2002/12/20 by Reese Harvey, Reese F. Harvey, Harvey, Reese F. +3
Computer Science · Mathematics · #37D15 (Primary) #49Q15 #58A12 (Secondary) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DG #math.DS #msc:37D15 #msc:49Q15 #msc:58A12
paper · pdf · doi:10.48550/arxiv.math/0212295
34 pages. This version is extended and widely revised. An introduction and many references are added and some corrections are made
openalex publication_date 2002/12/20 · arxiv created 2004/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new approach to Morse and Novikov theories, based on the deRham Federer theory of currents, using the finite volume flow technique of Harvey and Lawson. In the Morse case, we construct a noncompact analogue of the Morse complex, relating a Morse function to the cohomology with compact forward supports of the manifold. This complex is then used in Novikov theory, to obtain a geometric realization of the Novikov Complex as a complex of currents and a new characterization of Novikov Homology as cohomology with compact forward supports. Two natural ``backward-forward'' dualities are also established: a Lambda duality over the Novikov Ring and a Topological Vector Space duality over the reals.