Submission date: 13 November 2008

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.

Mathematics Subject Classification: 03C64, 57T20, 55P45

Keywords and phrases: definable group, Lie group, o-minimal homotopy

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