Hebrew University topology and geometry seminar

Abstract: I will explain how symplectic homology, originally defined as an invariant of convex exact symplectic manifolds, or Liouville domains, can be extended as an invariant of pairs of Liouville cobordisms. Invariance holds in this setting with respect to convex exact deformations of the symplectic structure. The purpose of this extension is to obtain a theory that satisfies suitable analogues of the Eilenberg-Steenrod axioms for a generalized co/homology theory. Various exact sequences (duality, surgery etc.) can be reinterpreted as instances of the long exact sequence of a pair. This construction provides a unifying perspective on linear homological invariants of symplectic objects with cylindrical ends (symplectic homology, linearized contact homology, Rabinowitz-Floer homology, wrapped Floer homology). Joint work with Kai Cieliebak.