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

Authors

Andrei Gabrielov
Nicolai Vorobjov

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.

Date of this Version

2009

DOI

10.1112/jlms/jdp006

Repository Citation

Gabrielov, Andrei and Vorobjov, Nicolai, "Approximation of definable sets by compact families, and upper bounds on homotopy and homology" (2009). Department of Earth, Atmospheric, and Planetary Sciences Faculty Publications. Paper 111.
http://dx.doi.org/10.1112/jlms/jdp006

Volume

80

Issue

2

Pages

35-54

Link Out to Full Text

http://jlms.oxfordjournals.org/content/80/1/35.full.pdf+html