11a
118
(K11a
118
)
A knot diagram
1
Linearized knot diagam
6 1 10 7 2 5 3 11 4 8 9
Solving Sequence
2,5
6 7 1 3
4,9
10 11 8
c
5
c
6
c
1
c
2
c
4
c
9
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
46
− 4u
45
+ ··· + b + 2, −2u
46
+ 2u
45
+ ··· + a + u, u
47
− 2u
46
+ ··· − 2u
2
− 1i
I
u
2
= hu
2
+ b, a + u, u
4
+ u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 51 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
= h2u
46
−4u
45
+· · ·+ b + 2, −2u
46
+2u
45
+· · ·+ a + u, u
47
−2u
46
+· · ·−2u
2
−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
7
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
4
=
u
4
+ u
2
+ 1
−u
4
a
9
=
2u
46
− 2u
45
+ ··· − 10u
3
− u
−2u
46
+ 4u
45
+ ··· − 4u
2
− 2
a
10
=
−u
42
− 5u
40
+ ··· − u
2
− 1
u
43
+ 5u
41
+ ··· + u
3
+ u
a
11
=
−u
46
+ u
45
+ ··· + u
2
+ 1
u
46
− 2u
45
+ ··· + 2u
2
+ 1
a
8
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
a
8
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
46
− 4u
45
+ ··· − 13u − 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
47
− 2u
46
+ ··· − 2u
2
− 1
c
2
, c
4
, c
6
u
47
+ 12u
46
+ ··· − 4u − 1
c
3
, c
9
u
47
− u
46
+ ··· + 56u + 16
c
7
u
47
− 2u
46
+ ··· + 692u − 241
c
8
, c
10
, c
11
u
47
− 5u
46
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
47
+ 12y
46
+ ··· − 4y −1
c
2
, c
4
, c
6
y
47
+ 48y
46
+ ··· + 20y −1
c
3
, c
9
y
47
+ 27y
46
+ ··· − 1472y −256
c
7
y
47
− 12y
46
+ ··· − 623952y −58081
c
8
, c
10
, c
11
y
47
− 45y
46
+ ··· − 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.323780 + 0.951481I
a = −1.040000 − 0.645980I
b = 0.039385 + 0.152748I
−2.98908 − 5.01589I −7.64324 + 7.88279I
u = −0.323780 − 0.951481I
a = −1.040000 + 0.645980I
b = 0.039385 − 0.152748I
−2.98908 + 5.01589I −7.64324 − 7.88279I
u = 0.279046 + 0.946930I
a = 0.56107 − 1.31422I
b = −1.13319 + 1.30432I
−5.33668 + 2.70197I −9.52160 − 4.32403I
u = 0.279046 − 0.946930I
a = 0.56107 + 1.31422I
b = −1.13319 − 1.30432I
−5.33668 − 2.70197I −9.52160 + 4.32403I
u = −0.162628 + 1.011340I
a = −0.246189 + 0.321696I
b = −0.52431 − 1.50699I
−10.43430 + 2.59019I −12.08721 − 0.43654I
u = −0.162628 − 1.011340I
a = −0.246189 − 0.321696I
b = −0.52431 + 1.50699I
−10.43430 − 2.59019I −12.08721 + 0.43654I
u = −0.228159 + 0.924111I
a = 0.482803 + 0.476440I
b = 0.496433 + 0.569748I
−3.55919 − 0.29784I −10.26703 + 0.71916I
u = −0.228159 − 0.924111I
a = 0.482803 − 0.476440I
b = 0.496433 − 0.569748I
−3.55919 + 0.29784I −10.26703 − 0.71916I
u = 0.708344 + 0.612950I
a = −0.171277 − 1.044900I
b = 0.358664 + 0.237870I
−4.59202 + 2.73053I −5.50356 − 3.27752I
u = 0.708344 − 0.612950I
a = −0.171277 + 1.044900I
b = 0.358664 − 0.237870I
−4.59202 − 2.73053I −5.50356 + 3.27752I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356410 + 1.011910I
a = 1.41420 + 0.68105I
b = −0.864275 − 0.447765I
−9.29934 − 8.73167I −9.77244 + 7.33268I
u = −0.356410 − 1.011910I
a = 1.41420 − 0.68105I
b = −0.864275 + 0.447765I
−9.29934 + 8.73167I −9.77244 − 7.33268I
u = 0.340688 + 0.794423I
a = −0.122254 + 0.637267I
b = 0.278704 − 0.519560I
