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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. 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.
List of contents
A Sphere; Surfaces, Folds, and Cusps; The Inside and Outside; Dimensions; Immersed Surfaces; Movies; Movie Moves; Taxonomic Summary; How Not to Turn the Sphere Inside-Out; A Physical Metaphor; Sarah's Thesis; The Eversion; The Double Point and Fold Surfaces.
About the author
J. Scott Carter is an Associate Professor of Sociology at the University of Central Florida. His research interests encompass several areas, including race and politics, racial attitudes, racial inequality in education, and Southern and urban place.
