Algebraic Topology Rational Homotopy Proceedings of a Conference hel
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moore con
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1318 Y. Felix
(Ed.)
Algebraic Topology Rational Homotopy Proceedings of a Conference held in Louvain-Ia-Neuve, Belgium, May 2-6, 1986
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editor
Yves Felix Universite Catholique de Louvain lnstitut de Mathernatique Pure et Appliquee 2, chemin du Cyclotron, 1348 Louvain-Ia-Neuve, Belgium
Mathematics Subject Classification (1980): 16A24, 17B56, 17B70, 55M30, 55P15, 55P35, 55P50, 55P62, 55R35, 55S 10 ISBN 3-540-19340-5 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-19340-5 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Printed in Germany
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INTRODUCTION
These notes contain the outcome and later developments arising from an algebraic topology meeting held in Louvain-IaNeuve, May 2-6, 1986. The purpose of the meeting was to discuss and promote new developments in algebra and algebraic topology in relation with rational homotopy. The text contains several survey papers (Anick, "Poincare series" ; Scheerer "Tame homotopy" ; Selick, "The Moore conjectures" ). The meeting was made possible by the generous financial support of the Fonds National de la Recherche Scientifique. Further support was provided by the Commissariat general aux relations internationales et le service de la recherche scientifique de la communaute francaise de Belgique. I would like to thank these institutions for their help. I wish to thank all the participants for their interest in this meeting. I also wish to give special thanks to J .C. Thomas who helped me very much before, during and after the conference.
Y.FELIX
TABLEOF CONlENTS
D. ANICK, Recent progress in Hilbert and Poincare series. M. AUBRY and J.M. LEMAIRE, Homotopie d'algebres de Lie et de leurs algebres enveloppantes. H. BAUES, Combinatorial homotopy. D. BURGHELEA and M. VIGUE-POIRRIER, Cyclic homology of commutative algebras I. B. CENKL and R. PORTER, Cohomology of nilmanifolds. J. DUPONT, A dual simplicial de Rham complex. W. DWYER and C. WILKERSON, Maps of B Z/pZ to BG. Y. FELIX and D. TANRE, Formalite d'une application et suite spectrale d'Eilenberg-Moore. Y. FELIX and J.C. THOMAS, An Euler-Poincare characteristic for l-connected spaces with noetherian rational cohomology. S. HALPERIN and J.M. LEMAIRE, Notions of category in differential algebra. J. LESCOT, Series de Poincare des modules multi-gradues sur les anneaux monomiaux. A. OUADGH
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