Local homology of abstract simplicial complexes
Algebraic Topology
2018-05-30 v1
Abstract
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds, or samplings thereof. While this is a vital perspective, the focus of this survey is squarely on the local homology of abstract simplicial complexes. Our motivation comes from the needs of the analysis of hypergraphs and graphs. In addition to presenting many classical facts in a unified way, this survey presents a few new results about how local homology generalizes useful tools from graph theory. The survey ends with a statistical comparison of graph invariants with local homology.
Keywords
Cite
@article{arxiv.1805.11547,
title = {Local homology of abstract simplicial complexes},
author = {Michael Robinson and Chris Capraro and Cliff Joslyn and Emilie Purvine and Brenda Praggastis and Stephen Ranshous and Arun Sathanur},
journal= {arXiv preprint arXiv:1805.11547},
year = {2018}
}
Comments
38 pages