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First steps in stable Hamiltonian topology
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First steps in stable Hamiltonian topology
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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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Cited by 1 Pith paper
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On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
Contact 3-manifolds admitting uniform spinal open books with planar pages have their weak, strong, and exact symplectic and Stein fillings classified by diffeomorphism classes of Lefschetz fibrations.
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