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