What is an almost normal surface? (English) Zbl 1279.57002

Hass, Joel

Hodgson, Craig D. (ed.) et al., Geometry and topology down under. A conference in honour of Hyam Rubinstein, Melbourne, Australia, July 11–22, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-8480-5/pbk). Contemporary Mathematics 597, 1-13 (2013).

Summary: A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. Patterns of stable and unstable geodesics can be used to characterize the 2-sphere among surfaces, and similar patterns of normal and almost normal surfaces led Rubinstein to an algorithm for recognizing the 3-sphere.
For the entire collection see [Zbl 1272.57002].

MSC:

57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57-03	History of manifolds and cell complexes
57N10	Topology of general \(3\)-manifolds (MSC2010)
53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature

Keywords:

normal surfaces; algorithms; recognizing the 3-sphere