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Preprint Number 294

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294. Annalisa Conversano and Anand Pillay
Connected components of definable groups and o-minimality I

Submission date: 1 February 2011.


(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and bounded orbits” by the first author which was posted in December (1012.4540v1; Modnet preprint Nr 284) and later withdrawn.)
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.

Mathematics Subject Classification: 03C64, 22F99

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