Topology of definable abelian groups in o-minimal structures

Details Topology of definable abelian groups in o-minimal structures Topology of definable abelian groups in o-minimal structures

2011-02-12

arxiv.org/abs/1102.2494v1

Mathematics

Logic

7 pages

Scientific paper

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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