Work

The First Roe Homology Group of Locally Finite Graphs

Year: 2025

Type: article

Abstract: We give a decomposition of the first group of so-called "Roe" homology of locally finite, connected graphs. We show that this group can be decomposed as a direct sum of two terms: the first counts the number of ends of the graph, while the second measures the existence of cycles that are not decomposable into smaller cycles (in some suitably coarse sense).

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13395

Authors: Rémi Bottinelli, Tom Kaiser

Institution: KU Leuven

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: G580951548, Formal languages and decision problems in groups, G8411960325