11a
257
(K11a
257
)
A knot diagram
1
Linearized knot diagam
4 8 1 2 11 10 3 5 6 7 9
Solving Sequence
2,5
4 1
3,9
8 7 11 6 10
c
4
c
1
c
3
c
8
c
7
c
11
c
5
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h178u
52
− 830u
51
+ ··· + 4b + 135, −82u
52
+ 389u
51
+ ··· + 4a − 64, u
53
− 6u
52
+ ··· + 5u − 1i
I
u
2
= hb + a, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u + 1i
* 2 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
= h178u
52
− 830u
51
+ · · · + 4b + 135, −82u
52
+ 389u
51
+ · · · + 4a −
64, u
53
− 6u
52
+ · · · + 5u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
41
2
u
52
−
389
4
u
51
+ ··· −
285
4
u + 16
−
89
2
u
52
+
415
2
u
51
+ ··· + 143u −
135
4
a
8
=
−24u
52
+
441
4
u
51
+ ··· +
287
4
u −
71
4
−
89
2
u
52
+
415
2
u
51
+ ··· + 143u −
135
4
a
7
=
8u
52
−
143
4
u
51
+ ··· −
109
4
u +
21
4
−
183
4
u
52
+ 210u
51
+ ··· +
559
4
u −
131
4
a
11
=
1
16
u
52
−
5
16
u
51
+ ··· +
15
4
u +
17
16
−
1
16
u
52
+
5
16
u
51
+ ··· +
1
4
u −
1
16
a
6
=
−0.937500u
52
+ 4.56250u
51
+ ··· + 3.37500u + 0.187500
9
8
u
52
−
11
2
u
51
+ ··· −
33
8
u + 1
a
10
=
−
1
16
u
52
+
5
16
u
51
+ ··· +
5
4
u −
1
16
−u
52
+
39
8
u
51
+ ··· +
37
8
u −
7
8
a
10
=
−
1
16
u
52
+
5
16
u
51
+ ··· +
5
4
u −
1
16
−u
52
+
39
8
u
51
+ ··· +
37
8
u −
7
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 95u
52
−
3551
8
u
51
+ ··· −
2445
8
u +
625
8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
53
− 6u
52
+ ··· + 5u − 1
c
2
, c
7
u
53
+ u
52
+ ··· + 32u − 32
c
5
u
53
+ 6u
52
+ ··· + 5u + 1
c
6
, c
9
, c
10
u
53
− 2u
52
+ ··· − u − 1
c
8
u
53
+ 2u
52
+ ··· − 353u − 505
c
11
u
53
− 12u
52
+ ··· + 577u − 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
53
− 52y
52
+ ··· − 3y −1
c
2
, c
7
y
53
+ 33y
52
+ ··· − 3584y −1024
c
5
y
53
+ 54y
51
+ ··· + 3y −1
c
6
, c
9
, c
10
y
53
− 48y
52
+ ··· − 5y −1
c
8
y
53
− 24y
52
+ ··· − 2730661y −255025
c
11
y
53
+ 12y
52
+ ··· − 67257y −5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982418 + 0.186223I
a = −0.479524 + 0.755081I
b = 0.048069 − 0.323425I
−1.84631 + 0.73042I 0
u = −0.982418 − 0.186223I
a = −0.479524 − 0.755081I
b = 0.048069 + 0.323425I
−1.84631 − 0.73042I 0
u = −0.760759 + 0.648532I
a = 0.116454 + 1.176580I
b = −0.921747 − 0.370981I
1.51168 − 4.33800I 0
u = −0.760759 − 0.648532I
a = 0.116454 − 1.176580I
b = −0.921747 + 0.370981I
1.51168 + 4.33800I 0
u = −0.964025 + 0.386334I
a = 0.434988 − 1.154090I
b = 0.204570 + 0.572039I
2.96531 + 2.94902I 0
u = −0.964025 − 0.386334I
a = 0.434988 + 1.154090I
b = 0.204570 − 0.572039I
2.96531 − 2.94902I 0
u = −0.680941 + 0.650505I
a = −0.138770 − 1.031700I
b = 0.944950 + 0.173323I
−3.50201 − 0.91026I 0
u = −0.680941 − 0.650505I
a = −0.138770 + 1.031700I
b = 0.944950 − 0.173323I
−3.50201 + 0.91026I 0
u = −0.407582 + 0.847824I
a = 0.393026 + 0.322879I
b = −1.32942 + 0.64140I
2.63587 + 9.48987I 0. − 7.65628I
u = −0.407582 − 0.847824I
a = 0.393026 − 0.322879I
b = −1.32942 − 0.64140I
2.63587 − 9.48987I 0. + 7.65628I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.433922 + 0.813375I
a = −0.340896 − 0.426596I
b = 1.261610 − 0.534848I
−2.67007 + 5.91475I 0. − 7.38929I
u = −0.433922 − 0.813375I
a = −0.340896 + 0.426596I
b = 1.261610 + 0.534848I
−2.67007 − 5.91475I 0. + 7.38929I
u = −0.554849 + 0.709779I
