Groups definable in o-minimal structures: structure theorem, G^000, definable amenability and bounded orbits

Abstract

We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of the G to G^00 functor. We ask further questions about types with bounded orbits in NIP theories.

22 pages The paper has been withdrawn because of a mistake in section 2. A correct version will be prepared and posted soon