In the general geometric setup for symplectic field theory the contact manifolds can be replaced by mapping tori MΦ of symplectic manifolds (M,ω) with symplectomorphisms Φ. While the cylindrical contact homology of MΦ is given by the Floer homologies of powers of Φ, the other algebraic invariants of symplectic field theory for MΦ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian Φ 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 MΦ ≅ S1 × M.
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Oliver Fabert, Contact homology of Hamiltonian mapping tori. Comment. Math. Helv. 85 (2010), no. 1, pp. 203–241DOI 10.4171/CMH/193