Publication: Topology of definable abelian groups in o-minimal structures
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2011-11-17
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London Mathematical Society
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Abstract
In this note, we prove that every definably connected, definably compact abelian definable group G in an o-minimal expansion of a real closed field with dim(G)≠4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.