An excursion in diagrammatic algebra : turning a sphere from red to blue / J. Scott Carter.

Format:

Book

Author/Creator:

Carter, J. Scott.

Series:

K & E series on knots and everything ; v. 48.

K & E series on knots and everything ; v. 48

Language:

English

Subjects (All):

Low-dimensional topology.

Physical Description:

xvi, 275 pages : illustrations (chiefly color) ; 24 cm.

Place of Publication:

[Hackensack] N.J. : World Scientific, [2012]

Summary:

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 with 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. No prior mathematical knowledge beyond high school is assumed, but the mathematically informed reader will benefit from the informal introduction of ideas. This volume will appeal to scientifically literate individuals who appreciate mathematical beauty. Book jacket.

Contents:

1 A Sphere 1

2 Surfaces, Folds, and Cusps 5

3 The Inside and Outside 7

4 Dimensions 9

5 Immersed Surfaces 21

6 Movies 29

7 Movie Moves 45

8 Taxonomic Summary 75

9 How Not to Turn the Sphere Inside-out 81

10 A Physical Metaphor 87

11 Sarah's Thesis 93

12 The Eversion 97

13 The Double Point and Fold Surfaces 263.

Notes:

Includes bibliographical references and index.

ISBN:

9789814374491

9814374490

OCLC:

754105036