Second Steps in Stable Hamiltonian Topology

Abstract

Stable Hamiltonian structures are defined on odd-dimensional manifolds M^{2m+1} by a pair of a 1-form and a closed 2-form (λ, ω) satisfying; λ ∧ ωm > 0, and ker(ω) ⊂ ker(dλ). They are a simultaneous generalization of contact structures and taut foliations defined by a closed 1-form. Stable Hamiltonian structures naturally arise when studying the Weinstein conjecture and the h-principle for contact structures and taut foliations. This thesis provides an extensive introduction to these structures. We conclude by treating a structure theorem by Cieliebak and Volkov on M^{3} induced by a stable Hamiltonian structure.