Noncompact surfaces, triangulations and rigidity

Power, Stephen (2025) Noncompact surfaces, triangulations and rigidity. Bulletin of the London Mathematical Society. ISSN 0024-6093 (In Press)

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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 R3. In particular, every noncompact surface has a (3,6)-tight triangulation that is minimally 3-rigid. A simplification of Richards' proof of Kerekjarto's classification of noncompact surfaces is also given.