Year: 2026
Type: preprint
Abstract: We propose the study of the class of groups that fix a point for every continuous action on any convex compact space. Oliver completed the corresponding program of classifying the finite groups that have this fixed-point property in finite dimensions. Turning to infinite groups, the Schauder--Tychonoff theorem establishes that the integers have the fixed-point property, but this has not been shown for any other infinite, finitely generated group. We establish a local transfer principle and use it to show, as a proof of concept, that $\mathbf{Z} \times (\mathbf{Z}/p\mathbf{Z})$ belongs to this class of groups.
Source: arXiv (Cornell University)
Authors: Monod, Nicolas, Tamuz, Omer, Teryoshin, Lizzy
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7221753986