English

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].

Keywords

Cite

@article{arxiv.1809.07240,
  title  = {Graph magnitude homology via algebraic Morse theory},
  author = {Yuzhou Gu},
  journal= {arXiv preprint arXiv:1809.07240},
  year   = {2018}
}