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arXiv · 2403.11986

Noncompact surfaces, triangulations and rigidity

Stephen C. Power
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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 Kerékjártó's classification of noncompact surfaces is also given.

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Stephen C. Power. 2025-04-04. Noncompact surfaces, triangulations and rigidity. https://arxiv.org/abs/2403.11986

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