11a
21
(K11a
21
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 9 3 11 10 5 8 7
Solving Sequence
7,11
8
1,3
2 6 4 10 9 5
c
7
c
11
c
2
c
6
c
3
c
10
c
8
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1428543776353u
40
+ 10013523822393u
39
+ ··· + 2380906293938b − 13661168161,
− 857126265809u
40
− 5059671029533u
39
+ ··· + 2380906293938a + 15522003749453,
u
41
+ 8u
40
+ ··· + 9u − 1i
I
u
2
= hb, −u
3
+ u
2
+ a − 3u + 2, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 45 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
= h1.43×10
12
u
40
+1.00×10
13
u
39
+· · ·+2.38×10
12
b−1.37×10
10
, −8.57×
10
11
u
40
−5.06×10
12
u
39
+· · ·+2.38×10
12
a+1.55×10
13
, u
41
+8u
40
+· · ·+9u−1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
0.360000u
40
+ 2.12510u
39
+ ··· − 57.3965u − 6.51937
−0.600000u
40
− 4.20576u
39
+ ··· − 5.97164u + 0.00573780
a
2
=
0.160000u
40
+ 0.886423u
39
+ ··· − 56.1906u − 6.68003
−0.400000u
40
− 2.96708u
39
+ ··· − 7.17757u + 0.166396
a
6
=
−0.604092u
40
− 5.23273u
39
+ ··· − 27.0571u − 2.48000
0.598354u
40
+ 4.78683u
39
+ ··· + 2.11593u − 0.600000
a
4
=
0.160000u
40
+ 0.668312u
39
+ ··· − 66.4027u − 8.31995
−0.600000u
40
− 4.14815u
39
+ ··· − 7.25524u − 0.0516402
a
10
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
−0.200000u
40
− 2.00411u
39
+ ··· − 22.3773u − 2.67998
−0.400000u
40
− 2.19754u
39
+ ··· + 2.95683u − 0.604092
a
5
=
−0.200000u
40
− 2.00411u
39
+ ··· − 22.3773u − 2.67998
−0.400000u
40
− 2.19754u
39
+ ··· + 2.95683u − 0.604092
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3866826976577
1190453146969
u
40
+
30172725798597
1190453146969
u
39
+ ··· +
97267270764267
1190453146969
u −
19437718983710
1190453146969
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
41
− 5u
40
+ ··· − 7u + 1
c
2
u
41
+ 17u
40
+ ··· − 21u + 1
c
3
, c
6
u
41
− u
40
+ ··· + 24u + 16
c
5
, c
9
u
41
− 2u
40
+ ··· + u + 1
c
7
, c
8
, c
10
c
11
u
41
+ 8u
40
+ ··· + 9u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
41
− 17y
40
+ ··· − 21y −1
c
2
y
41
+ 19y
40
+ ··· + 319y −1
c
3
, c
6
y
41
+ 27y
40
+ ··· − 3264y −256
c
5
, c
9
y
41
+ 8y
40
+ ··· + 9y −1
c
7
, c
8
, c
10
c
11
y
41
+ 52y
40
+ ··· + 289y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.371997 + 0.911661I
a = 0.0887599 − 0.0951085I
b = 0.944034 + 0.301769I
0.02027 + 4.12007I −7.00000 − 7.00432I
u = −0.371997 − 0.911661I
a = 0.0887599 + 0.0951085I
b = 0.944034 − 0.301769I
0.02027 − 4.12007I −7.00000 + 7.00432I
u = 0.123662 + 0.937506I
a = 0.94133 − 1.41174I
b = 0.152966 + 1.275670I
5.54405 + 0.90504I 0. − 2.30521I
u = 0.123662 − 0.937506I
a = 0.94133 + 1.41174I
b = 0.152966 − 1.275670I
5.54405 − 0.90504I 0. + 2.30521I
u = −0.744727 + 0.518203I
a = −0.330115 − 0.059884I
b = 0.127427 + 0.966899I
−0.343144 + 0.381292I −7.00000 + 0.I
u = −0.744727 − 0.518203I
