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 covers are contractible.
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The first author is partially supported by GEOR MTM2005-02568.
Third author is partially supported by GEOR MTM2005-02568 and Grupos UCM 910444.
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Berarducci, A., Mamino, M. & Otero, M. Higher homotopy of groups definable in o-minimal structures. Isr. J. Math. 180, 143–161 (2010). https://doi.org/10.1007/s11856-010-0098-6
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DOI: https://doi.org/10.1007/s11856-010-0098-6