Higher homotopy of groups definable in o-minimal structures

2008/09/29 by Alessandro Berarducci, Berarducci, Alessandro, Marcello Mamino +3 · 1 citation
Mathematics · #03C64 #55P45 #57T20 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.LO #msc:03C64 #msc:55P45 #msc:57T20

paper · pdf · doi:10.48550/arxiv.0809.4940

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

openalex publication_date 2008/09/29 · arxiv created 2009/11/27 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 cover are contractible.

Citations

• Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup

Cited by

• Locally definable homotopy

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