Connected components of definable groups and o-minimality I
نویسندگان
چکیده
We give examples of definable groups G (in a saturated model, sometimes o-minimal) such that G00 6= G000, yielding also new examples of “non G-compact” theories. We also prove that for G definable in a (saturated) o-minimal structure, G has a “bounded orbit” (i.e. there is a type of G whose stabilizer has bounded index) if and only if G is definably amenable, giving a positive answer to a conjecture of Newelski and Petrykowski in this special case of groups definable in ominimal structures. We also introduce and discuss further conjectures on bounded orbits in definable groups. These results and analyses are informed by a decomposition theorem for groups in o-minimal structures.
منابع مشابه
Connected components of definable groups, and o-minimality II
In this sequel to [3] we try to give a comprehensive account of the “connected components” G00 and G000 as well as the various quotients G/G00, G/G000, G00/G000, for G a group definable in a (saturated) ominimal expansion of a real closed field. Key themes are the structure of G00/G000 and the problem of “exactness” of the G 7→ G00 functor. We prove that the examples produced in [3] are typical...
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