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:

1 online resource (294 p.)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific Pub. Co., 2012.

Language Note:

English

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 and develop a facility for these diagrammatic computations. The text describes the essential topological ideas through metaphors t

Contents:

Preface; Contents; 1. A Sphere; 2. Surfaces, Folds, and Cusps; 3. The Inside and Outside; 4. Dimensions; 5. Immersed Surfaces; 6. Movies; Double Points and Triple Points; Critical Exchanges; Example; Summary; 7. Movie Moves; The Evolution in the Intrinsic Sphere; The Fold Set; Double Points and Triple Points; Double Points and Folds; Triple Points, Double Points, and Folds; Conclusion; 8. Taxonomic Summary; 9. How Not to Turn the Sphere Inside-out; 10. A Physical Metaphor; Gauss-Morse Codes; Summary; 11. Sarah's Thesis; 12. The Eversion; 13. The Double Point and Fold Surfaces; Conclusion

BibliographyIndex

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

981-4374-50-4

OCLC:

860491786