Connected components of definable groups and o-minimality I
Logic
2011-02-01 v1 Group Theory
Abstract
We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin, Newelski, Petrykovski. The examples also give new non G-compact first order theories.
Cite
@article{arxiv.1101.5705,
title = {Connected components of definable groups and o-minimality I},
author = {Annalisa Conversano and Anand Pillay},
journal= {arXiv preprint arXiv:1101.5705},
year = {2011}
}
Comments
26 pages. This paper corrects the paper "Groups definable in o-minimal structures: structure theorem, G^000, definable amenability, and bounded orbits" by the first author which was posted in December (1012.4540v1) and later withdrawn