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

A Gabrielov; Nicolai Vorobjov

doi:10.1112/jlms/jdp006

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

A Gabrielov, Nicolai Vorobjov

Research output: Contribution to journal › Article › peer-review

25 Citations (SciVal)

Abstract

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.

Original language	English
Pages (from-to)	35-54
Number of pages	20
Journal	Journal of the London Mathematical Society
Volume	80
Issue number	1
Early online date	9 May 2009
DOIs	https://doi.org/10.1112/jlms/jdp006
Publication status	Published - Aug 2009

Keywords

betti numbers
pfaffian sets

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10.1112/jlms/jdp006

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abstract = "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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AB - 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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KW - pfaffian sets

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DO - 10.1112/jlms/jdp006

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ER -

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

Abstract

Keywords

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