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

Journal of Symbolic Logic 74 (3):891-900 (2009)
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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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References found in this work

Type-definability, compact lie groups, and o-minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Forking and independence in o-minimal theories.Alfred Dolich - 2004 - Journal of Symbolic Logic 69 (1):215-240.

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