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.
|Autori interni:||BERARDUCCI, ALESSANDRO|
|Autori:||BERARDUCCI A; MAMINO M; OTERO M|
|Titolo:||Higher homotopy of groups definable in o-minimal structures|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.1007/s11856-010-0098-6|
|Appare nelle tipologie:||1.1 Articolo in rivista|