2004/09/30 by Thierry Zell
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis #math.AG #math.LO #msc:03C64 #msc:14P99
paper · pdf · doi:10.1007/s00454-008-9070-1
published as Discrete and Computational Geometry 40 (2008), 430--443. · 12 pages, 1 figure. v3: Proofs and bounds have been slightly improved
arxiv created 2006/10/03 · openalex publication_date 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskii's Pfaffian functions. In this paper, use the notion of format (or complexity) of a Pfaffian couple to derive explicit upper-bounds for the homology of its relative closure. Keywords: Pfaffian functions, fewnomials, o-minimal structures, Betti numbers.