2022/09/22 by Rezchikov, Semon · 2 citations
#FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2209.11165
We explain how to adapt the methods of Abouzaid-McLean-Smith to the setting of Hamiltonian Floer theory. We develop a language around equivariant ``⟨ k ⟩-manifolds'', which are a type of manifold-with-corners that suffices to capture the combinatorics of Floer-theoretic constructions. We describe some geometry which allows us to straightforwardly adapt Lashofs's stable equivariant smoothing theory and Bau-Xu's theory of FOP-perturbations to ⟨ k ⟩-manifolds. This allows us to compatibly smooth global Kuranishi charts on all Hamiltonian Floer trajectories at once, in order to extract a Floer complex and prove the Arnol'd conjecture over the integers. We also make first steps towards a further development of the theory, outlining the analog of bifurcation analysis in this setting, which can give short independence proofs of the independence of Floer-theoretic invariants of all choices involved in their construction.