English

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.

Keywords

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definable amenability, and bounded orbits" by the first author which was posted in December (1012.4540v1) and later withdrawn

R2 v1 2026-06-21T17:18:45.769Z