Definably compact groups definable in real closed fields.II

2017/05/21 by Barriga, Eliana
#03C64 #03C68 #20G20 #22B99 #22E15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1705.07370

Abstract

We continue the analysis of definably compact groups definable in a real closed field R. In [3], we proved that for every definably compact definably connected semialgebraic group G over 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. The above result and our study of locally definable covering homomorphisms for locally definable groups combine to prove that if such group G is in addition abelian, then its o-minimal universal covering group \widetildeG is definably isomorphic, as a locally definable group, to a connected open locally definable subgroup of the o-minimal universal covering group \widetildeH(R)⁰ of the group H(R)⁰ for some connected R-algebraic group H.

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