Elastic Graphs
Metric Geometry
2020-02-12 v3 Dynamical Systems
Abstract
An elastic graph is a graph with an elasticity associated to each edge. It may be viewed as a network made out of ideal rubber bands. If the rubber bands are stretched on a target space there is an elastic energy. We characterize when a homotopy class of maps from one elastic graph to another is loosening, i.e., decreases this elastic energy for all possible targets. This fits into a more general framework of energies for maps between graphs.
Keywords
Cite
@article{arxiv.1607.00340,
title = {Elastic Graphs},
author = {Dylan P. Thurston},
journal= {arXiv preprint arXiv:1607.00340},
year = {2020}
}
Comments
62 pages, 6 figures; v3: More background, proofs cleaned up