Event

Talk
How to count holomorphic curves
Prof. Dr. Klaus Mohnke (HU)
27 Jun 2005, 14:30 – 15:30

I will recall how certain non-compactness phenomena for solution spaces of (partial) differential equations lead algebraic structures: chain complexes in Floer theory, quantum cup product in Gromov-Witten theory. Symplectic field theory describes the algebraic formalism to count a more general class of holomorphic curves: maps of a punctured Riemann surface into symplectic manifolds with a certain end structure with controlled behaviour at the punctures. The non-compactness is a mixture of breaking Floer trajectories, Gromov bubbling and Deligne-Mumford pinching. Finally, I will attempt to outline what the invariants should give for the cotangent bundle of a closed manifold.

Related to:

• Klaus Mohnke