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).
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
@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
