Collapsing and essential coverings
Differential Geometry
2012-05-03 v1
Abstract
In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls forming essential coverings of the spaces in the family. In particular, this gives another view for Gromov's Betti number theorem.
Cite
@article{arxiv.1205.0441,
title = {Collapsing and essential coverings},
author = {Takao Yamaguchi},
journal= {arXiv preprint arXiv:1205.0441},
year = {2012}
}