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

Published online by Cambridge University Press:  12 March 2014

Alessandro Berarducci
Alessandro Berarducci*
Affiliation:
Universitá di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy, E-mail: berardu@dm.unipi.it
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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.

Keywords

Cohomologygroupso-minimality03C6422E1503H05
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 891 - 900
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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