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Morse Novikov theory and cohomology with forward supports

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Abstract

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 [HL]. 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.

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Authors and Affiliations

  1. Department of Mathematics, Rice University Houston, TX, 77005-1892

    F. Reese Harvey & Giulio Minervini

  2. Dipto. Matematico, Universita Bari, Via Orabona, 4, 70125, BARI, Italien

    F. Reese Harvey & Giulio Minervini

Authors
  1. F. Reese Harvey
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  2. Giulio Minervini
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Correspondence to F. Reese Harvey.

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Reese Harvey, F., Minervini, G. Morse Novikov theory and cohomology with forward supports. Math. Ann. 335, 787–818 (2006). https://doi.org/10.1007/s00208-006-0765-4

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  • DOI: https://doi.org/10.1007/s00208-006-0765-4

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