Title

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

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

Volume

80

Issue

2

Pages

35-54

Link Out to Full Text

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