Differential Calculus on Cayley Graphs
Discrete Mathematics
2015-05-05 v1 General Topology
Abstract
We conservatively extend classical elementary differential calculus to the Cartesian closed category of convergence spaces. By specializing results about the convergence space representation of directed graphs, we use Cayley graphs to obtain a differential calculus on groups, from which we then extract a Boolean differential calculus, in which both linearity and the product rule, also called the Leibniz identity, are satisfied.
Keywords
Cite
@article{arxiv.1504.08013,
title = {Differential Calculus on Cayley Graphs},
author = {Daniel R. Patten and Howard A. Blair and David W. Jakel and Robert J. Irwin},
journal= {arXiv preprint arXiv:1504.08013},
year = {2015}
}
Comments
12 pages, 4 figures. First author was supported in part by an NRC Fellowship. Second Author was supported in part by AFRL Contract No. F8713-13-2-0116GI