11a
219
(K11a
219
)
A knot diagram
1
Linearized knot diagam
7 1 9 11 10 2 6 4 3 5 8
Solving Sequence
4,11 5,8
9 1 3 2 10 6 7
c
4
c
8
c
11
c
3
c
2
c
10
c
5
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −u
20
− u
19
+ ··· + 8a + 1, u
21
+ 13u
19
+ ··· + 12u
3
− 1i
I
u
2
= h−2624442537u
27
+ 1988686630u
26
+ ··· + 16455396275b − 10223804083,
19079838812u
27
− 18444082905u
26
+ ··· + 16455396275a + 108956181733,
u
28
− u
27
+ ··· + 6u + 1i
I
u
3
= hb + u, a
3
+ a
2
+ 2a + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 55 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
= hb − u, −u
20
− u
19
+ · · · + 8a + 1, u
21
+ 13u
19
+ · · · + 12u
3
− 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
1
8
u
20
+
1
8
u
19
+ ··· −
25
8
u −
1
8
u
a
9
=
1
8
u
20
+
1
8
u
19
+ ··· −
17
8
u −
1
8
u
a
1
=
1
8
u
20
−
1
8
u
19
+ ··· −
3
8
u −
1
8
−
1
8
u
20
−
1
8
u
19
+ ··· +
9
8
u +
1
8
a
3
=
1
8
u
20
−
1
8
u
19
+ ··· −
1
8
u +
9
8
u
2
a
2
=
−
3
8
u
20
+
5
8
u
19
+ ··· +
7
8
u −
1
8
1
4
u
18
−
1
4
u
17
+ ··· −
1
4
u +
1
4
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
1
8
u
20
+
1
8
u
19
+ ··· −
17
8
u −
1
8
−
1
8
u
20
−
1
8
u
19
+ ··· +
9
8
u +
1
8
a
7
=
1
8
u
20
+
1
8
u
19
+ ··· −
17
8
u −
1
8
−
1
8
u
20
−
1
8
u
19
+ ··· +
9
8
u +
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
5
2
u
20
+ u
19
+
65
2
u
18
+ 15u
17
+ 177u
16
+
181
2
u
15
+
1023
2
u
14
+ 280u
13
+ 806u
12
+
907
2
u
11
+
599u
10
+ 316u
9
+
119
2
u
8
−
27
2
u
7
− 88u
6
− 49u
5
+
99
2
u
4
+
129
2
u
3
+ 17u
2
+ 12u +
11
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
21
+ 3u
20
+ ··· + 3u − 2
c
2
, c
7
u
21
+ 7u
20
+ ··· + 21u − 4
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
21
+ 13u
19
+ ··· + 12u
3
− 1
c
11
u
21
− 15u
20
+ ··· + 2103u − 266
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
21
+ 7y
20
+ ··· + 21y −4
c
2
, c
7
y
21
+ 15y
20
+ ··· + 1137y −16
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
21
+ 26y
20
+ ··· + 24y
2
− 1
c
11
y
21
+ 3y
20
+ ··· + 343765y −70756
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626749 + 0.333863I
a = 1.66451 − 0.51604I
b = −0.626749 + 0.333863I
2.49171 − 5.86529I 9.54952 + 8.01834I
u = −0.626749 − 0.333863I
a = 1.66451 + 0.51604I
b = −0.626749 − 0.333863I
2.49171 + 5.86529I 9.54952 − 8.01834I
u = 0.629746 + 0.248411I
a = −1.60683 − 0.39158I
b = 0.629746 + 0.248411I
3.16640 + 0.40908I 11.72672 − 2.09398I
u = 0.629746 − 0.248411I
a = −1.60683 + 0.39158I
b = 0.629746 − 0.248411I
3.16640 − 0.40908I 11.72672 + 2.09398I
u = −0.020126 + 1.386560I
a = 0.15798 + 1.61235I
b = −0.020126 + 1.386560I
−3.09312 − 3.11987I 1.81385 + 2.72222I
u = −0.020126 − 1.386560I
a = 0.15798 − 1.61235I
b = −0.020126 − 1.386560I
−3.09312 + 3.11987I 1.81385 − 2.72222I
u = −0.049869 + 0.513457I
a = 0.28009 − 1.88738I
b = −0.049869 + 0.513457I
1.38918 + 2.68088I 7.84813 − 2.28119I
u = −0.049869 − 0.513457I
a = 0.28009 + 1.88738I
