Hyperbolic Manifolds and Discrete Groups
This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization
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Hyperbolic Manifolds and Discrete Groups
Michael Kapovich
Reprint of the 2001Edition Birkh¨auser Boston • Basel • Berlin
Michael Kapovich Department of Mathematics University of California, Davis 1 Shields Ave. Davis, CA 95616-8633 U.S.A. [email protected]
Originally published in the Progress in Mathematics Series
ISBN 978-0-8176-3904-4 (hardcover) ISBN 978-0-8176-4912-8 (softcover) DOI 10.1007/978-0-8176-4913-5
e-ISBN 978-0-8176-4913-5
Library of Congress Control Number: 2009926317 Mathematics Subject Classification (2000): Primary: 30F40, 57M50; Secondary: 22E40, 53C20 c Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2001, First softcover printing 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkha¨user Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY, 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Printed on acid-free paper
Birkhäuser Boston is part of Springer Science+Business Media (www.birkhäuser.com)
Michael Kapovich
Hyperbolic Manifolds and Discrete Groups
Birkhauser Boston • Basel • Berlin
Michael Kapovich Department of Mathematics University of Utah Salt Lake City, UT 84109 U.S.A
Ubrary of Congress Cataloging-in-Publication Data Kapovich, Michael, 1963Hyperbolic manifolds and discrete groups I Michael Kapovich. p. em.- (Progress in mathematics; v. 183) Includes bibliographical references and index. ISBN 0-8176-3904-7- ISBN 3-7643-3904-7 1. Hyperbolic spaces. 2. Discrete groups. I. Title. II. Progress in mathematics (Boston, Mass.); vol. 183. QA685.K36 2000 516.9--{jc21
00-044529 CIP
AMS Subject Classifications: Primary: 30F40, 57M50; Secondary : 22£40, 53C20
Printed on acid-free paper ©2001 Birkhauser Boston
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All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser Boston, c/o Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, m
