Connected components of definable groups and o-minimality I

Published 29 Jan 2011 in math.LO and math.GR | (1101.5705v1)

Abstract: We give examples of groups G such that G⁰⁰ 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.

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