11a
39
(K11a
39
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 9 3 11 5 6 8
Solving Sequence
5,10
6
2,11
4 1 9 7 3 8
c
5
c
10
c
4
c
1
c
9
c
6
c
3
c
8
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
− u
53
+ ··· + b − 3u, −2u
54
+ 2u
53
+ ··· + a + 6u, u
55
− 2u
54
+ ··· + 2u + 1i
I
u
2
= hb + 1, u
3
+ a − 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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
54
−u
53
+· · ·+b−3u, −2u
54
+2u
53
+· · ·+a+6u, u
55
−2u
54
+· · ·+2u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
2u
54
− 2u
53
+ ··· + 13u
2
− 6u
−u
54
+ u
53
+ ··· − 2u
2
+ 3u
a
11
=
u
−u
3
+ u
a
4
=
u
54
− u
53
+ ··· − 5u + 1
−u
54
+ u
53
+ ··· − 3u
2
+ 2u
a
1
=
u
9
− 4u
7
+ 5u
5
− 2u
3
+ u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
9
=
−u
u
a
7
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
3u
54
− 3u
53
+ ··· + 11u
2
− 7u
−u
54
+ u
53
+ ··· − u
2
+ 3u
a
8
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
54
+ 4u
53
+ ··· + 3u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
55
− 6u
54
+ ··· − 8u + 1
c
2
u
55
+ 24u
54
+ ··· + 8u + 1
c
3
, c
7
u
55
+ u
54
+ ··· + 64u + 32
c
5
, c
9
, c
10
u
55
− 2u
54
+ ··· + 2u + 1
c
6
u
55
+ 6u
54
+ ··· + 302u + 77
c
8
, c
11
u
55
− 8u
54
+ ··· + 94u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
55
− 24y
54
+ ··· + 8y −1
c
2
y
55
+ 20y
54
+ ··· − 220y −1
c
3
, c
7
y
55
+ 33y
54
+ ··· − 14848y −1024
c
5
, c
9
, c
10
y
55
− 52y
54
+ ··· + 14y −1
c
6
y
55
− 20y
54
+ ··· + 146490y −5929
c
8
, c
11
y
55
+ 48y
54
+ ··· + 4314y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.078520 + 0.133677I
a = 0.516431 + 0.026697I
b = 0.912992 + 0.503784I
1.55049 − 1.99776I 0
u = 1.078520 − 0.133677I
a = 0.516431 − 0.026697I
b = 0.912992 − 0.503784I
1.55049 + 1.99776I 0
u = −0.405577 + 0.698559I
a = 1.19426 − 1.95218I
b = 1.131320 + 0.693924I
4.79235 − 10.53540I −0.79776 + 8.38025I
u = −0.405577 − 0.698559I
a = 1.19426 + 1.95218I
b = 1.131320 − 0.693924I
4.79235 + 10.53540I −0.79776 − 8.38025I
u = −0.429702 + 0.678403I
a = −0.970506 + 0.157558I
b = 0.496725 − 0.933713I
6.73070 − 4.57214I 1.95904 + 4.03979I
u = −0.429702 − 0.678403I
a = −0.970506 − 0.157558I
b = 0.496725 + 0.933713I
6.73070 + 4.57214I 1.95904 − 4.03979I
u = −0.544877 + 0.580820I
a = −0.164386 + 0.526147I
b = 1.103900 − 0.704264I
5.32499 + 6.24906I 0.59828 − 2.50741I
u = −0.544877 − 0.580820I
a = −0.164386 − 0.526147I
b = 1.103900 + 0.704264I
5.32499 − 6.24906I 0.59828 + 2.50741I
u = −0.510509 + 0.609052I
a = 0.325943 − 1.106180I
b = 0.541319 + 0.917635I
7.04434 + 0.29231I 2.77654 + 2.24461I
u = −0.510509 − 0.609052I
a = 0.325943 + 1.106180I
b = 0.541319 − 0.917635I
7.04434 − 0.29231I 2.77654 − 2.24461I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412834 + 0.641001I
a = −0.42450 − 2.15007I
b = −0.881787 + 0.589772I
1.48241 + 4.33310I −1.64326 − 6.16138I
u = 0.412834 − 0.641001I
a = −0.42450 + 2.15007I
b = −0.881787 − 0.589772I
1.48241 − 4.33310I −1.64326 + 6.16138I
u = 0.458268 + 0.584600I
a = 0.817122 + 0.781457I
b = −0.813432 − 0.582817I
1.70221 − 0.32794I −0.771677 − 0.468923I
u = 0.458268 − 0.584600I
a = 0.817122 − 0.781457I
b = −0.813432 + 0.582817I
