English

The Graph Laplacian and Morse Inequalities

Mathematical Physics 2019-08-14 v1 math.MP

Abstract

The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten theory for cell complexes. We describe the general framework of graph quantum mechanics and we produce discrete versions of the Hodge theorems and energy cut-offs within this formulation.

Keywords

Cite

@article{arxiv.1704.08354,
  title  = {The Graph Laplacian and Morse Inequalities},
  author = {Ivan Contreras and Boyan Xu},
  journal= {arXiv preprint arXiv:1704.08354},
  year   = {2019}
}

Comments

14 pages, 10 figures

R2 v1 2026-06-22T19:29:05.962Z