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arXiv · 1102.2494

Topology of definable abelian groups in o-minimal structures

Elias Baro·Alessandro Berarducci
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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.

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Elias Baro, Alessandro Berarducci. 2011-02-12. Topology of definable abelian groups in o-minimal structures. https://doi.org/10.1112/blms%2Fbdr108

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