Quantitative study of semi-Pfaffian sets

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

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Algebraic Geometry, Logic, 14P99 (Primary) 03C98 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/69805

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0401079
 http://arxiv.org/abs/math/0401079

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arXiv