Cyclic Homology
From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent res
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Editors
S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin 1. Hormander M.-A. Knus A. Kupiainen J. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N. J. A. Sloane J.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger J. Coates S.R.S. Varadhan
301
Springer-Verlag Berlin Heidelberg GmbH
Jean -Louis Loday
Cyclic Homology Second Edition With 24 Figures
Springer
Jean-Louis Loday Institut de Recherche Mathematique Avancee Centre National de la Recherche Scientifique 7, rue Rene Descartes F-67084 Strasbourg, France
Library of Congress Cataloging-in-Publication Data Loday, Jean-Louis. Cyclic homology I Jean-Louis Loday. - znd ed. p. cm. - (Grundlehren der mathematischen Wissenschaften; 301) Includes bibliographical references and index. ISBN 978-3-642-08316-7 ISBN 978-3-662-11389-9 (eBook) DOI 10.1007/978-3-662-11389-9 1. Homology theory. I. Tide. II. Series. QA61Z.3.L63 1998 51Z' .55-dc21 97-22418 CIP
Mathematics Subject Classification (1991): Primary:
14Fxx, 16E40, 17B56, 18F25, 18Gxx, 19-xx, 46Lxx, 55-xx Secondary: 05A19, 16E30, 16R30, 16Wxx, 17D99, 20B30, 57R20, 58B30 ISSN 0072-7830 ISBN 978-3-642-08316-7
This work is subject to copyright. AU rights are reserved, whether the whole or part ofthe material is concerned, specificaUy the rights oftranslation, reprinting, reuse of illustrations, re citation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current vers ion, and permis sion for use must always be obtained from Springer-Verlag Berlin Heidelherg GmhH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1992, 1998 OriginaUy published by Springer-Verlag Berlin Heidelberg New York in 1998 Cover design: MetaDesign plus GmbH, Berlin Data conversion: Satztechnik K. Steingraeber, Heidelberg, Germany, using a Springer TEX macro-package 41/3III-S 4 3 2 Printed on acid-free paper SPIN: 1I7686S4
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Preface to the Second Edition
Apart from correction of misprints, inaccuracies and errors, the main difference between the second edition and the first is the addition of a new chapter on Mac Lane (co)homology, written jointly with Teimuraz Pirashvili. It is related to Hochschild homology, to algebraic K-theory and cohomology of small categories as treated in the previous chapters (see the introduction to Chapter 13). Appendix C has been modified accordingly. The first list of references was reasonably up to date for papers dealing with cyclic homology until 1992. It contains all the references mentioned in Chapters 1 to 12 and in the appendices. Chapter 13 has its own list of references. Since the publication of the first edition numerous results on the cyclic theory have appeared, namely about the periodic theory,
