2004/01/08 by Thierry Zell, Zell, Thierry · 1 citation
Mathematics · #14P99 (Primary) 03C98 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #math.AG #math.LO #msc:03C98 #msc:14P99
paper · pdf · doi:10.48550/arxiv.math/0401079
Author's PhD thesis. Approx. 130 pages, no figures
arxiv created 2004/01/08 · arxiv updated 2009/12/01
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.