Retraction Theorems for Group Compactifications
Group Theory
2025-09-15 v1 Dynamical Systems
Abstract
We characterize group compactifications of discrete groups for which there exists an equivariant retraction onto the boundary. In particular, we prove an equivariant analogue of Brouwer's No-Retraction theorem for large classes of group compactifications, which includes actions of hyperbolic groups on their Gromov boundary.
Cite
@article{arxiv.2509.10072,
title = {Retraction Theorems for Group Compactifications},
author = {Yair Hartman and Aranka Hrušková and Mehrdad Kalantar and Tomer Zimhoni},
journal= {arXiv preprint arXiv:2509.10072},
year = {2025}
}