−0.34710 + 1.73528I −0.42828 − 4.75697I
u = 0.340688 − 0.794423I
a = −0.122254 − 0.637267I
b = 0.278704 + 0.519560I
−0.34710 − 1.73528I −0.42828 + 4.75697I
u = 0.683839 + 0.940887I
a = −0.548528 − 0.398362I
b = 0.617662 − 0.068827I
−5.43573 + 2.43943I −7.50586 − 2.89264I
u = 0.683839 − 0.940887I
a = −0.548528 + 0.398362I
b = 0.617662 + 0.068827I
−5.43573 − 2.43943I −7.50586 + 2.89264I
u = −0.834781 + 0.823539I
a = 1.25208 + 1.37561I
b = −2.22075 + 1.02814I
1.68842 + 0.66706I −2.90341 + 0.I
u = −0.834781 − 0.823539I
a = 1.25208 − 1.37561I
b = −2.22075 − 1.02814I
1.68842 − 0.66706I −2.90341 + 0.I
u = 0.815351 + 0.845486I
a = 1.63790 + 0.06363I
b = −1.65919 − 1.45595I
2.81443 + 1.97841I −3.90653 − 2.24549I
u = 0.815351 − 0.845486I
a = 1.63790 − 0.06363I
b = −1.65919 + 1.45595I
2.81443 − 1.97841I −3.90653 + 2.24549I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.857523 + 0.824218I
a = −1.55042 + 1.32128I
b = 2.82438 + 0.47847I
4.54046 − 2.88310I −0.74757 + 2.68199I
u = 0.857523 − 0.824218I
a = −1.55042 − 1.32128I
b = 2.82438 − 0.47847I
4.54046 + 2.88310I −0.74757 − 2.68199I
u = 0.885800 + 0.806423I
a = 0.87468 − 2.17600I
b = −3.02165 + 0.59943I
−1.16589 − 7.05931I −3.99587 + 3.23207I
u = 0.885800 − 0.806423I
a = 0.87468 + 2.17600I
b = −3.02165 − 0.59943I
−1.16589 + 7.05931I −3.99587 − 3.23207I
u = −0.846893 + 0.876661I
a = −1.243050 − 0.582712I
b = 1.61840 − 1.14508I
6.78103 − 1.89076I 3.32003 + 1.86990I
u = −0.846893 − 0.876661I
a = −1.243050 + 0.582712I
b = 1.61840 + 1.14508I
6.78103 + 1.89076I 3.32003 − 1.86990I
u = 0.789107 + 0.937549I
a = −0.18516 + 1.60290I
b = 1.69367 − 0.69541I
2.52856 + 4.03641I −4.47860 − 2.87730I
u = 0.789107 − 0.937549I
a = −0.18516 − 1.60290I
b = 1.69367 + 0.69541I
2.52856 − 4.03641I −4.47860 + 2.87730I
u = −0.793086 + 0.958197I
a = −1.31875 − 1.11688I
b = 3.24344 − 0.25353I
1.27181 − 6.75017I −3.82680 + 4.90142I
u = −0.793086 − 0.958197I
a = −1.31875 + 1.11688I
b = 3.24344 + 0.25353I
1.27181 + 6.75017I −3.82680 − 4.90142I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.827450 + 0.929808I
a = 0.652950 + 1.101310I
b = −2.09248 − 0.31110I
6.61449 − 4.34054I 3.06304 + 3.52446I
u = −0.827450 − 0.929808I
a = 0.652950 − 1.101310I
b = −2.09248 + 0.31110I
6.61449 + 4.34054I 3.06304 − 3.52446I
u = 0.805855 + 0.968008I
a = 1.48174 − 1.44769I
b = −2.97050 − 0.63587I
4.09177 + 9.07422I 0. − 7.57119I
u = 0.805855 − 0.968008I
a = 1.48174 + 1.44769I
b = −2.97050 + 0.63587I
4.09177 − 9.07422I 0. + 7.57119I
u = −0.880114 + 0.921081I
a = 1.22606 − 1.28739I
b = 0.27179 + 2.45585I
4.07979 − 3.25139I −6.94110 + 0.I
u = −0.880114 − 0.921081I
a = 1.22606 + 1.28739I
b = 0.27179 − 2.45585I
4.07979 + 3.25139I −6.94110 + 0.I
u = 0.811281 + 0.991380I
a = −2.18383 + 0.73777I
b = 3.18948 + 1.96415I
−1.74737 + 13.34970I 0. − 7.91325I
u = 0.811281 − 0.991380I
a = −2.18383 − 0.73777I
b = 3.18948 − 1.96415I
−1.74737 − 13.34970I 0. + 7.91325I
u = −0.689977 + 0.164527I
a = −1.53731 − 0.89142I
b = 0.350409 + 0.785923I
−6.58964 + 5.02938I −4.60471 − 3.19808I
