Morse Novikov theory and cohomology with forward supports
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. 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.
Keywords
Cite
@article{arxiv.math/0212295,
title = {Morse Novikov theory and cohomology with forward supports},
author = {Reese F. Harvey and G. Minervini},
journal= {arXiv preprint arXiv:math/0212295},
year = {2007}
}
Comments
34 pages. This version is extended and widely revised. An introduction and many references are added and some corrections are made