Towards the cosymplectic topology

Abstract In this article, the cosymplectic analogue of symplectic flux homomorphism a compact connected manifold ( M , η ω ) \left(M,\eta ,\omega ) with ∂ = ∅ \partial M=\varnothing is studied. This continuous map respect to C 0 {C}^{0} -metric, whose kernel by smooth arcs and coincides subgroup all weakly Hamiltonian diffeomorphisms. We discuss Weinstein’s chart, derive that group G {G}_{\eta }\left(M) diffeomorphisms isotopic identity locally contractible. A study an Polterovich’s regularization process for co-Hamiltonian isotopies follows. Finally, we Moser’s stability theorems conformal manifolds.