Real Algebraic and Analytic Geometry

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334. Annalisa Conversano , Anand Pillay:
Connected components of definable groups and o-minimality I.

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Submission: 2011, December 2.

Abstract:
(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and bounded orbits by the first author which was posted in December (1012.4540v1; Modnet preprint Nr 284) and later withdrawn.)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 (2010): 03C64, 22F99.

Full text: http://arxiv.org/pdf/1101.5705


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