Morse Novikov theory and cohomology with forward supports

Details Morse Novikov theory and cohomology with forward supports Morse Novikov theory and cohomology with forward supports

2002-12-20

arxiv.org/abs/math/0212295v2

Mathematics

Differential Geometry

34 pages. This version is extended and widely revised. An introduction and many references are added and some corrections are

Scientific paper

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.

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