First steps in stable Hamiltonian topology

By Kai Cieliebak, E. Volkov. 2010

49 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ac4fa4c4bf7e18390c494d366a493e562b5ec327

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Algebraic Torsion in Contact Manifolds (2010, methodology): “f ωtames an almost complex structure J that preserves ξ and is also tamed by the natural conformal symplectic structure on ξ. Under this deﬁnition, one can use an existence result of Cieliebak-Volkov [CV] to show that weak and stable ﬁllability are equivalent, see [MNW] for details. Thus SFT also gi”
Reeb orbits and the minimal discrepancy of an isolated singularity (2014, background): “Most material from this section is taken from [6] and from [16].”