Graph magnitude homology via algebraic Morse theory
Combinatorics
2018-09-20 v1 Algebraic Topology
Abstract
We compute magnitude homology of various graphs using algebraic Morse theory. Specifically, we (1) give an alternative proof that trees are diagonal, (2) identify a new class of diagonal graphs, (3) prove that the icosahedral graph is diagonal, and (4) compute the magnitude homology of cycles. These results answer several questions of Hepworth and Willerton [HW17].
Cite
@article{arxiv.1809.07240,
title = {Graph magnitude homology via algebraic Morse theory},
author = {Yuzhou Gu},
journal= {arXiv preprint arXiv:1809.07240},
year = {2018}
}