Covers of groups definable in o-minimal structures

Details Covers of groups definable in o-minimal structures Covers of groups definable in o-minimal structures

2001-04-29

arxiv.org/abs/math/0104282v1

Mathematics

Logic

69 pages, submited

Scientific paper

We develop in this paper the theory of covers for Hausdorff properly $\bigvee $-definable manifolds with definable choice in an o-minimal structure $\N$. In particular, we show that given an $\N$-definably connected $\N$-definable group $G$ we have $1\to \pi_1(G)\to \tilde{G}\stackrel{p}\to G\to 1$ in the category of strictly properly $\bigvee $-definable groups with strictly properly $\bigvee $-definable homomorphisms, where $\pi_1(G)$ is the o-minimal fundamental group of $G$.

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