There is no formal registration to this workshop. But if you intend
to attend the lecture please inform Mrs. Rhinow via email at
mathsekr@uni-muenster.de .
The workshop is supported by SFB 878 - Groups, Geometry &
Actions.
Schedule: All lectures will be in lecture hall M4 in this building.
Friday:
3 - 4 pm: Federica Pasquotto
(Amsterdam):
Isolation and the Weinstein Conjecture for open
manifolds (
Abstract)
4 - 5 pm: Coffee break
5 - 6 pm: Klaus Niederkrüger
(Toulouse / Rényi Institute):
Vanishing contact homology for
overtwisted manifolds (
Abstract)
Dinner
Saturday:
10 - 11 am: Otto van Koert (Seoul):
Contact geometry of the unbounded component in restricted
three-body problem (
Abstract)
11:00 - 11:30 am: Coffee break
11:30 - 12:30 am: Fan Ding (Peking):
Strongly symplectic fillability of contact torus bundles (
Abstract)
Lunch
Abstracts:
1) Federica Pasquotto (Amsterdam): In this talk I
will discuss some existing results about existence of periodic Reeb
orbits on open contact manifolds. After that, I will define (under
appropriate assumptions) a version of contact homology for compact
contact manifolds with boundary, which contains information about
the periodic Reeb orbits and which can be extended to non-compact
manifolds. In particular, I will describe how the construction
works for a fundamental class of non-compact examples ("contact
hyperboloids"). This is joint work with Oliver Fabert and Rob
Vandervorst.
2) Klaus Niederkrüger (Toulouse / Rényi Institute): The
recent classification of overtwisted contact manifolds by Borman,
Eliashberg and Murphy raises the question to understand if
overtwistedness can be characterized in terms of contact homology.
As Bourgeois and van Koert have shown, contact homology vanishes for
overtwisted contact structures, but the question of the converse
implication is still unsolved (even in dimension 3). An
indication that this statement might be false can be found in the
discovery of non-loose Legendrians with vanishing contact homology
by Ekholm.
I will sketch a proof by Bourgeois and myself dating from 2007 that
contact homology vanishes for manifolds having a plastikstufe.
Casals-Murphy-Presas have shown that certain plastikstufes imply
overtwistedness, but in my opinion it is unlikely that this might be
true for general plastikstufe, and I'll finish my talk by proposing
a candidate for a possibly non-overtwisted contact structure that
contains a plastikstufe. These candidates are based on a
beautiful and extremely simple construction by Presas. This is joint
work with Frédéric Bourgeois.
3) Otto van Koert (Seoul): Contact geometry of the unbounded
component in restricted three-body problem
We discuss the unbounded component in the restricted three-body
problem, and describe a way to compactify it to a contact manifold.
This involves a controlled modification of the dynamics at infinity.
It turns out that we will always lose dynamical convexity, but we
still have some control, and it is possible to construct a system of
global surfaces of section for small mass ratio. The contact
geometry of this problem will play a role when trying to apply
holomorphic curves to RTBP above the second Lagrange point. This is
work in progress.
4) Fan Ding (Peking): Strongly symplectic fillability of contact
torus bundles
We determine Stein fillability and strongly symplectic fillability
of some tight contact structures on torus bundles whose monodromies
are matrices in SL(2,Z) with trace less than or equal to -2. This is
joint work with Youlin Li.
Organized by A. Abbondandolo, P. Albers, B. Bramham, S. Sabatini, K.
Zehmisch
May 2016