Submission date: 3 April 2019. PAPER WITHDRAWN, 26 APRIL 2020

Abstract:

Let G be a definably compact definable C^r group and 1 ≤ r < ∞. Let X be an affine definable C^r G manifold. Suppose that f: X → R is a G invariant definably proper surjective submersive definable C^r function.
We prove that there exists a definable C^r G diffeomorphism h=(h', f): X → X^* × R, where X^* denotes X ∩ f^{-1}(0).

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

Keywords and phrases: O-minimal, definable C^r G manifolds, G invariant definably proper definable C^r functions, definable C^r G trivial.

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