The Kunneth formula in Floer homology for manifolds with restricted contact type boundary

Abstract

We prove the Kunneth formula in Floer (co)homology for manifolds with restricted contact type boundary. We use Viterbo's definition of Floer homology, involving the symplectic completion by adding a positive cone over the boundary. The Kunneth formula implies the vanishing of Floer (co)homology for subcritical Stein manifolds. Other applications include the Weinstein conjecture in certain product manifolds, obstructions to exact Lagrangian embeddings, existence of holomorphic curves with Lagrangian boundary condition, as well as symplectic capacities.

21 pages, 3 figures. Major reorganization and shortening of the first version. Many more details for the proof of the present version's Theorem C are given. The statement and proof of Proposition 3 are corrected. This is the final version of the paper, to appear in Mathematische Annalen