Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
Journal of Symbolic Logic 74 (3):891-900 (2009)
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 cohomologyDOI
10.2178/jsl/1245158089
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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.
A descending chain condition for groups definable in o -minimal structures.Alessandro Berarducci, Margarita Otero, Yaa’cov Peterzil & Anand Pillay - 2005 - Annals of Pure and Applied Logic 134 (2):303-313.
Sheaf cohomology in o-minimal structures.Mário J. Edmundo, Gareth O. Jones & Nicholas J. Peatfield - 2006 - Journal of Mathematical Logic 6 (2):163-179.