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.

Higher homotopy of groups definable in o-minimal structures

Berarducci, Alessandro;Mamino, Marcello;Otero, Margarita
2010-01-01

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.
2010
Berarducci, Alessandro; Mamino, Marcello; Otero, Margarita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/912556
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