Higher homotopy of groups definable in o-minimal structures

Alessandro Berarducci, Marcello Mamino, Margarita Otero

Published 2008-09-29, updated 2009-11-27Version 2

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.