3,235 research outputs found
Definable group extensions in semi-bounded o-minimal structures
In this note we show: Let ℛ = 〈 R, <, +, 0,...〉 be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([2]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈 Rm, +〉.FCT Financiamento Base 2008 - USFL/1/209; FCT grant SFRH/BPD/35000/200
Connected components of definable groups and o-minimality I
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.Comment: 26 pages. 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) and later withdraw
Group covers, o-minimality, and categoricity
We study the model theory of covers of groups definable in o-minimal
structures. This includes the case of covers of compact real Lie groups. In
particular we study categoricity questions, pointing out some notable
differences with the case of covers of complex algebraic groups studied by
Zilber and his students. We also discuss from a model-theoretic point of view
the following question, related to "Milnor's conjecture": is a finite central
extension (as an abstract group) of a compact Lie group also a topological
extension?Comment: 24 page
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