How surfaces intersect in space : an introduction to topology / J. Scott Carter.

Author
Carter, J. Scott [Browse]
Format
Book
Language
English
Εdition
2nd ed.
Published/​Created
Singapore ; River Edge, N.J. : World Scientific, ©1995.
Description
xviii, 318 pages : illustrations ; 23 cm.

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Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA611 .C377 1995 Browse related items Request

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    Summary note
    This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Möbius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced. In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space. Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface. Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view. This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
    Bibliographic references
    Includes bibliographical references (p. 305-311) and index.
    Contents
    • 1. Surface and Space
    • 2. Non-orientable Surfaces
    • 3. Curves and Knots
    • 4. Other Three Dimensional Spaces
    • 5. Relationships
    • 6. Surfaces in 4-Dimensions
    • 7. Higher Dimensional Spaces.
    ISBN
    • 9810220820
    • 9789810220822
    • 9810220669 ((pbk.))
    • 9789810220662 ((pbk.))
    • 0000098102
    • 9780000098108
    • 0000098108
    LCCN
    95210785
    OCLC
    32897228
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