Submission date: 17 July 2012.

Abstract:

Let G be a compact definable C^r group, X a compact affine definable C^r G manifold and 2 \le r <\infty. We prove that the set of equivariant definable Morse functions on X whose loci are finite unions of nondegenerate critical orbits

Mathematics Subject Classification: 14P10, 14P20, 57R35, 58A05, 03C64.

Keywords and phrases: Definably complete structures, Morse theory, equivariant definable Morse functions.

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