On the homotopy type of definable groups in an o-minimal structure

Details On the homotopy type of definable groups in an o-minimal structure On the homotopy type of definable groups in an o-minimal structure

2009-05-07

arxiv.org/abs/0905.1069v2

Mathematics

Logic

21 pages

Scientific paper

Given a definably compact group G in a saturated o-minimal structure, there is a canonical homomorphism from G to a compact real Lie group F(G). We establish a similar result for the (o-mininimal) universal cover of a definably compact group. We also show that F(G) determines the definable homotopy type of G. A crucial step is to show that the fundamental group of an open subset of F(G) is isomorphic to the definable fundamental group of its preimage in G. Our results depend on the study of the o-minimal fundamental groupoid of G.

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