a = −0.330115 + 0.059884I
b = 0.127427 − 0.966899I
−0.343144 − 0.381292I −7.00000 + 0.I
u = −0.860587 + 0.281389I
a = 0.620418 + 0.125659I
b = 0.383866 − 1.083520I
−1.07493 + 4.80769I −9.34122 − 6.74048I
u = −0.860587 − 0.281389I
a = 0.620418 − 0.125659I
b = 0.383866 + 1.083520I
−1.07493 − 4.80769I −9.34122 + 6.74048I
u = 0.250188 + 0.801720I
a = −1.38496 + 1.41699I
b = −0.452932 − 1.292530I
4.35267 − 4.76438I −1.23872 + 3.17616I
u = 0.250188 − 0.801720I
a = −1.38496 − 1.41699I
b = −0.452932 + 1.292530I
4.35267 + 4.76438I −1.23872 − 3.17616I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298760 + 0.775703I
a = 0.30126 + 2.51541I
b = 0.152801 − 0.776585I
−1.09017 + 1.98652I −2.92718 − 5.89159I
u = −0.298760 − 0.775703I
a = 0.30126 − 2.51541I
b = 0.152801 + 0.776585I
−1.09017 − 1.98652I −2.92718 + 5.89159I
u = −0.402696 + 1.111770I
a = −0.448898 − 1.278070I
b = −0.300924 + 1.194930I
4.72505 + 4.10019I 0
u = −0.402696 − 1.111770I
a = −0.448898 + 1.278070I
b = −0.300924 − 1.194930I
4.72505 − 4.10019I 0
u = −0.563543 + 1.076360I
a = 0.77154 + 1.22276I
b = 0.544305 − 1.241970I
3.04149 + 9.59886I 0
u = −0.563543 − 1.076360I
a = 0.77154 − 1.22276I
b = 0.544305 + 1.241970I
3.04149 − 9.59886I 0
u = −0.094895 + 0.764233I
a = 0.081309 + 0.430953I
b = −0.903364 + 0.108240I
0.550320 + 0.199179I −3.56736 − 0.22812I
u = −0.094895 − 0.764233I
a = 0.081309 − 0.430953I
b = −0.903364 − 0.108240I
0.550320 − 0.199179I −3.56736 + 0.22812I
u = −0.560839 + 0.097240I
a = 1.30596 − 1.04621I
b = 0.579988 + 0.456802I
−3.06538 + 0.92602I −14.9814 − 0.1523I
u = −0.560839 − 0.097240I
a = 1.30596 + 1.04621I
b = 0.579988 − 0.456802I
−3.06538 − 0.92602I −14.9814 + 0.1523I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369951 + 0.353558I
a = 0.185674 − 0.401147I
b = −0.276914 + 0.386438I
−0.304070 + 1.129050I −4.15006 − 5.99735I
u = −0.369951 − 0.353558I
a = 0.185674 + 0.401147I
b = −0.276914 − 0.386438I
−0.304070 − 1.129050I −4.15006 + 5.99735I
u = −0.12602 + 1.51041I
a = −0.013258 − 0.326775I
b = 0.008065 + 0.612774I
5.86173 + 3.10796I 0
u = −0.12602 − 1.51041I
a = −0.013258 + 0.326775I
b = 0.008065 − 0.612774I
5.86173 − 3.10796I 0
u = 0.379955 + 0.102142I
a = 0.22338 + 1.77156I
b = −0.210011 + 1.175300I
2.27591 + 2.55277I −0.28600 − 3.41736I
u = 0.379955 − 0.102142I
a = 0.22338 − 1.77156I
b = −0.210011 − 1.175300I
2.27591 − 2.55277I −0.28600 + 3.41736I
u = −0.06786 + 1.66115I
a = 0.00695 + 2.26459I
b = 0.022295 − 1.118440I
7.48443 + 3.29627I 0
u = −0.06786 − 1.66115I
a = 0.00695 − 2.26459I
b = 0.022295 + 1.118440I
7.48443 − 3.29627I 0
u = −0.02762 + 1.66408I
a = 0.518524 − 0.032043I
b = −1.212440 + 0.190127I
9.18847 + 0.68171I 0
u = −0.02762 − 1.66408I
a = 0.518524 + 0.032043I
b = −1.212440 − 0.190127I
9.18847 − 0.68171I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06444 + 1.66622I
