English

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.

Keywords

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

R2 v1 2026-06-28T15:24:33.886Z