Quantitative study of semi-Pfaffian sets

Details Quantitative study of semi-Pfaffian sets Quantitative study of semi-Pfaffian sets

2004-01-08

arxiv.org/abs/math/0401079v1

Mathematics

Algebraic Geometry

Author's PhD thesis. Approx. 130 pages, no figures

Scientific paper

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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