a = −0.40564 + 1.80984I
b = −0.63341 − 1.39654I
13.0504 − 5.9463I 0
u = 0.06444 − 1.66622I
a = −0.40564 − 1.80984I
b = −0.63341 + 1.39654I
13.0504 + 5.9463I 0
u = −0.09721 + 1.68666I
a = −0.502494 − 0.093711I
b = 1.213200 + 0.228523I
9.10647 + 5.94562I 0
u = −0.09721 − 1.68666I
a = −0.502494 + 0.093711I
b = 1.213200 − 0.228523I
9.10647 − 5.94562I 0
u = 0.02231 + 1.69742I
a = 0.26842 − 1.88152I
b = 0.37989 + 1.47255I
14.9053 + 0.3952I 0
u = 0.02231 − 1.69742I
a = 0.26842 + 1.88152I
b = 0.37989 − 1.47255I
14.9053 − 0.3952I 0
u = −0.11803 + 1.73749I
a = −0.21725 − 1.84068I
b = −0.41152 + 1.45863I
14.7445 + 6.3325I 0
u = −0.11803 − 1.73749I
a = −0.21725 + 1.84068I
b = −0.41152 − 1.45863I
14.7445 − 6.3325I 0
u = −0.16530 + 1.73400I
a = 0.35701 + 1.74321I
b = 0.65439 − 1.38049I
12.7852 + 12.6394I 0
u = −0.16530 − 1.73400I
a = 0.35701 − 1.74321I
b = 0.65439 + 1.38049I
12.7852 − 12.6394I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0589447
a = −10.7359
b = −0.523441
−1.19034 −8.28720
9
II. I
u
2
= hb, −u
3
+ u
2
+ a − 3u + 2, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
3
=
u
3
− u
2
+ 3u − 2
0
a
2
=
u
3
− u
2
+ 2u − 2
u
a
6
=
1
0
a
4
=
u
3
− u
2
+ 3u − 2
0
a
10
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
5
=
u
−u
a
5
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
3
− 2u
2
+ 7u − 13
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
6
u
4
c
5
u
4
− u
3
+ u
2
+ 1
c
7
, c
8
u
4
− u
3
+ 3u
2
− 2u + 1
c
9
u
4
+ u
3
+ u
2
+ 1
c
10
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
7
, c
8
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.95668 + 1.22719I
b = 0
−1.85594 − 1.41510I −10.51825 + 2.96122I
u = 0.395123 − 0.506844I
a = −0.95668 − 1.22719I
b = 0
−1.85594 + 1.41510I −10.51825 − 2.96122I
u = 0.10488 + 1.55249I
a = −0.043315 + 0.641200I
b = 0
5.14581 − 3.16396I −8.98175 + 2.83489I
u = 0.10488 − 1.55249I
a = −0.043315 − 0.641200I
b = 0
5.14581 + 3.16396I −8.98175 − 2.83489I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
41
− 5u
40
+ ··· − 7u + 1)
c
2
((u + 1)
4
)(u
41
+ 17u
40
+ ··· − 21u + 1)
c
3
, c
6
u
4
(u
41
− u
40
+ ··· + 24u + 16)
c
4
((u + 1)
4
)(u
41
− 5u
40
+ ··· − 7u + 1)
c
5
(u
4
− u
3
+ u
2
+ 1)(u
41
− 2u
40
+ ··· + u + 1)
c
7
, c
8
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
41
+ 8u
40
+ ··· + 9u − 1)
c
9
(u
4
+ u
3
+ u
2
+ 1)(u
41
− 2u
40
+ ··· + u + 1)
c
10
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
41
+ 8u
40
+ ··· + 9u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
41
− 17y
40
+ ··· − 21y −1)
c
2
((y −1)
4
)(y
41
+ 19y
40
+ ··· + 319y −1)
c
3
, c
6
y
4
(y
41
+ 27y
40
+ ··· − 3264y −256)
c
5
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
41
+ 8y
40
+ ··· + 9y −1)
c
7
, c
8
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
41
+ 52y
40
+ ··· + 289y −1)
15
