B-Contact structures on tentacular hyperboloids

Abstract

This paper connects two different approaches to the analysis of Hamiltonian dynamics on non-compact energy hypersurfaces - b-symplectic geometry with its singular symplectic form and Floer techniques for tentacular Hamiltonians. More precisely, we show how to equip tentacular hyperboloids with a b-contact structure. We construct a b3-symplectic manifold (X,Z,ωb), such that each connected component of X∖Z is symplectomorphic to the standard symplectic space (T⁎Rn,ω0). For a tentacular hyperboloid S⊆T⁎Rn we look at its copies in X∖Z and show that their completion in (X,Z,ωb) is a smooth hypersurface of b-contact type.