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- W4300766307 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 $bigvee$-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 $phi$ from a generic definable neighborhood of the identity of $G$ into the group $Hleft(Rright)$ of $R$-points of $H$ such that $phi$ acts as a group homomorphism inside its domain. This result is used in [2] to prove that the o-minimal universal covering group of an abelian connected definably compact group definable in a sufficiently saturated real closed field $R$ is, up to locally definable isomorphisms, an open connected locally definable subgroup of the o-minimal universal covering group of the $R$-points of some $R$-algebraic group." @default.
- W4300766307 created "2022-10-04" @default.
- W4300766307 creator A5012980774 @default.
- W4300766307 date "2017-03-24" @default.
- W4300766307 modified "2023-09-27" @default.
- W4300766307 title "Definably compact groups definable in real closed fields. I" @default.
- W4300766307 doi "https://doi.org/10.48550/arxiv.1703.08606" @default.
- W4300766307 hasPublicationYear "2017" @default.
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