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).
@article{10_37236_13395,
author = {R\'emi Bottinelli and Tom Kaiser},
title = {The first {Roe} homology group of locally finite graphs},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/13395},
zbl = {8120107},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13395/}
}
TY - JOUR
AU - Rémi Bottinelli
AU - Tom Kaiser
TI - The first Roe homology group of locally finite graphs
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/13395/
DO - 10.37236/13395
ID - 10_37236_13395
ER -
%0 Journal Article
%A Rémi Bottinelli
%A Tom Kaiser
%T The first Roe homology group of locally finite graphs
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/13395/
%R 10.37236/13395
%F 10_37236_13395
Rémi Bottinelli; Tom Kaiser. The first Roe homology group of locally finite graphs. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13395
