Combinatorial Ricci Curvature for Polyhedral Surfaces and Posets
Combinatorics
2014-06-19 v1
Abstract
The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not behave analogously to smooth surfaces with respect to negative curvature. We extend this curvature to vertices and faces in such a way that the problems with combinatorial Ricci curvature are mostly resolved. The discussion is stated in terms of ranked posets.
Cite
@article{arxiv.1406.4598,
title = {Combinatorial Ricci Curvature for Polyhedral Surfaces and Posets},
author = {Ethan Bloch},
journal= {arXiv preprint arXiv:1406.4598},
year = {2014}
}
Comments
16 pages, 4 figures