Topological complexity of the relative closure of a semi-Pfaffian couple

Mathematics – Algebraic Geometry

Scientific paper

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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.

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