Higher homotopy of groups definable in o-minimal structures

Details Higher homotopy of groups definable in o-minimal structures Higher homotopy of groups definable in o-minimal structures

2008-09-29

arxiv.org/abs/0809.4940v2

Mathematics

Logic

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

Scientific paper

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.

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