Members’ Seminar

Pseudo-holomorphic curves play a fundamental role in the study of symplectic manifolds. Compactness and gluing theorems allow to extract algebra out of analysis. The focus of this talk are certain invariants which are constructed using pseudo-holomorphic curves and which have a homological flavor: symplectic homology, linearized contact homology, Rabinowitz-Floer homology. These can be understood from a unified point of view relating to the classical Eilenberg-Steenrod axioms in algebraic topology. Along the way, I will also present some dynamical consequences of this approach. The talk builds on joint work, partly published, partly in progress, with Frédéric Bourgeois, Kai Cieliebak, Urs Frauenfelder.