Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 74, Issue 3 (2009), 891-900.
Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
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.
Article information
Source
J. Symbolic Logic, Volume 74, Issue 3 (2009), 891-900.
Dates
First available in Project Euclid: 16 June 2009
Permanent link to this document
https://projecteuclid.org/euclid.jsl/1245158089
Digital Object Identifier
doi:10.2178/jsl/1245158089
Mathematical Reviews number (MathSciNet)
MR2548466
Zentralblatt MATH identifier
1181.03042
Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality 22E15: General properties and structure of real Lie groups 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
Keywords
Cohomology groups o-minimality
Citation
Berarducci, Alessandro. Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup. J. Symbolic Logic 74 (2009), no. 3, 891--900. doi:10.2178/jsl/1245158089. https://projecteuclid.org/euclid.jsl/1245158089
