Gradient flow of the norm squared of a moment map

Abstract

We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat's proof is an adaptation of Lojasiewicz's argument for analytic functions to functions which are locally analytic.

6 pages, expository. (v2) exposition changed following referee's suggestions. To appear in l'Enseignement Math'ematique

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