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; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on is homotopic to a stable Hamiltonian structure which cannot be embedded in . Moreover, we derive a structure theorem for stable Hamiltonian structures in dimension three, study sympectic cobordisms between stable Hamiltonian structures, and discuss implications for the foundations of symplectic field theory.
Cite this article
Kai Cieliebak, Evgeny Volkov, First steps in stable Hamiltonian topology. J. Eur. Math. Soc. 17 (2015), no. 2, pp. 321–404DOI 10.4171/JEMS/505