Strict -triangulations – a new approach to desingularization
Wiesław Pawłucki
Jagiellonian University, Kraków, Poland
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Abstract
Let be any real closed field expanded by some o-minimal structure. Let be a definable and continuous mapping defined on a definable, closed, bounded subset of . Let be a finite family of definable subsets of contained in . Let be any positive integer. We prove that then there exists a finite simplicial complex in and a definable homeomorphism , where , such that for each simplex , the restriction of to its relative interior is a -embedding of into and moreover both and are of class in the sense that they have definable -extensions defined on an open definable neighborhood of in . We then call a pair a strict -triangulation of . In addition, this triangulation can be made compatible with in the sense that for each , is a union of some , where . We also give an application to approximation theory.
Cite this article
Wiesław Pawłucki, Strict -triangulations – a new approach to desingularization. J. Eur. Math. Soc. 26 (2024), no. 10, pp. 3863–3909
DOI 10.4171/JEMS/1335