2012/08/02 by Joel Hass, Hass, Joel
Mathematics · #53A04 #57M25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53A04 #msc:57M25
paper · pdf · doi:10.48550/arxiv.1208.0568
arxiv created 2012/10/16 · arxiv updated 2012/10/17
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 characterize the 3-sphere among 3-manifolds. Analogous patterns of normal and almost normal surfaces led Rubinstein to an algorithm for recognizing the 3-sphere.