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Mathematics > Logic

arXiv:0711.2502 (math)
[Submitted on 15 Nov 2007]

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

Authors:Alessandro Berarducci
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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 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.
Comments: 11 pages
Subjects: Logic (math.LO); Algebraic Topology (math.AT)
MSC classes: 03C64; 22E15; 03H05
Cite as: arXiv:0711.2502 [math.LO]
  (or arXiv:0711.2502v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.0711.2502

Submission history

From: Alessandro Berarducci [view email]
[v1] Thu, 15 Nov 2007 20:26:02 UTC (12 KB)
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