Symplectic and Contact Geometry
July 8 - 9, 2016
in Münster
as part of the

Bochum – Köln – Münster Seminar on Symplectic and Contact Geometry

and on occasion of

Hansjörg Geiges' 50th birthday

There is no formal registration to this workshop. But if you intend to attend the lecture please inform Mrs. Rhinow via email at .

The workshop is supported by SFB 878 - Groups, Geometry & Actions.

All lectures will be in lecture hall M4 in this building.


2 pm: Welcome – Foyer of the Neubau (Orleansring 12)

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)



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)



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