Higher homotopy of groups definable in o-minimal structures

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.

13 pages, to be published in the Israel Journal of Mathematics

References in corpus (1)

• Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup

Cited by in corpus (1)

• Locally definable homotopy