Retraction Theorems for Group Compactifications

2025/09/12 by Yair Hartman, Hartman, Yair, Aranka Hrušková +5
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Medical Imaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2509.10072

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.

Citations

• Charmenability of arithmetic groups of product type
• The Poisson formula for groups with hyperbolic properties

Related

• A retraction theorem for topological fundamental groups with application to the Hawaiian earring
• Gromov boundaries as Markov compacta
• K-theory and actions on Euclidean retracts
• Similar relatively hyperbolic actions of a group
• Quasi-retracts of groups