# Description

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.

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 Codes

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 Codes

**Key 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*