Abstract
AbstractLet be an o-minimal structure over a real closed field R. Given a simplicial complex K and some definable subsets S1, …, Sl of its realization ∣K∣ in R we prove that there exist a subdivision K′ of K and a definable triangulation φ′: ∣K′∣ → ∣K∣ of ∣K∣ partitioning S1, …, Sl with φ′ definably homotopic to id∣K∣. As an application of this result we obtain the semialgebraic Hauptvermutung.
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