Noncompact surfaces, triangulations and rigidity
Combinatorics
2025-04-08 v3 Geometric Topology
Abstract
Every noncompact surface is shown to have a (3,6)-tight triangulation, and applications are given to the generic rigidity of countable bar-joint frameworks in R^3. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Ker\'ekj\'art\'o's classification of noncompact surfaces is also given.
Cite
@article{arxiv.2403.11986,
title = {Noncompact surfaces, triangulations and rigidity},
author = {Stephen C. Power},
journal= {arXiv preprint arXiv:2403.11986},
year = {2025}
}
Comments
Improved version. Accepted for the Bulletin of the London Mathematical Society