Submission date: 28 December 2008.

Abstract:

We study relative equivariant definable trivilaity of proper equivariant differential functions and simultaneous equivariant definable differential compactfications of non-compact equivariant definable differential manifolds and its non-compact equivariant definable differential submanifolds.

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

Keywords and phrases: O-minimal, definable C^r G manifolds, G invariant proper definable C^r functions, definable C^r G trivial, Nash G trivial, definable C^{\infty} G compactifications.

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