English

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

R2 v1 2026-06-22T14:41:00.654Z