Splitting definably compact groups in o-minimal structures

Details Splitting definably compact groups in o-minimal structures Splitting definably compact groups in o-minimal structures

2010-01-13

arxiv.org/abs/1001.2229v2

J. Symbolic Logic, 76 (3), (Sept. 2011), 973-986

Mathematics

Logic

final version 13 pages

Scientific paper

An argument of A.Borel 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.

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