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
- DOI: 10.1112/jlms/jdp006
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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.
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