a = 0.217443 + 0.777212I
b = −1.072060 + 0.149681I
−1.20946 + 2.41405I 0. − 4.08041I
u = −0.554849 − 0.709779I
a = 0.217443 − 0.777212I
b = −1.072060 − 0.149681I
−1.20946 − 2.41405I 0. + 4.08041I
u = −0.455576 + 0.714744I
a = 0.149975 + 0.576727I
b = −1.027580 + 0.397314I
−1.05950 + 2.27821I 0. − 2.78604I
u = −0.455576 − 0.714744I
a = 0.149975 − 0.576727I
b = −1.027580 − 0.397314I
−1.05950 − 2.27821I 0. + 2.78604I
u = −0.280767 + 0.714209I
a = 0.082115 − 0.233998I
b = 0.850866 − 0.798684I
4.99265 + 1.07686I 5.54603 − 2.94632I
u = −0.280767 − 0.714209I
a = 0.082115 + 0.233998I
b = 0.850866 + 0.798684I
4.99265 − 1.07686I 5.54603 + 2.94632I
u = −1.249920 + 0.188145I
a = 1.31747 − 0.73074I
b = −0.601101 + 0.517228I
2.25469 − 0.67746I 0
u = −1.249920 − 0.188145I
a = 1.31747 + 0.73074I
b = −0.601101 − 0.517228I
2.25469 + 0.67746I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.309040 + 0.052760I
a = −0.419594 − 1.100620I
b = 0.36327 + 1.84192I
2.89086 − 4.92095I 0
u = 1.309040 − 0.052760I
a = −0.419594 + 1.100620I
b = 0.36327 − 1.84192I
2.89086 + 4.92095I 0
u = 1.349770 + 0.028214I
a = 0.209932 + 0.804803I
b = −0.18196 − 1.58583I
−3.20353 − 1.98495I 0
u = 1.349770 − 0.028214I
a = 0.209932 − 0.804803I
b = −0.18196 + 1.58583I
−3.20353 + 1.98495I 0
u = −1.384270 + 0.010881I
a = −1.89998 + 0.04672I
b = 1.086340 − 0.036544I
−3.24184 + 0.00358I 0
u = −1.384270 − 0.010881I
a = −1.89998 − 0.04672I
b = 1.086340 + 0.036544I
−3.24184 − 0.00358I 0
u = −1.41369 + 0.09323I
a = 2.01362 − 0.40791I
b = −1.167340 + 0.325383I
−5.17639 + 3.49609I 0
u = −1.41369 − 0.09323I
a = 2.01362 + 0.40791I
b = −1.167340 − 0.325383I
−5.17639 − 3.49609I 0
u = −1.42461 + 0.12859I
a = −2.04808 + 0.56618I
b = 1.187440 − 0.454960I
−0.01422 + 7.04483I 0
u = −1.42461 − 0.12859I
a = −2.04808 − 0.56618I
b = 1.187440 + 0.454960I
−0.01422 − 7.04483I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43980 + 0.26155I
a = −1.64867 − 0.07993I
b = 1.43587 + 0.98145I
−0.57753 − 4.59375I 0
u = 1.43980 − 0.26155I
a = −1.64867 + 0.07993I
b = 1.43587 − 0.98145I
−0.57753 + 4.59375I 0
u = 0.094833 + 0.506795I
a = 1.277970 + 0.040231I
b = −0.118381 − 1.080780I
6.40428 + 3.28310I 8.64938 − 3.46229I
u = 0.094833 − 0.506795I
a = 1.277970 − 0.040231I
b = −0.118381 + 1.080780I
6.40428 − 3.28310I 8.64938 + 3.46229I
u = 1.49730 + 0.26665I
a = 1.66735 − 0.24380I
b = −1.46502 − 0.70007I
−7.38726 − 5.90070I 0
u = 1.49730 − 0.26665I
a = 1.66735 + 0.24380I
b = −1.46502 + 0.70007I
−7.38726 + 5.90070I 0
u = 1.49777 + 0.31809I
a = 1.95330 − 0.24247I
b = −1.71613 − 0.71417I
−3.5199 − 13.7301I 0
u = 1.49777 − 0.31809I
a = 1.95330 + 0.24247I
b = −1.71613 + 0.71417I
−3.5199 + 13.7301I 0
u = 1.50330 + 0.29927I
a = −1.85081 + 0.27564I
b = 1.62759 + 0.68002I
−8.94669 − 9.97082I 0
u = 1.50330 − 0.29927I
a = −1.85081 − 0.27564I
b = 1.62759 − 0.68002I
−8.94669 + 9.97082I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297732 + 0.359699I
a = −2.02123 − 0.17904I
b = 0.728284 + 0.956131I
5.56278 − 5.20660I 8.08747 + 4.37223I
u = 0.297732 − 0.359699I
a = −2.02123 + 0.17904I
b = 0.728284 − 0.956131I
5.56278 + 5.20660I 8.08747 − 4.37223I
u = 1.52827 + 0.22236I
a = 1.40930 − 0.42475I
b = −1.244310 − 0.531664I
−8.05943 − 5.77245I 0
u = 1.52827 − 0.22236I
a = 1.40930 + 0.42475I
b = −1.244310 + 0.531664I
