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Event

Lecture Event
SFB-Colloquium at ZIB
E. Volkov, K. Mohnke
1 Jul 2008, 16:00 – 19:00

Program

Talk
Symplectic cobordisms between stable Hamiltonian structures
Dr. Evgeny Volkov (HU Berlin)
1 Jul 2008, 16:00 – 17:00

A stable Hamiltonian structure on a closed oriented $ 3$ -manifold $ M$ is a pair $ \textstyle(\lambda, \omega)$ where $ \lambda$ is a $ 1$ -form and $ \omega$ is a nowhere zero closed $ 2$ -form such that the relation $ \lambda\wedge\omega>0$ holds and $ d\lambda = f\omega$ for some smooth function $ f$ on $ M$ . This generalizes the notion of a contact structure in the following sense: for a contact form $ \lambda$ on $ M$ the pair $ (\lambda, $ ±$ d\lambda)$ is a stable Hamiltonian structure. The notion of a symplectic cobordism between contact structures generalizes to the case of stable Hamiltonian structures in a straightforward way. The main concern of the talk is the problem of existence of a symplectic cobordism between two given stable Hamiltonian structures. We will illustrate this problem on concrete examples always looking back at the simpler case of contact structures.

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Lecture Events 2008