LD on Hamiltonian isotopic after coordinate permutation A non - - PDF document
Exotic embeddings of cubes joint work with Joe Brendel and Felix Schlent A symplectic cube C a the disk of a a are D a D D D a a cube a a n times il act 1 a Yes il in cas ways many different essentially Il LD on
embeddings of
cubes
joint work with Joe Brendel and Felix Schlent
C
a
D
a
the disk of
are
a a a
a
a
a
cube
n times
a
1
il
act
in
many
ways
cas
essentially
different
Il
coordinate permutation
a
non isotopicbyfluer Hoher Wysocki
A
1
as
isotopic to standard
as
too little space
to embed
are
some
further previous
results
non
isotopic embeddings by
Gutt Usher and
Dimitrogler Rizell Theorem
Brendel Schleck M
et
non isotopic embeddings
a
1
grows arbitrarily large when
a
cas
at
least
two
embeddings
un
ca
three embeddings
1,1 3
version et
the
same theorem for
1341
na isotopie embeddings
la
B
psy
grows arbitrarily large
when
a
DU
least
cas
least two
cas
Furlermore
a
for
embedding
closed monotone
Dezzo
surfaces
particular
the
degree
is
then
gnous
a
a
KE g
end
a
1
her
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Q
KE g
Pialttiangular degenendons
f6
Clip blown up 3 times
l
r
r
Q
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Clip blownup 4 lines
less
probably also with
from degeneration to
Pic
1 tone surfaces
their
number
growing arbitrarily large
i
e
blown up
1,2 5,47 and8
times
Markov's
and Markov type
equations
and
geometry
Markov 1879
3 abc
0,6
ce
numerology
such GB c
called Markov'striple
Hacking Prokhorov
advancing
au earlier workofManetti
2010
classified
projective tone surfaces with
Piet
and
having
T
singularities aha Wahl
Q Gorenstein
sinoothable tonic singularities
and noticed
they
are
snoothoble
globally
vanishing local to global obstructions
Answery
where
lake
isa Markov triple
clin
11,421,145,2
more constructive proofs are also available log
now
car
smoothing
is
a
projective
3 foff
singulart
smooth
c
unit cl disk
Xt Xtz
symplecto
characteristic
norphisa
foliation
in
µ
Ë
t.net
symplectomorphic
x Xt
Smooth
t
p
singular
locus d
part
locus
vanishing cycles
Anything embedded to the smooth locus of to
gets
transported to Xt
idea et using Markov triples
to
symplectic
geometry of
EP goes back
to
2010 pmprint
Calkin and Usuich
have
upgraded Markov triples
to Markov lathe
triangle t.eu CIR
corresponding to
tric dans of Playa i
introduced
mutations
0,6 c
a 6,308 c
g
Markov triangle
étoki
sobe
a geometric
representation
d
Markov's equation
10,07 10,0
ad
C
Zleugtha
Each
cone
Pp is
a
singularity
Zheights
V
length
normalized
area
à height
la
l
In
a
i
là
pr 9211
Convex Hull
Using tonic fan
mutations
corresponding to Markov's
mutations Ca b c Cabisab c
an
integer
functions
points d Ta
Conjecture G U
2010
function
is
the
counting Maslow 2
disk
function for
some corresponding
Lagrangian
a b c
C
proved
by
Vianna
Pascalelf Touleonog
Dimitroglu Rizell Ekholm Tanking
et al
us
construct
ça directly from smoothing
d
Galvin M
unpublished
Symplecticolly
Pca
is
given
by
a
dual
N MY lattice
triangle OqqcN.IR
Ss
C Mor Re R
R
i ÏÏ
G U
mutations
and dual matelas
cf almost tonimutadia
polygon
we
consider
integer
they
intersect
Note
it
is not
generally
the barycenter
ctntediteda
The fiber
is
a
monotone
Lagrangian tonus
contained
in the Smooth
locus
d
Plan
c 1
then
à
Ebasis
f2
1
Healy
singular points
removing
hypotenuse
gives Etat in
the
Smooth
locus of
Eté
embeds to
1PM 1,1
are
area et K Sabc
the
hypotenuse taken with multiplicity ab
is
the huit
a family d lires
is
he approximating
sharp
l
embeds to
embedding
Eco A dË Ü3
embeds to BH
d
A
la.by
is
Casals
Vianna
Markov triple
cubes
are
in
ab
ab
aÆÆ
a
a
Hab
C
bissectrice
c
BU
BY SILLÉ
consecutive odd Fibonacci doubles la
d
are not
Hamiltonian isotopic
since
already the restrictions to pifs
can
not
be
Hamiltonian
isotopic
survives stabilization by
taking products
with
BY ofother monotone nlds coulanty cubes
finish
case by
consideration
following representation of the goldensedan
r
Kc
F
ç
goldensectionellipsoid
r
s
z
s
is
the
integer
center of inscribed circle
even continuous
ÉË
n'bed
le
L
bissectrice
intersection point
t
Cubes
sources
can
be traded
in
How about targets
is
possible degree
9
there
are
degree
they have
Markov type equations
perimeter M
a
battu triangle
area
A
gives
cap
Kahler bric
variety
w
HYXOI.IQ
Il
work
proportional
formula
3
m
12
Et
Milnornumbers et cornes
l
May have I
singularities
M méthylène
main.ua dc2
Markov
type
equations
maêtnebkhei
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ma à
tn
c
m.mn 12 na n
m
abc
must be integer
Prokhorov
14
Marteau type equations
them
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solutions with less then
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e
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