Analytic torsion for graphs
Combinatorics
2022-01-25 v1 Discrete Mathematics
Abstract
Analytic torsion is a functional on graphs which only needs linear algebra to be defined. In the continuum it corresponds to the Ray-Singer analytic torsion. We have formulas for analytic torsion if the graph is contractible or if it is a discrete sphere. A key insight is that analytic torsion is the super determinant of the Dirac operator of the graph.
Cite
@article{arxiv.2201.09412,
title = {Analytic torsion for graphs},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:2201.09412},
year = {2022}
}
Comments
30 pages, 17 figures