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- W4287728246 abstract "We say that a sequence of proper geodesic spaces $X_i$ consists of textit{almost homogeneous spaces} if there is a sequence of discrete groups of isometries $G_i leq Iso(X_i)$ such that diam$(X_i/G_i)to 0$ as $i to infty$. We show that if a sequence $X_i$ of almost homogeneous spaces converges in the pointed Gromov--Hausdorff sense to a space $X$, then $X$ is a nilpotent locally compact group equipped with an invariant geodesic metric. Under the above hypotheses, we show that if $X$ is semi-locally-simply-connected, then it is a nilpotent Lie group equipped with an invariant Finsler or sub-Finsler metric, and for large enough $i$, there are subgroups $Lambda_i leq pi_1(X_i) $ with surjective morphisms $Lambda_ito pi_1(X)$." @default.
- W4287728246 created "2022-07-26" @default.
- W4287728246 creator A5051185367 @default.
- W4287728246 date "2020-07-03" @default.
- W4287728246 modified "2023-09-29" @default.
- W4287728246 title "Limits of almost homogeneous spaces and their fundamental groups" @default.
- W4287728246 doi "https://doi.org/10.48550/arxiv.2007.01985" @default.
- W4287728246 hasPublicationYear "2020" @default.
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