u = −0.689977 − 0.164527I
a = −1.53731 + 0.89142I
b = 0.350409 − 0.785923I
−6.58964 − 5.02938I −4.60471 + 3.19808I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412032 + 0.515876I
a = 1.082960 + 0.365898I
b = −0.467743 − 0.314327I
0.483129 + 1.240200I 2.11511 − 5.50878I
u = 0.412032 − 0.515876I
a = 1.082960 − 0.365898I
b = −0.467743 + 0.314327I
0.483129 − 1.240200I 2.11511 + 5.50878I
u = −0.160236 + 0.579743I
a = −1.03520 + 1.13349I
b = 0.691220 + 0.719972I
−2.00613 − 0.73127I −7.95587 − 2.97532I
u = −0.160236 − 0.579743I
a = −1.03520 − 1.13349I
b = 0.691220 − 0.719972I
−2.00613 + 0.73127I −7.95587 + 2.97532I
u = −0.532528 + 0.151857I
a = 0.891221 − 0.043389I
b = −0.132594 − 0.683828I
−0.60484 + 1.87329I −1.11748 − 3.89488I
u = −0.532528 − 0.151857I
a = 0.891221 + 0.043389I
b = −0.132594 + 0.683828I
−0.60484 − 1.87329I −1.11748 + 3.89488I
u = 0.494353
a = −2.75136
b = 0.826082
−2.69658 −2.16950
9
II. I
u
2
= hu
2
+ b, a + u, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
7
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
3
+ u
2
+ 1
a
4
=
−u
3
u
3
+ u
2
+ 1
a
9
=
−u
−u
2
a
10
=
−u
−u
2
a
11
=
−2u
u
3
− u
2
+ u
a
8
=
u
−u
3
− u
a
8
=
u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
− 6u − 5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ u
2
+ 1
c
2
, c
6
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
, c
9
u
4
c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
5
u
4
+ u
3
+ u
2
+ 1
c
8
(u − 1)
4
c
10
, c
11
(u + 1)
4
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
4
, c
6
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
9
y
4
c
8
, c
10
, c
11
(y −1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −0.351808 − 0.720342I
b = 0.395123 − 0.506844I
−1.85594 + 1.41510I −5.13523 − 6.85627I
u = 0.351808 − 0.720342I
a = −0.351808 + 0.720342I
b = 0.395123 + 0.506844I
−1.85594 − 1.41510I −5.13523 + 6.85627I
u = −0.851808 + 0.911292I
a = 0.851808 − 0.911292I
b = 0.10488 + 1.55249I
5.14581 − 3.16396I 0.63523 + 2.29471I
u = −0.851808 − 0.911292I
a = 0.851808 + 0.911292I
b = 0.10488 − 1.55249I
5.14581 + 3.16396I 0.63523 − 2.29471I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ 1)(u
47
− 2u
46
+ ··· − 2u
2
− 1)
c
2
, c
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
47
+ 12u
46
+ ··· − 4u − 1)
c
3
, c
9
u
4
(u
47
− u
46
+ ··· + 56u + 16)
c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
47
+ 12u
46
+ ··· − 4u − 1)
c
5
(u
4
+ u
3
+ u
2
+ 1)(u
47
− 2u
46
+ ··· − 2u
2
− 1)
c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
47
− 2u
46
+ ··· + 692u − 241)
c
8
((u − 1)
4
)(u
47
− 5u
46
+ ··· − 2u + 1)
c
10
, c
11
((u + 1)
4
)(u
47
− 5u
46
+ ··· − 2u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
47
+ 12y
46
+ ··· − 4y −1)
c
2
, c
4
, c
6
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
47
+ 48y
46
+ ··· + 20y −1)
c
3
, c
9
y
4
(y
47
+ 27y
46
+ ··· − 1472y −256)
c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
47
− 12y
46
+ ··· − 623952y −58081)
c
8
, c
10
, c
11
((y −1)
4
)(y
47
− 45y
46
+ ··· − 14y −1)
15
