Submission date: 4 October 2007

Abstract:

We work over an o-minimal expansion of a real closed field R. Given a closed simplicial complex K and a finite number of definable subsets of its realization |K| in R we prove that there exists a triangulation (K',f) of |K| compatible with the definable subsets such that K' is a subdivision of K and f is definably homotopic to the identity on |K|.

Mathematics Subject Classification: 03C64, 32B25

Keywords and phrases: o-minimal homotopy, normal triangulations, o-minimality

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