Connected components of definable groups and o-minimality I
classification
🧮 math.LO
math.GR
keywords
groupsdefinableexamplesgiveamenableanswerboundedcomponents
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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.
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