文档介绍：Fred H. Croom
Basic Concepts of
Algebraic Topology
Springer-Verlag
New York Heidelberg Berlin
Fred H. Croom
The University of the South
Sewanee, Tennessee 37375
USA
Editorial Board
F. W. Gehring P. R. Halmos
University of Michigan University of California,
Department of Mathematics Department of Mathematics
Ann Arbor, Michigan 48104 Santa Barbara, California 93106
USA USA
AMS Subject Classifications: 55-01
Library of Congress Cataloging in Publication Data
Croom, Fred H 1941-
Basic concepts of algebraic topology.
(Undergraduate texts in mathematics)
Bibliography: p.
Includes index.
1. Algebraic topology. I. Title.
77-16092
All rights reserved.
No part of this book may be translated or reproduced in any form without written permission
from Springer-Verlag.
© 1978 by Springer-Verlag, New York Inc.
Printed in the United States of America.
987654321
ISBN 0-387-90288-0 Springer-Verlag New York
ISBN 3-540-90288-0 Springer-Verlag Berlin Heidelberg
Preface
This text is intended as a one semester introduction to algebraic topology
at the undergraduate and beginning graduate levels. Basically, it covers
simplicial homology theory, the fundamental group, covering spaces, the
higher homotopy groups and introductory singular homology theory.
The text follows a broad historical outline and uses the proofs of the
discoverers of the important theorems when this is consistent with the
elementary level of the course. This method of presentation is intended to
reduce the abstract nature of algebraic topology to a level that is palatable
for the beginning student and to provide motivation and cohesion that are
often lacking in abstact treatments. The text emphasizes the geometric
approach to algebraic topology and attempts to show the importance of
topological concepts by applying them to problems of geometry and
analysis.
The prerequisites for this cour