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
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