Splitting definably compact groups in o-minimal structures
Logic
2011-10-25 v2
Abstract
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.
Cite
@article{arxiv.1001.2229,
title = {Splitting definably compact groups in o-minimal structures},
author = {Marcello Mamino},
journal= {arXiv preprint arXiv:1001.2229},
year = {2011}
}
Comments
final version 13 pages