Submission date: 26 August 2015.

Abstract:

Let X be a definable C^r manifold, Y_1, Y_2 definably compact definable C^r submanifolds of X such that dim Y_1+dim Y_2 < dim X and Y_1 has a trivial normal bundle. We prove that there exists a definable isotopy {h_p}_{p in J} such that h_0=id_X and h_1(Y_1) \cap Y_2=\emptyset.

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

Keywords and phrases: O-minimal, real closed fields, definable isotopies

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