Contact homology of Hamiltonian mapping tori

Fabert, Oliver

doi:10.4171/CMH/193

Commentarii Mathematici Helvetici

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Volume 85, Issue 1, 2010, pp. 203–241

DOI: 10.4171/CMH/193

Published online: 2009-12-23

Contact homology of Hamiltonian mapping tori

Oliver Fabert^[1]

(1) Vrije Universiteit Amsterdam, Netherlands

In the general geometric setup for symplectic field theory the contact manifolds can be replaced by mapping tori M_Φ of symplectic manifolds (M,ω) with symplectomorphisms Φ. While the cylindrical contact homology of M_Φ is given by the Floer homologies of powers of Φ, the other algebraic invariants of symplectic field theory for M_Φ 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 M_Φ ≅ S¹ × M.

Keywords: Symplectic field theory, Floer homology, J-holomorphic curve

Fabert Oliver: Contact homology of Hamiltonian mapping tori. Comment. Math. Helv. 85 (2010), 203-241. doi: 10.4171/CMH/193