b = −0.049869 − 0.513457I
1.38918 − 2.68088I 7.84813 + 2.28119I
u = −0.358971 + 0.369522I
a = 1.22004 − 0.88408I
b = −0.358971 + 0.369522I
−1.99273 − 1.21629I 2.57418 + 5.92996I
u = −0.358971 − 0.369522I
a = 1.22004 + 0.88408I
b = −0.358971 − 0.369522I
−1.99273 + 1.21629I 2.57418 − 5.92996I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31097 + 1.49970I
a = 1.257710 + 0.336801I
b = −0.31097 + 1.49970I
−8.25449 − 7.57688I 3.21336 + 3.12167I
u = −0.31097 − 1.49970I
a = 1.257710 − 0.336801I
b = −0.31097 − 1.49970I
−8.25449 + 7.57688I 3.21336 − 3.12167I
u = −0.18915 + 1.52129I
a = 0.833836 + 0.568249I
b = −0.18915 + 1.52129I
−10.20410 − 4.07649I 2.56533 + 2.84794I
u = −0.18915 − 1.52129I
a = 0.833836 − 0.568249I
b = −0.18915 − 1.52129I
−10.20410 + 4.07649I 2.56533 − 2.84794I
u = 0.33859 + 1.51855I
a = −1.273830 + 0.223483I
b = 0.33859 + 1.51855I
−9.5708 + 13.4578I 1.56507 − 7.58317I
u = 0.33859 − 1.51855I
a = −1.273830 − 0.223483I
b = 0.33859 − 1.51855I
−9.5708 − 13.4578I 1.56507 + 7.58317I
u = 0.14072 + 1.58052I
a = −0.556156 + 0.432838I
b = 0.14072 + 1.58052I
−12.61950 − 0.61749I −1.09619 + 1.91653I
u = 0.14072 − 1.58052I
a = −0.556156 − 0.432838I
b = 0.14072 − 1.58052I
−12.61950 + 0.61749I −1.09619 − 1.91653I
u = 0.25937 + 1.56915I
a = −0.961257 + 0.271014I
b = 0.25937 + 1.56915I
−15.0783 + 6.7163I −2.88981 − 3.97813I
u = 0.25937 − 1.56915I
a = −0.961257 − 0.271014I
b = 0.25937 − 1.56915I
−15.0783 − 6.7163I −2.88981 + 3.97813I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374847
a = −1.03218
b = 0.374847
0.610872 16.2600
7
II.
I
u
2
= h−2.62 × 10
9
u
27
+ 1.99 × 10
9
u
26
+ · · · + 1.65 × 10
10
b − 1.02 × 10
10
, 1.91 ×
10
10
u
27
−1.84×10
10
u
26
+· · ·+1.65×10
10
a+1.09×10
11
, u
28
−u
27
+· · ·+6u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
8
=
−1.15949u
27
+ 1.12085u
26
+ ··· − 31.4295u − 6.62130
0.159488u
27
− 0.120853u
26
+ ··· + 5.42946u + 0.621304
a
9
=
−u
27
+ u
26
+ ··· − 26u − 6
0.159488u
27
− 0.120853u
26
+ ··· + 5.42946u + 0.621304
a
1
=
−1.49816u
27
+ 1.73027u
26
+ ··· − 37.4676u − 7.20397
0.338676u
27
− 0.609413u
26
+ ··· + 7.03817u + 0.582669
a
3
=
−0.621304u
27
+ 0.780792u
26
+ ··· − 15.8797u + 2.70164
−0.0386351u
27
− 0.140553u
26
+ ··· + 0.335626u − 0.840512
a
2
=
−0.251205u
27
+ 0.244139u
26
+ ··· − 4.73991u − 4.26868
0.464204u
27
− 0.736552u
26
+ ··· + 3.57003u + 0.996329
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
−0.860293u
27
+ 0.936481u
26
+ ··· − 23.2248u − 5.89350
0.0244857u
27
− 0.155424u
26
+ ··· + 4.35668u + 0.358891
a
7
=
−0.860293u
27
+ 0.936481u
26
+ ··· − 23.2248u − 5.89350
0.0244857u
27
− 0.155424u
26
+ ··· + 4.35668u + 0.358891
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7485203784
16455396275
u
27
−
4244606112
3291079255
u
26
+ ··· −
308226995468
16455396275
u +
121631108806
16455396275
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
14
− u
13
+ ··· + u + 1)
2
c
2
, c
