2019/12/29 by Stéphane Tchuiaga, Tchuiaga, S., P. Bikorimana +1
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1912.12642
openalex publication_date 2019/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the geometry of the group of all co-Hamiltonian diffeomorphisms of a compact cosymplectic manifold (M, ω, η). The fix-point theory for co-Hamiltonian diffeomorphisms is studied, and we use Arnold's conjecture to predict the exact minimum number of fix point that such a diffeomorphism must have (this minimum number is at least 1). It follows that the generating function of any co-Hamiltonian isotopy is a constant function along it orbits. Therefore, we study the co-Hofer norms for co-Hamiltonian isotopies, and establish several co-Hamiltonian and almost co-Hamiltonian analogues of some approximations lemmas and reparameterizations lemmas found in the theory of Hamiltonian dynamics, we define two C0-co-Hamiltonian topologies, and use these topologies to define the spaces of cohameomorphisms, and almost cohameomorphisms. Finally, we raise several important questions for future studies.