Contact homology of Hamiltonian mapping tori

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Abstract

In the general geometric setup for symplectic field theory the contact manifolds can be replaced by mapping toriMØ of symplectic manifolds (M,ω) with symplectomorphisms Ø. While the cylindrical contact homology of MØ is given by the Floer homologies of powers of Ø, the other algebraic invariants of symplectic field theory for MØ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian Ø we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer,Wysocki and Zehnder. We use our result to compute the full contact homology of MØ ≅ S
Original languageEnglish
Pages (from-to)203-241
JournalCommentarii Mathematici Helvetici
Volume85
Issue number1
DOIs
Publication statusPublished - 2010

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