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.
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