Geometric approach to graph magnitude homology
Algebraic Topology
2020-03-19 v1
Abstract
In this paper, we introduce a new method to compute magnitude homology of general graphs. To each direct sum component of magnitude chain complexes, we assign a pair of simplicial complexes whose simplicial chain complex is isomorphic to it. First we states our main theorem specialized to trees, which gives another proof for the known fact that trees are diagonal. After that, we consider general graphs, which may have cycles. We also demonstrate some computation as an application.
Cite
@article{arxiv.2003.08058,
title = {Geometric approach to graph magnitude homology},
author = {Yasuhiko Asao and Kengo Izumihara},
journal= {arXiv preprint arXiv:2003.08058},
year = {2020}
}
Comments
Every comment welcome. This is a master thesis of the second author