An Excursion in Diagrammatic Algebra: Turning a Sphere from Red to Blue (Series on Knots & Everything 48)

An Excursion in Diagrammatic Algebra: Turning a Sphere from Red to Blue (Series on Knots & Everything 48)

By: J. Scott Carter (author)Hardback

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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.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.

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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.

Product Details

  • publication date: 09/12/2011
  • ISBN13: 9789814374491
  • Format: Hardback
  • Number Of Pages: 296
  • ID: 9789814374491
  • weight: 567
  • ISBN10: 9814374490

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  • Saver Delivery: Yes
  • 1st Class Delivery: Yes
  • Courier Delivery: Yes
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