Real Algebraic and Analytic Geometry
Submission: 2007, October 4.
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 (2000): 03C64, 32B25.
Keywords and Phrases: o-minimal homotopy, normal triangulations, o-minimality.
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