Abstract

this paper we present a new approach to Morse theory based on the de Rham - Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic settings. Moreover, the methods are substantially stronger than the classical ones and have interesting applications to geometry. They lead, for example, to formulas relating characteristic forms and singularities of bundle maps. The ideas came from addressing the following. Question. Given a smooth flow ' t : X ! X on a manifold X, when does the limit P(ff) j lim t!1 '

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