Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
Alessandro Berarducci
Source: J. Symbolic Logic Volume 74, Issue 3 (2009), 891-900.
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.
Primary Subjects: 03C64, 22E15, 03H05
Keywords: Cohomology; groups; o-minimality
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158089
Digital Object Identifier: doi:10.2178/jsl/1245158089
Zentralblatt MATH identifier:
05609394
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