Stephen Smale  rst identi ed the possibility of, for ten points, what topological action in which a sphere is turned inside out?
A book by J. Scott Carter about this thing describes it as  an Exercise in Diagrammatic Algebra . Rob Kusner proposed an optimal method of doing this based on saddle points in Willmore energy. A recent one of these things was discovered by Aitchison and called the holiverse. One class of these things, their  minimax  type, is constructed by using a half-way model such as Boy's surface or   Morin's surface. One method for doing this, Thurston's corrugations, was featured in a video produced by the Geometry Center entitled  Outside In . Stephen Smale  rst identi ed the possibility of, for ten points, what topological action in which a sphere is turned inside out?
A book by J. Scott Carter about this thing describes it as  an Exercise in Diagrammatic Algebra .
sphere eversion [after  sphere , accept just eversion, accept descrip- tive answers mentioning turning a sphere inside out until  turned ]