Approximation of definable sets by compact families, and upper bounds on homotopy and homology

• Autores: Andrei Gabrielov, Nicolai Vorobjov
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 1, 2009, págs. 35-54
• Idioma: inglés
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• Resumen

  • We prove new upper bounds on homotopy and homology groups of o-minimal sets in terms of their approximations by compact o-minimal sets. In particular, we improve the known upper bounds on Betti numbers of semialgebraic sets defined by quantifier-free formulae and obtain, for the first time, a singly exponential bound on Betti numbers of sub-Pfaffian sets.