1.70221 + 0.32794I −0.771677 + 0.468923I
u = −0.415395 + 0.603187I
a = −0.756841 + 1.109310I
b = −1.302130 + 0.031330I
0.07504 − 1.93289I −0.05787 + 3.96687I
u = −0.415395 − 0.603187I
a = −0.756841 − 1.109310I
b = −1.302130 − 0.031330I
0.07504 + 1.93289I −0.05787 − 3.96687I
u = −1.265410 + 0.116454I
a = −0.756900 − 0.079067I
b = −1.162780 + 0.205267I
0.59955 − 1.29811I 0
u = −1.265410 − 0.116454I
a = −0.756900 + 0.079067I
b = −1.162780 − 0.205267I
0.59955 + 1.29811I 0
u = 1.297170 + 0.044309I
a = 1.149320 + 0.636439I
b = −0.351487 − 0.343411I
2.99828 + 0.14721I 0
u = 1.297170 − 0.044309I
a = 1.149320 − 0.636439I
b = −0.351487 + 0.343411I
2.99828 − 0.14721I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.288550 + 0.158962I
a = −0.51700 − 2.28808I
b = −1.022630 + 0.390914I
1.08244 + 3.51008I 0
u = 1.288550 − 0.158962I
a = −0.51700 + 2.28808I
b = −1.022630 − 0.390914I
1.08244 − 3.51008I 0
u = −1.292250 + 0.245052I
a = 0.94579 − 1.66072I
b = 1.053490 + 0.579410I
3.09735 − 8.51931I 0
u = −1.292250 − 0.245052I
a = 0.94579 + 1.66072I
b = 1.053490 − 0.579410I
3.09735 + 8.51931I 0
u = 0.659363 + 0.177799I
a = 0.370767 + 0.659351I
b = 0.825967 − 0.561444I
1.63950 + 2.24198I 1.57550 − 4.32492I
u = 0.659363 − 0.177799I
a = 0.370767 − 0.659351I
b = 0.825967 + 0.561444I
1.63950 − 2.24198I 1.57550 + 4.32492I
u = 0.108922 + 0.669976I
a = 2.05168 + 0.39909I
b = 0.999297 − 0.553816I
−1.25442 + 5.19790I −5.46768 − 6.87562I
u = 0.108922 − 0.669976I
a = 2.05168 − 0.39909I
b = 0.999297 + 0.553816I
−1.25442 − 5.19790I −5.46768 + 6.87562I
u = 0.223843 + 0.635800I
a = 0.619795 + 0.836958I
b = 0.682905 + 0.426557I
−0.093506 + 0.957018I −1.47250 − 1.22419I
u = 0.223843 − 0.635800I
a = 0.619795 − 0.836958I
b = 0.682905 − 0.426557I
−0.093506 − 0.957018I −1.47250 + 1.22419I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.345750 + 0.196757I
a = −0.348002 + 0.275917I
b = 0.325642 − 0.591557I
4.93016 − 3.86526I 0
u = −1.345750 − 0.196757I
a = −0.348002 − 0.275917I
b = 0.325642 + 0.591557I
4.93016 + 3.86526I 0
u = −1.39666 + 0.23010I
a = −0.011407 − 0.386009I
b = 0.636512 − 0.224540I
5.07190 − 4.05462I 0
u = −1.39666 − 0.23010I
a = −0.011407 + 0.386009I
b = 0.636512 + 0.224540I
5.07190 + 4.05462I 0
u = −1.43083 + 0.02750I
a = −0.66190 − 1.48550I
b = 0.838321 + 0.728876I
7.99304 − 2.76322I 0
u = −1.43083 − 0.02750I
a = −0.66190 + 1.48550I
b = 0.838321 − 0.728876I
7.99304 + 2.76322I 0
u = 0.220263 + 0.502370I
a = 0.543936 + 0.221214I
b = 0.182425 + 0.252129I
−0.008201 + 1.198200I −0.25143 − 5.38204I
u = 0.220263 − 0.502370I
a = 0.543936 − 0.221214I
b = 0.182425 − 0.252129I
−0.008201 − 1.198200I −0.25143 + 5.38204I
u = −0.046404 + 0.536106I
a = −2.41342 + 1.29245I
b = −1.047030 − 0.274962I
−3.02612 − 0.98819I −10.81757 + 0.62676I
u = −0.046404 − 0.536106I
a = −2.41342 − 1.29245I
b = −1.047030 + 0.274962I
−3.02612 + 0.98819I −10.81757 − 0.62676I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45734 + 0.22515I
a = 0.507704 − 0.942507I
b = −1.341850 − 0.047444I
6.09964 + 4.98197I 0
u = 1.45734 − 0.22515I
a = 0.507704 + 0.942507I
b = −1.341850 + 0.047444I
6.09964 − 4.98197I 0
u = −1.46520 + 0.21259I
a = 1.47883 − 1.30859I
b = −0.786253 + 0.638767I
7.88540 − 2.59431I 0