7
, c
11
(u
14
+ 5u
13
+ ··· + 3u + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
28
− u
27
+ ··· + 6u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
14
+ 5y
13
+ ··· + 3y + 1)
2
c
2
, c
7
, c
11
(y
14
+ 9y
13
+ ··· + 15y + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
28
+ 23y
27
+ ··· + 16y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903414 + 0.423724I
a = 1.12702 + 1.02376I
b = −0.21970 − 1.44931I
−3.28987 + 8.93586I 4.00000 − 7.26077I
u = 0.903414 − 0.423724I
a = 1.12702 − 1.02376I
b = −0.21970 + 1.44931I
−3.28987 − 8.93586I 4.00000 + 7.26077I
u = 0.821921 + 0.594799I
a = 0.892891 + 0.877803I
b = −0.09440 − 1.45565I
−7.93259 + 2.76747I −1.41762 − 3.21377I
u = 0.821921 − 0.594799I
a = 0.892891 − 0.877803I
b = −0.09440 + 1.45565I
−7.93259 − 2.76747I −1.41762 + 3.21377I
u = 0.709754 + 0.808180I
a = 0.550947 + 0.736144I
b = 0.06255 − 1.43472I
−4.48016 − 3.41271I 1.89400 + 2.62516I
u = 0.709754 − 0.808180I
a = 0.550947 − 0.736144I
b = 0.06255 + 1.43472I
−4.48016 + 3.41271I 1.89400 − 2.62516I
u = −0.830600 + 0.398708I
a = −1.18688 + 0.93008I
b = 0.20839 − 1.39977I
−2.09958 − 3.41271I 6.10600 + 2.62516I
u = −0.830600 − 0.398708I
a = −1.18688 − 0.93008I
b = 0.20839 + 1.39977I
−2.09958 + 3.41271I 6.10600 − 2.62516I
u = 0.081869 + 0.917517I
a = 0.228572 − 1.240560I
b = −0.132090 + 0.159270I
1.35286 + 2.76747I 9.41762 − 3.21377I
u = 0.081869 − 0.917517I
a = 0.228572 + 1.240560I
b = −0.132090 − 0.159270I
1.35286 − 2.76747I 9.41762 + 3.21377I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428554 + 0.809341I
a = −0.422476 + 0.298820I
b = −0.088503 − 1.263820I
−3.31269 − 1.37770I 3.11410 + 4.12207I
u = −0.428554 − 0.809341I
a = −0.422476 − 0.298820I
b = −0.088503 + 1.263820I
−3.31269 + 1.37770I 3.11410 − 4.12207I
u = −0.503703 + 0.626414I
a = −0.789243 + 0.320757I
b = 0.009651 − 1.290270I
−3.26705 − 1.37770I 4.88590 + 4.12207I
u = −0.503703 − 0.626414I
a = −0.789243 − 0.320757I
b = 0.009651 + 1.290270I
−3.26705 + 1.37770I 4.88590 − 4.12207I
u = −0.088503 + 1.263820I
a = 0.373414 + 0.021953I
b = −0.428554 − 0.809341I
−3.31269 + 1.37770I 3.11410 − 4.12207I
u = −0.088503 − 1.263820I
a = 0.373414 − 0.021953I
b = −0.428554 + 0.809341I
−3.31269 − 1.37770I 3.11410 + 4.12207I
u = 0.009651 + 1.290270I
a = 0.509500 − 0.148574I
b = −0.503703 − 0.626414I
−3.26705 + 1.37770I 4.88590 − 4.12207I
u = 0.009651 − 1.290270I
a = 0.509500 + 0.148574I
b = −0.503703 + 0.626414I
−3.26705 − 1.37770I 4.88590 + 4.12207I
u = 0.20839 + 1.39977I
a = 0.934651 − 0.300202I
b = −0.830600 − 0.398708I
−2.09958 + 3.41271I 6.10600 − 2.62516I
u = 0.20839 − 1.39977I
a = 0.934651 + 0.300202I
b = −0.830600 + 0.398708I
−2.09958 − 3.41271I 6.10600 + 2.62516I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06255 + 1.43472I
a = −0.679426 + 0.112500I
b = 0.709754 − 0.808180I
−4.48016 + 3.41271I 1.89400 − 2.62516I
u = 0.06255 − 1.43472I
a = −0.679426 − 0.112500I
