11a
265
(K11a
265
)
A knot diagram
1
Linearized knot diagam
8 5 1 2 11 10 4 3 7 6 9
Solving Sequence
7,10
6 11
3,5
2 9 1 4 8
c
6
c
10
c
5
c
2
c
9
c
11
c
3
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−3051064229120u
53
− 209833800856320u
52
+ ··· + 578826226766096229b + 3885666844,
− 3.04606 × 10
12
u
53
− 2.09713 × 10
14
u
52
+ ··· + 5.78826 × 10
17
a + 1.06118 × 10
18
, u
54
+ u
53
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 54 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
= h−3.05×10
12
u
53
−2.10×10
14
u
52
+· · ·+5.79×10
17
b+3.89×10
9
, −3.05×
10
12
u
53
−2.10×10
14
u
52
+· · ·+5.79×10
17
a+1.06×10
18
, u
54
+u
53
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
−u
u
3
+ u
a
3
=
5.26248 × 10
−6
u
53
+ 0.000362307u
52
+ ··· − 2.47819u − 1.83333
5.27112 × 10
−6
u
53
+ 0.000362516u
52
+ ··· + 3.16667u − 6.71301 × 10
−9
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
1.21040 × 10
−6
u
53
+ 0.0000804923u
52
+ ··· − 3.23347u − 1.01667
1.19100 × 10
−6
u
53
+ 0.0000798962u
52
+ ··· + 3.18333u − 1.72656 × 10
−9
a
9
=
u
u
a
1
=
u
5
+ 2u
3
− u
u
5
+ 3u
3
+ u
a
4
=
−7.89546 × 10
−7
u
53
− 0.0000401538u
52
+ ··· − 2.31083u − 1.75000
−6.83885 × 10
−7
u
53
− 0.0000369648u
52
+ ··· + 3.25000u + 1.91977 × 10
−9
a
8
=
−0.00581270u
53
− 0.00326390u
52
+ ··· − 0.253465u + 0.116715
0.0000208391u
53
+ 0.00252101u
52
+ ··· + 2.48502u + 0.00250009
a
8
=
−0.00581270u
53
− 0.00326390u
52
+ ··· − 0.253465u + 0.116715
0.0000208391u
53
+ 0.00252101u
52
+ ··· + 2.48502u + 0.00250009
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
613554862282394952
192942075588698743
u
53
−
459136890023638500
192942075588698743
u
52
+···+
755304846551017564
192942075588698743
u+
883739019103167146
192942075588698743
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 3u
53
+ ··· + u + 1
c
2
, c
4
u
54
+ u
53
+ ··· + 9u + 1
c
3
u
54
− 9u
53
+ ··· − u + 1
c
5
, c
6
, c
9
c
10
u
54
− u
53
+ ··· − 3u + 1
c
7
u
54
− 3u
53
+ ··· + 15u − 1
c
8
u
54
− u
53
+ ··· − 39u + 7
c
11
u
54
+ 13u
53
+ ··· + 657u + 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 9y
53
+ ··· + 3y + 1
c
2
, c
4
y
54
− 35y
53
+ ··· − 9y + 1
c
3
y
54
− 3y
53
+ ··· − 9y + 1
c
5
, c
6
, c
9
c
10
y
54
+ 61y
53
+ ··· + 3y + 1
c
7
y
54
− 55y
53
+ ··· − 413y + 1
c
8
y
54
− 43y
53
+ ··· − 317y + 49
c
11
y
54
+ 5y
53
+ ··· + 103347y + 9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.545362 + 0.766936I
a = −0.188047 − 0.903445I
b = −0.949767 − 0.409626I
1.00016 − 3.95703I −3.00000 + 11.79776I
u = 0.545362 − 0.766936I
a = −0.188047 + 0.903445I
b = −0.949767 + 0.409626I
1.00016 + 3.95703I −3.00000 − 11.79776I
u = −0.172970 + 1.046260I
a = −1.181840 + 0.461864I
b = −0.428067 − 0.337725I
5.26922 − 5.01222I 0
u = −0.172970 − 1.046260I
a = −1.181840 − 0.461864I
b = −0.428067 + 0.337725I
5.26922 + 5.01222I 0
u = −0.561965 + 0.693690I
a = 0.31746 + 1.44112I
b = −1.53183 + 1.30909I