−8.05943 + 5.77245I 0
u = 1.53880 + 0.17846I
a = −1.142980 + 0.488982I
b = 1.010830 + 0.467594I
−10.80810 − 1.96242I 0
u = 1.53880 − 0.17846I
a = −1.142980 − 0.488982I
b = 1.010830 − 0.467594I
−10.80810 + 1.96242I 0
u = 1.54665 + 0.14104I
a = 0.909678 − 0.537410I
b = −0.805465 − 0.419819I
−6.20214 + 1.77875I 0
u = 1.54665 − 0.14104I
a = 0.909678 + 0.537410I
b = −0.805465 + 0.419819I
−6.20214 − 1.77875I 0
u = 0.234258 + 0.285587I
a = 2.09531 − 0.08804I
b = −0.631451 − 0.724461I
0.17010 − 2.09238I 3.71444 + 4.57317I
u = 0.234258 − 0.285587I
a = 2.09531 + 0.08804I
b = −0.631451 + 0.724461I
0.17010 + 2.09238I 3.71444 − 4.57317I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.025576 + 0.363456I
a = −1.41418 + 0.47907I
b = 0.134953 + 0.733098I
0.824240 + 0.967983I 5.68123 − 4.85193I
u = 0.025576 − 0.363456I
a = −1.41418 − 0.47907I
b = 0.134953 − 0.733098I
0.824240 − 0.967983I 5.68123 + 4.85193I
u = 0.260469
a = −2.68640
b = 0.794640
2.04678 5.78300
10
II. I
u
2
= hb + a, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
1
=
−1
0
a
3
=
0
−1
a
9
=
a
−a
a
8
=
0
−a
a
7
=
0
−a
a
11
=
−a
2
− 1
a
2
a
6
=
a
4
+ a
2
+ 1
−a
4
a
10
=
−a
2
− 1
−a
4
a
10
=
−a
2
− 1
−a
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
4
− 4a
3
+ 2a
2
− 5a + 2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
7
u
5
c
3
, c
4
(u + 1)
5
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
6
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
9
, c
10
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
3
, c
4
(y −1)
5
c
2
, c
7
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
6
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −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 = −1.00000
a = −0.339110 + 0.822375I
b = 0.339110 − 0.822375I
−1.31583 + 1.53058I −0.02714 − 4.76366I
u = −1.00000
a = −0.339110 − 0.822375I
b = 0.339110 + 0.822375I
−1.31583 − 1.53058I −0.02714 + 4.76366I
u = −1.00000
a = 0.766826
b = −0.766826
0.756147 −2.80750
u = −1.00000
a = 0.455697 + 1.200150I
b = −0.455697 − 1.200150I
4.22763 − 4.40083I 4.43089 + 2.80751I
u = −1.00000
a = 0.455697 − 1.200150I
b = −0.455697 + 1.200150I
4.22763 + 4.40083I 4.43089 − 2.80751I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
53
− 6u
52
+ ··· + 5u − 1)
c
2
, c
7
u
5
(u
53
+ u
52
+ ··· + 32u − 32)
c
3
, c
4
((u + 1)
5
)(u
53
− 6u
52
+ ··· + 5u − 1)
c
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
53
+ 6u
52
+ ··· + 5u + 1)
c
6
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
53
− 2u
52
+ ··· − u − 1)
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
53
+ 2u
52
+ ··· − 353u − 505)
c
9
, c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
53
− 2u
52
+ ··· − u − 1)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
53
− 12u
52
+ ··· + 577u − 73)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
5
)(y
53
− 52y
52
+ ··· − 3y −1)
c
2
, c
7
y
5
(y
53
+ 33y
52
+ ··· − 3584y −1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
53
+ 54y
51
+ ··· + 3y −1)
c
6
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
53
− 48y
52
+ ··· − 5y −1)
c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
53
− 24y
52
+ ··· − 2730661y −255025)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
53
+ 12y
52
+ ··· − 67257y −5329)
16
