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

2009/05/07 by Alessandro Berarducci, Berarducci, A., Marcello Mamino +1
Mathematics · Medicine · #03C64 #03H05 #22E15 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Pituitary Gland Disorders and Treatments

paper · pdf · doi:10.48550/arxiv.0905.1069

openalex publication_date 2009/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On central extensions and definably compact groups in o-minimal structures

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