2.46124 + 12.12320I 0.08589 − 9.41589I
u = −0.561965 − 0.693690I
a = 0.31746 − 1.44112I
b = −1.53183 − 1.30909I
2.46124 − 12.12320I 0.08589 + 9.41589I
u = −0.506554 + 0.624526I
a = 0.086447 − 0.728121I
b = 1.52442 − 0.61745I
−1.47018 + 6.23173I −3.03340 − 8.93677I
u = −0.506554 − 0.624526I
a = 0.086447 + 0.728121I
b = 1.52442 + 0.61745I
−1.47018 − 6.23173I −3.03340 + 8.93677I
u = 0.670771 + 0.429255I
a = 0.279527 − 0.397115I
b = −0.026389 − 0.348007I
−0.67521 − 2.21346I −9.82154 + 8.24478I
u = 0.670771 − 0.429255I
a = 0.279527 + 0.397115I
b = −0.026389 + 0.348007I
−0.67521 + 2.21346I −9.82154 − 8.24478I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.411382 + 0.638832I
a = 0.14437 − 1.44846I
b = 0.95232 − 1.40932I
3.27194 + 4.12688I 4.58912 − 9.06876I
u = −0.411382 − 0.638832I
a = 0.14437 + 1.44846I
b = 0.95232 + 1.40932I
3.27194 − 4.12688I 4.58912 + 9.06876I
u = 0.499596 + 0.521821I
a = −0.436226 − 0.083526I
b = 0.207048 + 0.493590I
−0.70487 − 1.75962I −4.58587 + 3.17454I
u = 0.499596 − 0.521821I
a = −0.436226 + 0.083526I
b = 0.207048 − 0.493590I
−0.70487 + 1.75962I −4.58587 − 3.17454I
u = −0.293339 + 0.635944I
a = 0.850317 − 1.011600I
b = −0.428431 − 0.192704I
4.01735 + 0.63222I 7.39930 − 2.66782I
u = −0.293339 − 0.635944I
a = 0.850317 + 1.011600I
b = −0.428431 + 0.192704I
4.01735 − 0.63222I 7.39930 + 2.66782I
u = −0.659334 + 0.232085I
a = 0.346734 − 1.144240I
b = 1.24395 + 0.77928I
1.09662 − 8.00461I −2.60038 + 4.65248I
u = −0.659334 − 0.232085I
a = 0.346734 + 1.144240I
b = 1.24395 − 0.77928I
1.09662 + 8.00461I −2.60038 − 4.65248I
u = 0.393123 + 0.559225I
a = 0.37563 + 4.16236I
b = 2.99641 + 0.60734I
1.56763 − 1.75278I −6.2825 − 17.5292I
u = 0.393123 − 0.559225I
a = 0.37563 − 4.16236I
b = 2.99641 − 0.60734I
1.56763 + 1.75278I −6.2825 + 17.5292I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148291 + 1.360240I
a = −0.709327 + 0.835990I
b = −0.329247 + 0.393163I
4.94656 − 5.25128I 0
u = 0.148291 − 1.360240I
a = −0.709327 − 0.835990I
b = −0.329247 − 0.393163I
4.94656 + 5.25128I 0
u = −0.000111 + 0.622884I
a = −0.308967 − 0.550291I
b = −0.810890 + 0.336840I
1.31595 − 1.53064I 2.46645 + 4.42217I
u = −0.000111 − 0.622884I
a = −0.308967 + 0.550291I
b = −0.810890 − 0.336840I
1.31595 + 1.53064I 2.46645 − 4.42217I
u = −0.541870 + 0.294917I
a = −0.16659 + 1.62943I
b = −0.870080 − 0.000654I
−2.42907 − 2.60276I −6.59954 + 2.27110I
u = −0.541870 − 0.294917I
a = −0.16659 − 1.62943I
b = −0.870080 + 0.000654I
−2.42907 + 2.60276I −6.59954 − 2.27110I
u = 0.615568
a = −0.465542
b = 0.796207
−1.10777 −11.9580
u = −0.04794 + 1.44591I
a = 0.30412 − 1.67700I
b = 0.023300 − 0.933728I
2.95011 − 0.80061I 0
u = −0.04794 − 1.44591I
a = 0.30412 + 1.67700I
b = 0.023300 + 0.933728I
2.95011 + 0.80061I 0
u = 0.346728 + 0.415892I
a = −0.41230 − 2.49448I
b = −2.30227 + 0.40921I
1.12331 − 0.98698I 7.38443 + 9.46034I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346728 − 0.415892I
a = −0.41230 + 2.49448I
