The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.Contents:A SphereSurfaces, Folds, and CuspsThe Inside and OutsideDimensionsImmersed SurfacesMoviesMovie MovesTaxonomic SummaryHow Not to Turn the Sphere Inside-OutA Physical MetaphorSarah's ThesisThe EversionThe Double Point and Fold Surfaces
Readership: Researchers in mathematics.
Keywords:Topology;Sphere Eversion;Double Point;Triple Point;Symmetric Monoidal 2-Category;Fold Lines;Space-Time;Regular Homotopy;Bend;Fold;Cusp;Surfaces;Smale;Bernard Morin;Mobius Band;Movies;Movie Moves;Quadruple Point;Saddle Point;General Position;Double-Decker Set;Lips;Beak-to-Beak;Horizontal Cusp;Gauss Morse CodesKey Features:Most sphere eversions that are available are computer illustrations. One cannot stop the animations, look inside, and understand how one got from here to there. The illustrations that the author has given show each step in intricate detailThis is a book rather than a film. As such, it provides insight and in-depth analyses that cannot be presented in filmThese illustrations are drawn essentially by hand with computer software. They are remarkable for their subtle nature and each illustration is a work of art unto itselfReviews:
"Innumerable three-color illustrations support the text."CHOICE
"This book, written in a very friendly style, is an introduction to topology related to sphere eversion."MathSciNet