ··· + 8y − 1)
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
(y
15
− y
14
+ ··· + 16y − 1)
2
· (y
23
− 5y
22
+ ··· + 4028y − 1156)
c
11
y(y
2
− 2y + 2)
2
(y
15
+ 11y
14
+ ··· − 84y
2
− 1)
2
· (y
23
+ 7y
22
+ ··· − 489796y − 98596)
23
