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

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

2007-10-16

arxiv.org/abs/0710.3028v1

Mathematics

Algebraic Geometry

20 pages, 2 figures

Scientific paper

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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