First steps in stable Hamiltonian topology

Details First steps in stable Hamiltonian topology First steps in stable Hamiltonian topology

2010-03-26

arxiv.org/abs/1003.5084v3

Mathematics

Symplectic Geometry

104 pages, 3 figures, reference added

Scientific paper

In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable Hamiltonian structures that are not homotopic to a positive contact structure; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on the 3-sphere is homotopic to a stable Hamiltonian structure which cannot be embedded in 4-space. Moreover, we derive a structure theorem in dimension three and classify stable Hamiltonian structures supported by an open book. We also discuss implications for the foundations of symplectic field theory.

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