Year: 2024
Type: article
Abstract: The aim of this paper is to apply the framework developed by Sam and Snowden to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Proudfoot. Our main results concern the magnitude homology of graphs introduced by Hepworth and Willerton, and we prove that it is a finitely generated functor (on graphs of bounded genus). More precisely, for graphs of bounded genus, we prove that magnitude cohomology, in each homological degree, has rank which grows at most polynomially in the number of vertices, and that its torsion is bounded. As a consequence, we obtain analogous results for path homology of (undirected) graphs.
DOI: 10.1112/blms.13143
Authors: Luigi Caputi, Carlo Collari
Institutions: University of Bologna, University of Pisa
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Università di Pisa, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, European Research Council, Instytut Matematyczny, Polskiej Akademii Nauk, HORIZON EUROPE European Research Council
OpenAlex ID: W4402393503