Limits of almost homogeneous spaces and their fundamental groups

  • Sergio Zamora

    Max Planck Institute for Mathematics, Bonn, Germany
Limits of almost homogeneous spaces and their fundamental groups cover
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Abstract

We say that a sequence of proper geodesic spaces consists of almost homogeneous spaces if there is a sequence of discrete groups of isometries with diam as . We show that if a sequence of pointed almost homogeneous spaces converges in the pointed Gromov–Hausdorff sense to a space , then is a nilpotent locally compact group equipped with an invariant geodesic metric. Under the above hypotheses, we show that if is semi-locally-simply-connected, then it is a nilpotent Lie group equipped with an invariant sub-Finsler metric, and for large enough, is a subgroup of a quotient of .

Cite this article

Sergio Zamora, Limits of almost homogeneous spaces and their fundamental groups. Groups Geom. Dyn. 18 (2024), no. 3, pp. 761–798

DOI 10.4171/GGD/792