Steven G. Krantz
David Saltman (Chair)
B. B. ripacojiOB
BjieMeHTbi KOM6nHaTopHOH H #H(f)(j)epeHrj;jiajibHoM TonojiorHH
MIIHMO, MocKBa, 2004
Translated from the Russian by Olga Sipacheva
2000 Mathematics Subject Classification. Primary 57-01;
Secondary 57Mxx, 57Rxx.
This work was originally published in Russian by M I I H M O under the title "9jieMeHTbi
KOM6HHaTopHoM H OTc^epeHiTHajiBHoM TonojiorHH" © 2004. Th e present translation
was created under license for the American Mathematical Society and is published by
For additional information and updates on this book, visit
w w w . a m s . o r g / b o o k p a g e s / g s m - 7 4
Library of Congress Cataloging-in-Publication Data
Prasolov, V. V. (Viktor Vasil'evich)
[Elementy kombinatornoi i differentsial'noi topologii. English]
Elements of combinatorial and differential topology / V. V. Prasolov ; [translated from the
Russian by Olga Sipacheva].
p. cm. — (Graduate studies in mathematics, ISSN 106^5-7339 ; v. 74)
Includes bibliographical references and index.
ISBN 0-8218-3809-1 (acid-free paper)
1. Combinatorial topology. 2. Differential topology. 3. Low-dimensional topology. 4. Topo-
logical manifolds. I. Title. II. Series.
Copying and reprinting. Individual readers of this publication, and nonprofit libraries
acting for them, are permitted to make fair use of the material, such as to copy a chapter for use
in teaching or research. Permission is granted to quote brief passages from this publication in
reviews, provided the customary acknowledgment of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this publication
is permitted only under license from the American Mathematical Society. Requests for such
permission should be addressed to the Acquisitions Department, American Mathematical Society,
201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by
e-mail to email@example.com.
© 2006 by the American Mathematical Society. All rights reserved.
The American Mathematical Society retains all rights
except those granted to the United States Government.
Printed in the United States of America.
@ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 11 10 09 08 07 06