Splitting definably compact groups in o-minimal structures

Journal of Symbolic Logic 76 (3):973 - 986 (2011)

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 Definable groups   o-minimality   fibre bundles
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DOI 10.2178/jsl/1309952529
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