2008/02/20 by Ralph L. Cohen, Cohen, Ralph L. · 1 citation
Mathematics · #55N20 #57R58 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55N20 #msc:57R58
paper · pdf · doi:10.48550/arxiv.0802.2752
22 pages
arxiv created 2008/02/20 · openalex publication_date 2008/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we describe and continue the study begun by the author, Jones, and Segal, of the homotopy theory that underlies Floer theory. In that paper the authors addressed the question of realizing a Floer complex as the celluar chain complex of a CW -spectrum or pro-spectrum, where the attaching maps are determined by the compactified moduli spaces of connecting orbits. The basic obstructions to the existence of this realization are the smoothness of these moduli spaces, and the existence of compatible collections of framings of their stable tangent bundles. In this note we describe a generalization of this, to show that when these moduli spaces are smooth, and are oriented with respect to a generalized cohomology theory E^*, then a Floer E_* -homology theory can be defined. In doing this we describe a functorial viewpoint on how chain complexes can be realized by E -module spectra, generalizing the stable homotopy realization criteria given earlier by the author, Jones, and Segal. Since these moduli spaces, if smooth, will be manifolds with corners, we give a discussion about the appropriate notion of orientations of manifolds with corners.