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

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Abstract

We prove the Künneth 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 Künneth 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.

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  1. Department of Mathematics, ETH, Rämistrasse 101, 8092, Zürich, Switzerland

    Alexandru Oancea

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  1. Alexandru Oancea
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Correspondence to Alexandru Oancea.

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Supported by ENS Lyon, École Polytechnique (Palaiseau) and ETH (Zürich).

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Oancea, A. The Künneth formula in Floer homology for manifolds with restricted contact type boundary. Math. Ann. 334, 65–89 (2006). https://doi.org/10.1007/s00208-005-0700-0

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