Limits of almost homogeneous spaces and their fundamental groups
Groups, geometry, and dynamics, Tome 18 (2024) no. 3, pp. 761-798
Voir la notice de l'article provenant de la source EMS Press
We say that a sequence of proper geodesic spaces Xn consists of almost homogeneous spaces if there is a sequence of discrete groups of isometries Gn≤Iso(Xn) with diam(Xn/Gn)→0 as n→∞. We show that if a sequence (Xn,pn) of pointed almost homogeneous spaces converges in the pointed Gromov–Hausdorff sense to a space (X,p), 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 sub-Finsler metric, and for n large enough, π1(X) is a subgroup of a quotient of π1(Xn).
Classification :
53C23, 22D99, 22E20, 22E40, 51F99
Mots-clés : fundamental group, Gromov–Hausdorff convergence, discrete groups, equivariant convergence
Mots-clés : fundamental group, Gromov–Hausdorff convergence, discrete groups, equivariant convergence
Affiliations des auteurs :
Sergio Zamora 1
Sergio Zamora. Limits of almost homogeneous spaces and their fundamental groups. Groups, geometry, and dynamics, Tome 18 (2024) no. 3, pp. 761-798. doi: 10.4171/ggd/792
@article{10_4171_ggd_792,
author = {Sergio Zamora},
title = {Limits of almost homogeneous spaces and their fundamental groups},
journal = {Groups, geometry, and dynamics},
pages = {761--798},
year = {2024},
volume = {18},
number = {3},
doi = {10.4171/ggd/792},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/792/}
}
Cité par Sources :