Normal triangulations in o-minimal structures
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2010
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Association for Symbolic Logic
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Baro E. Normal triangulations in o-minimal structures. J Symb Log 2010;75:275–88. https://doi.org/10.2178/jsl/1264433921.
Abstract
Let R 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 K0 of K and a definable triangulation '0: |K0| ! |K| of |K| partitioning S1, . . . , Sl with '0 definably homotopic to id|K|. As an application of this result we obtain the semialgebraic Hauptvermutung.