Journal of Symbolic Logic

Splitting definably compact groups in o-minimal structures

Marcello Mamino

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Abstract

An argument of A. Borel [Bor-61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 3 (2011), 973-986.

Dates
First available in Project Euclid: 6 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1309952529

Digital Object Identifier
doi:10.2178/jsl/1309952529

Mathematical Reviews number (MathSciNet)
MR2849254

Zentralblatt MATH identifier
1247.03062

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality 55S40: Sectioning fiber spaces and bundles

Keywords
Definable groups o-minimality fibre bundles

Citation

Mamino, Marcello. Splitting definably compact groups in o-minimal structures. J. Symbolic Logic 76 (2011), no. 3, 973--986. doi:10.2178/jsl/1309952529. https://projecteuclid.org/euclid.jsl/1309952529


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