Higher homotopy of groups definable in o-minimal structures
Logic
2009-11-27 v2
Abstract
It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal cover are contractible.
Keywords
Cite
@article{arxiv.0809.4940,
title = {Higher homotopy of groups definable in o-minimal structures},
author = {Alessandro Berarducci and Marcello Mamino and Margarita Otero},
journal= {arXiv preprint arXiv:0809.4940},
year = {2009}
}
Comments
13 pages, to be published in the Israel Journal of Mathematics