2024/09/17 by Bonciocat, Ciprian Mircea · 2 citations
#53D05 (Secondary) #55P42 (Primary) 37D15 #57R19 #57R58 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2409.11278
In 1995, Cohen, Jones and Segal proposed a method of upgrading any given Floer homology to a stable homotopy-valued invariant. For a generic pseudo-gradient Morse-Bott flow on a closed smooth manifold M, we rigorously construct the alleged stable normal framings, which are an essential ingredient in their construction, and give a rigorous proof that the resulting stable homotopy type recovers Σ^∞+ M. We further show that other systems of compatible stable normal framings recover Thom spectra ME, for all reduced KO-theory classes E on M. Our paper also includes a construction of the smooth corner structure on compactified moduli spaces of broken flow lines with free endpoint, a formal construction of Piunikhin-Salamon-Schwarz type continuation maps, and a way to relax the stable normal framing condition to orientability in orthogonal spectra.