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Splitting definably compact groups in o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Marcello Mamino
Marcello Mamino*
Affiliation:
Classe di Scienze - Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy, E-mail: m.mamino@sns.it
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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.

Keywords

03C6455S40Definable groupso-minimalityfibre bundles

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 973 - 986
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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