C1-triangulations of semialgebraic sets

Toru Ohmoto, Masahiro Shiota

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We show that every semialgebraic set admits a semialgebraic triangulation such that each closed simplex is C1 differentiable. As an application, we give a straightforward definition of the integration ∫X ω over a compact semialgebraic subset X of a differential form ω on an ambient semialgebraic manifold. This provides a significant simplification of the theory of semialgebraic singular chains and integrations without using geometric measure theory. Our results hold over every (possibly non-archimedian) real closed field.

Original languageEnglish
Pages (from-to)765-775
Number of pages11
JournalJournal of Topology
Issue number3
Publication statusPublished - 2017
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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