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arXiv · 1505.03970

$C^1$-triangulations of semialgebraic sets

Toru Ohmoto·Masahiro Shiota
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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.

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Toru Ohmoto, Masahiro Shiota. 2015-05-15. $C^1$-triangulations of semialgebraic sets. https://doi.org/10.1112/topo.12024

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