b = 0.709754 + 0.808180I
−4.48016 − 3.41271I 1.89400 + 2.62516I
u = −0.09440 + 1.45565I
a = −0.866285 − 0.089303I
b = 0.821921 − 0.594799I
−7.93259 − 2.76747I −1.41762 + 3.21377I
u = −0.09440 − 1.45565I
a = −0.866285 + 0.089303I
b = 0.821921 + 0.594799I
−7.93259 + 2.76747I −1.41762 − 3.21377I
u = −0.21970 + 1.44931I
a = −1.005660 − 0.250758I
b = 0.903414 − 0.423724I
−3.28987 − 8.93586I 4.00000 + 7.26077I
u = −0.21970 − 1.44931I
a = −1.005660 + 0.250758I
b = 0.903414 + 0.423724I
−3.28987 + 8.93586I 4.00000 − 7.26077I
u = −0.132090 + 0.159270I
a = −3.16703 − 4.63750I
b = 0.081869 + 0.917517I
1.35286 + 2.76747I 9.41762 − 3.21377I
u = −0.132090 − 0.159270I
a = −3.16703 + 4.63750I
b = 0.081869 − 0.917517I
1.35286 − 2.76747I 9.41762 + 3.21377I
13
III. I
u
3
= hb + u, a
3
+ a
2
+ 2a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
1
a
8
=
a
−u
a
9
=
a − u
−u
a
1
=
a
2
u
a + u
a
3
=
−au
−1
a
2
=
a
2
u + au + u
−a
2
− au − 1
a
10
=
−u
0
a
6
=
0
1
a
7
=
a
−a − u
a
7
=
a
−a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
− 4a − 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
+ u
4
+ 2u
2
+ 1
c
2
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
2
+ 1)
3
c
11
u
6
− 3u
4
+ 2u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
3
+ y
2
+ 2y + 1)
2
c
2
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y + 1)
6
c
11
(y
3
− 3y
2
+ 2y + 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.215080 + 1.307140I
b = − 1.000000I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 1.000000I
a = −0.215080 − 1.307140I
b = − 1.000000I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 1.000000I
a = −0.569840
b = − 1.000000I
−4.40332 −3.01950
u = − 1.000000I
a = −0.215080 + 1.307140I
b = 1.000000I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = − 1.000000I
a = −0.215080 − 1.307140I
b = 1.000000I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = − 1.000000I
a = −0.569840
b = 1.000000I
−4.40332 −3.01950
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
+ u
4
+ 2u
2
+ 1)(u
14
− u
13
+ ··· + u + 1)
2
(u
21
+ 3u
20
+ ··· + 3u − 2)
c
2
, c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
14
+ 5u
13
+ ··· + 3u + 1)
2
· (u
21
+ 7u
20
+ ··· + 21u − 4)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
((u
2
+ 1)
3
)(u
21
+ 13u
19
+ ··· + 12u
3
− 1)(u
28
− u
27
+ ··· + 6u + 1)
c
11
(u
6
− 3u
4
+ 2u
2
+ 1)(u
14
+ 5u
13
+ ··· + 3u + 1)
2
· (u
21
− 15u
20
+ ··· + 2103u − 266)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
3
+ y
2
+ 2y + 1)
2
)(y
14
+ 5y
13
+ ··· + 3y + 1)
2
· (y
21
+ 7y
20
+ ··· + 21y −4)
c
2
, c
7
((y
3
+ 3y
2
+ 2y −1)
2
)(y
14
+ 9y
13
+ ··· + 15y + 1)
2
· (y
21
+ 15y
20
+ ··· + 1137y −16)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
((y + 1)
6
)(y
21
+ 26y
20
+ ··· + 24y
2
− 1)(y
28
+ 23y
27
+ ··· + 16y + 1)
c
11
((y
3
− 3y
2
+ 2y + 1)
2
)(y
14
+ 9y
13
+ ··· + 15y + 1)
2
· (y
21
+ 3y
20
+ ··· + 343765y −70756)
19
