Submission date: 16 February 2011.

Abstract:

In this note we show that every definably connected, definably compact abelian definable group in an o-minimal expansion of a real closed field of dimension not 4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semialgebraic case the result holds for all dimensions.

Mathematics Subject Classification: 03C64

Keywords and phrases: o-minimality, definable groups

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