Posted in
Speaker:
Kai Zehmisch
Affiliation:
U. of Cologne
Date:
Mon, 16/01/2012 - 16:30 - 17:15
Location:
MPIM Lecture Hall
Parent event:
Geometric Topology Seminar In this talk I will report on a joint work with Hansjörg Geiges. We study holomorphic spheres in
certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave
end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this
to confirm the strong Weinstein conjecture (predicting the existence of null-homologous Reeb
links) for various higher-dimensional contact manifolds, including contact type hypersurfaces in
subcritical Stein manifolds and in cotangent bundles with a base manifold, which is a product
with the circle. The quantitative character of this result leads to the definition of a symplectic
capacity, and in turn to a proof of symplectic non-squeesing.
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