u = −1.46520 − 0.21259I
a = 1.47883 + 1.30859I
b = −0.786253 − 0.638767I
7.88540 + 2.59431I 0
u = −1.46151 + 0.23703I
a = 0.35860 + 2.60378I
b = −0.903696 − 0.627740I
7.52118 − 7.54900I 0
u = −1.46151 − 0.23703I
a = 0.35860 − 2.60378I
b = −0.903696 + 0.627740I
7.52118 + 7.54900I 0
u = 1.46676 + 0.25976I
a = 0.13179 + 2.56805I
b = 1.150220 − 0.701224I
10.8274 + 14.0334I 0
u = 1.46676 − 0.25976I
a = 0.13179 − 2.56805I
b = 1.150220 + 0.701224I
10.8274 − 14.0334I 0
u = 1.47287 + 0.24797I
a = −1.38353 − 1.05356I
b = 0.483891 + 0.966514I
12.8723 + 7.9548I 0
u = 1.47287 − 0.24797I
a = −1.38353 + 1.05356I
b = 0.483891 − 0.966514I
12.8723 − 7.9548I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48811 + 0.18811I
a = −1.12025 − 1.22948I
b = 1.099520 + 0.737359I
11.90410 − 3.49537I 0
u = 1.48811 − 0.18811I
a = −1.12025 + 1.22948I
b = 1.099520 − 0.737359I
11.90410 + 3.49537I 0
u = 1.48611 + 0.20604I
a = −0.20805 + 1.92611I
b = 0.576460 − 0.947356I
13.50700 + 2.65879I 0
u = 1.48611 − 0.20604I
a = −0.20805 − 1.92611I
b = 0.576460 + 0.947356I
13.50700 − 2.65879I 0
u = −0.217641
a = 2.44944
b = −0.855618
−1.24884 −7.99830
10
II. I
u
2
= hb + 1, u
3
+ a − 2u, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
−u
3
+ 2u
−1
a
11
=
u
−u
3
+ u
a
4
=
−u
3
+ 2u + 1
−1
a
1
=
−1
0
a
9
=
−u
u
a
7
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
3
=
−u
3
+ 2u + 1
−1
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
+ u
2
+ 8u − 3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
7
u
5
c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
8
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
9
, c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.629714
b = −1.00000
0.756147 −2.23020
u = −0.309916 + 0.549911I
a = −0.871221 + 1.107660I
b = −1.00000
−1.31583 − 1.53058I −6.94263 + 4.09764I
u = −0.309916 − 0.549911I
a = −0.871221 − 1.107660I
b = −1.00000
−1.31583 + 1.53058I −6.94263 − 4.09764I
u = 1.41878 + 0.21917I
a = 0.186078 − 0.874646I
b = −1.00000
4.22763 + 4.40083I −2.94226 − 4.18967I
u = 1.41878 − 0.21917I
a = 0.186078 + 0.874646I
b = −1.00000
4.22763 − 4.40083I −2.94226 + 4.18967I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
55
− 6u
54
+ ··· − 8u + 1)
c
2
((u + 1)
5
)(u
55
+ 24u
54
+ ··· + 8u + 1)
c
3
, c
7
u
5
(u
55
+ u
54
+ ··· + 64u + 32)
c
4
((u + 1)
5
)(u
55
− 6u
54
+ ··· − 8u + 1)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
55
− 2u
54
+ ··· + 2u + 1)
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
55
+ 6u
54
+ ··· + 302u + 77)
c
8
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
55
− 8u
54
+ ··· + 94u − 7)
c
9
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
55
− 2u
54
+ ··· + 2u + 1)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
55
− 8u
54
+ ··· + 94u − 7)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
55
− 24y
54
+ ··· + 8y −1)
c
2
((y −1)
5
)(y
55
+ 20y
54
+ ··· − 220y −1)
c
3
, c
7
y
5
(y
55
+ 33y
54
+ ··· − 14848y −1024)
c
5
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
55
− 52y
54
+ ··· + 14y −1)
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
55
− 20y
54
+ ··· + 146490y −5929)
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
55
+ 48y
54
+ ··· + 4314y −49)
16
