A Reeb sphere theorem in graph theory
Combinatorics
2019-03-26 v1 Discrete Mathematics
Differential Geometry
Abstract
We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere S(x). In the Morse case these graphs are either spheres, the empty graph or the product of two spheres.
Cite
@article{arxiv.1903.10105,
title = {A Reeb sphere theorem in graph theory},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:1903.10105},
year = {2019}
}
Comments
17 oages 4 figures