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Quantitative study of semi-Pfaffian sets

Thierry Zell
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Abstract

We study the topological complexity of sets defined using Khovanskii's Pfaffian functions, in terms of an appropriate notion of format for those sets. We consider semi- and sub-Pfaffian sets, but more generally any definable set in the o-minimal structure generated by the Pfaffian functions, using the construction of that structure via Gabrielov's notion of limit sets. All the results revolve around giving effective upper-bounds on the Betti numbers (for the singular homology) of those sets. Keywords: Pfaffian functions, fewnomials, o-minimal structures, tame topology, spectral sequences, Morse theory.

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Thierry Zell. 2004-01-08. Quantitative study of semi-Pfaffian sets. https://arxiv.org/abs/math/0401079

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