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

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

2007-11-15

arxiv.org/abs/0711.2502v1

Mathematics

Logic

11 pages

Scientific paper

By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an expansion 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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