Topology of definable abelian groups in o-minimal structures

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.

7 pages

References in corpus (2)

• PL and differential topology in o-minimal structure
• Lie-like decompositions of groups definable in o-minimal structures

Cited by in corpus (2)

• O-minimal Hauptvermutung for polyhedra II
• Groups definable in o-minimal structures: various properties and a diagram