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September 2009 Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
Alessandro Berarducci
J. Symbolic Logic 74(3): 891-900 (September 2009). DOI: 10.2178/jsl/1245158089

Abstract

By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an extension of a compact Lie group by a torsion free normal divisible subgroup, called its infinitesimal subgroup. We show that the infinitesimal subgroup is cohomologically acyclic. This implies that the functorial correspondence between definably compact groups and Lie groups preserves the cohomology.

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Alessandro Berarducci. "Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup." J. Symbolic Logic 74 (3) 891 - 900, September 2009. https://doi.org/10.2178/jsl/1245158089

Information

Published: September 2009
First available in Project Euclid: 16 June 2009

zbMATH: 1181.03042
MathSciNet: MR2548466
Digital Object Identifier: 10.2178/jsl/1245158089

Subjects:
Primary: 03C64, 03H05, 22E15

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 3 • September 2009
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