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Finite volume flows and Morse theory. (English) Zbl 1001.58005

This paper is devoted to a new approach to Morse theory based on the de Rham-Federer theory of currents. The authors derive the full classical theory in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic settings. They also present interesting applications to geometry. For example their approach leads to formulas relating characteristic forms and singularities of bundle maps.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
53C65 Integral geometry
58A25 Currents in global analysis
57R70 Critical points and critical submanifolds in differential topology
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