Vol. 70, No. 3, pp. 222–232 (2018)

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Filtered Lagrangian Floer homology of product manifolds

J. Nikoli‚ć

University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia E-mail: jovanadj@matf.bg.ac.rs

Abstract: In this note we construct a commutative diagram in filtered Lagrangian Floer homology that involves a product of certain Lagrangian submanifolds. As a corollary, we prove the K\"{u}nneth formula for Lagrangian Floer homology. We also prove that the K\"{u}nneth formula for Lagrangian Floer homology lifts through a Lagrangian type of Piunikhin-Salamon-Schwarz map to the K\"{u}nneth formula for Morse homology.

Keywords: Filtered Lagrangian Floer homology; K\"unneth formula; PSS isomorphism.

Classification (MSC2000): 53D40; 55U25, 53D12

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