Detecting virtual homomorphisms via Banach metrics
Abstract
Abstract We introduce the notion of Banach metrics on finitely generated infinite groups. This extends the notion of a Cayley graph (as a metric space). Our motivation comes from trying to detect the existence of virtual homomorphisms into $$\mathbb {Z}$$ Z . We show that detection of such homomorphisms through metric functional boundaries of Cayley graphs isn’t always possible. However, we prove that it is always possible to do so through a metric functional boundary of some Banach metric on the group.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometric Analysis and Curvature Flows
Mathematics and Applications
Publication details
- Journal / source
- Geometriae Dedicata
- Volume
- 220
- Issue
- 1
- Publication date
- 19 January 2026
- Language
- EN