A GH-compactification of CAT$(0)$-groups via totally disconnected, unimodular actions

Autor:	Cavallucci, Nicola
Rok vydání:	2023
Předmět:	Mathematics - Metric Geometry Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff sense of sequences $(X_j,G_j)$, where the $X_j$'s are proper, geodesically complete, uniformly packed, CAT$(0)$-spaces and the $G_j$'s are closed, totally disconnected, unimodular, uniformly cocompact groups of isometries. We show that the class of metric quotients $G/X$, where $X$ and $G$ are as above, is compact under Gromov-Hausdorff convergence. In particular it is a geometric compactification of the class of locally geodesically complete, locally compact, locally CAT$(0)$-spaces with uniformly packed universal cover and uniformly bounded diameter. Comment: arXiv admin note: text overlap with arXiv:2304.10763
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.05640 Zobrazit plný text záznamu View this record from Arxiv