b = −2.30227 − 0.40921I
1.12331 + 0.98698I 7.38443 − 9.46034I
u = 0.496604
a = −0.826100
b = 0.696774
−1.13235 −10.5020
u = 0.07837 + 1.54926I
a = 1.86936 + 1.70184I
b = 2.37253 + 0.73488I
7.92145 − 2.31500I 0
u = 0.07837 − 1.54926I
a = 1.86936 − 1.70184I
b = 2.37253 − 0.73488I
7.92145 + 2.31500I 0
u = 0.13720 + 1.55270I
a = 0.040303 − 0.953011I
b = −0.542375 − 0.985698I
6.29079 − 4.01270I 0
u = 0.13720 − 1.55270I
a = 0.040303 + 0.953011I
b = −0.542375 + 0.985698I
6.29079 + 4.01270I 0
u = −0.04879 + 1.56688I
a = 1.45840 − 1.17346I
b = 1.72999 − 1.25663I
8.64965 − 1.05444I 0
u = −0.04879 − 1.56688I
a = 1.45840 + 1.17346I
b = 1.72999 + 1.25663I
8.64965 + 1.05444I 0
u = 0.10731 + 1.56661I
a = −2.89723 − 2.74617I
b = −2.89407 − 0.64960I
8.80102 − 3.53795I 0
u = 0.10731 − 1.56661I
a = −2.89723 + 2.74617I
b = −2.89407 + 0.64960I
8.80102 + 3.53795I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14576 + 1.57745I
a = −1.40684 + 1.66633I
b = −2.06161 + 1.25521I
5.94961 + 8.61448I 0
u = −0.14576 − 1.57745I
a = −1.40684 − 1.66633I
b = −2.06161 − 1.25521I
5.94961 − 8.61448I 0
u = −0.08890 + 1.58461I
a = 0.610813 + 0.478237I
b = 1.332270 + 0.248255I
11.59780 + 2.07370I 0
u = −0.08890 − 1.58461I
a = 0.610813 − 0.478237I
b = 1.332270 − 0.248255I
11.59780 − 2.07370I 0
u = −0.11679 + 1.58495I
a = −0.47013 + 2.67136I
b = −0.82660 + 2.34169I
10.82650 + 6.06392I 0
u = −0.11679 − 1.58495I
a = −0.47013 − 2.67136I
b = −0.82660 − 2.34169I
10.82650 − 6.06392I 0
u = −0.372639 + 0.159058I
a = −1.55778 + 0.98703I
b = −0.893238 − 0.244729I
2.00449 − 1.26243I −0.21146 + 2.28876I
u = −0.372639 − 0.159058I
a = −1.55778 − 0.98703I
b = −0.893238 + 0.244729I
2.00449 + 1.26243I −0.21146 − 2.28876I
u = −0.16943 + 1.60101I
a = 0.78343 − 2.47982I
b = 1.68631 − 1.83629I
10.1949 + 14.8555I 0
u = −0.16943 − 1.60101I
a = 0.78343 + 2.47982I
b = 1.68631 + 1.83629I
10.1949 − 14.8555I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16913 + 1.62019I
a = 0.64236 + 1.39992I
b = 1.033010 + 0.913072I
9.06286 − 6.69333I 0
u = 0.16913 − 1.62019I
a = 0.64236 − 1.39992I
b = 1.033010 − 0.913072I
9.06286 + 6.69333I 0
u = −0.01419 + 1.65792I
a = 0.271821 + 0.270288I
b = −0.453188 + 0.515678I
14.5155 − 4.5567I 0
u = −0.01419 − 1.65792I
a = 0.271821 − 0.270288I
b = −0.453188 − 0.515678I
14.5155 + 4.5567I 0
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
54
+ 3u
53
+ ··· + u + 1
c
2
, c
4
u
54
+ u
53
+ ··· + 9u + 1
c
3
u
54
− 9u
53
+ ··· − u + 1
c
5
, c
6
, c
9
c
10
u
54
− u
53
+ ··· − 3u + 1
c
7
u
54
− 3u
53
+ ··· + 15u − 1
c
8
u
54
− u
53
+ ··· − 39u + 7
c
11
u
54
+ 13u
53
+ ··· + 657u + 99
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 9y
53
+ ··· + 3y + 1
c
2
, c
4
y
54
− 35y
53
+ ··· − 9y + 1
c
3
y
54
− 3y
53
+ ··· − 9y + 1
c
5
, c
6
, c
9
c
10
y
54
+ 61y
53
+ ··· + 3y + 1
c
7
y
54
− 55y
53
+ ··· − 413y + 1
c
8
y
54
− 43y
53
+ ··· − 317y + 49
c
11
y
54
+ 5y
53
+ ··· + 103347y + 9801
12
