Mathematics – Algebraic Geometry
Scientific paper
2004-08-31
Discrete and Computational Geometry 40 (2008), 430--443.
Mathematics
Algebraic Geometry
12 pages, 1 figure. v3: Proofs and bounds have been slightly improved
Scientific paper
10.1007/s00454-008-9070-1
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.
Zell Thierry
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