$C^1$-triangulations of semialgebraic sets

Abstract

We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is $C^1$ differentiable. As an application, we give a straightforward definition of the integration ${\int }_X\omega$ over a compact semialgebraic subset $X$ of a differential form $\omega$ on an ambient algebraic manifold, that provides a significant simplification of the theory of semialgebraic singular chains and integrations. Our results hold over every (possibly non-archimedian) real closed field.

12 pages

Cited by in corpus (3)

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