Submission date: 24 March 2017

Abstract:

We study definably compact definably connected groups definable in a sufficiently saturated real closed field R. We introduce the notion of group-generic point for ∨-definable groups and show the existence of group-generic points for definably compact groups definable in a sufficiently saturated o-minimal expansion of a real closed field. We use this notion along with some properties of generic sets to prove that for every definably compact definably connected group G definable in R there are a connected R-algebraic group H, a definable injective map φ from a generic definable neighborhood of the identity of G into the group H(R) of R-points of H such that φ acts as a group homomorphism inside its domain. This result is used in [3] to establish a characterization of the abelian definably compact definably connected groups definable in R through its o-minimal universal covering group.

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Full text arXiv 1703.08606: pdf, ps.