Manifolds and Modular Forms
During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, St
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Friedrich Hirzebruch · Thomas Berger Rainer Jung
Manifolds and Modular Forms A Publication of the Max-Planck-Institut für Mathematik, Bonn Second Edition
Friedrich Hirzebruch Thomas Berger Rainer jung
Manifolds and Modular Forms
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Edited by Klas Diederich Vol. E 2:
M. Knebusch/M. Kolster: Wittrings
Vol. E 3:
G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part B
Vol. E 5:
P. Stiller: Automorphic Forms and the Picard Number of an Elliptic Surface
Vol. E 6:
G. Faltings/G. Wustholz et al.: Rational Points*
Vol. E 7:
W. Stoll: Value Distribution Theory for Meromorphic Maps
Vol. E 9:
A Howard/P.-M. Wong (Eds.): Contribution to Several Complex Variables
Vol. E 10: A J. Tromba (Ed.): Seminar of New Results in Nonlinear Partial Differential Equations* Vol. E 13: Y. Andre: G-Functions and Geometry* Vol. E 14: U. Cegrell: Capacities in Complex Analysis Vol. E 15: J.-P. Serre: lectures on the Mordeii-Weil Theorem Vol. E 16: K. lwasaki/H. Kimura/S. Shimomura/M. Yoshida: From Gauss to Painleve Vol. E 17: K. Diederich (Ed.): Complex Analysis Vol. E 18: W. W. J. Hulsbergen: Conjectures in Arithmetic Algebraic Geometry Vol. E 19: R. Rocke: lectures on Nonlinear Evolution Equations Vol. E 20:
F. Hirzebruch, Th. Berger, R. Jung: Manifolds and Modular Forms*
Vol. E 21:
H. Fujimoto: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
Vol. E 22: D. V. Anosov/A A Bolibruch: The Riemann-Hilbert Problem Vol. E 23: A P. Fordy/J. C. Wood (Eds.): Harmonic Maps and Integrable Systems Vol. E 24: D. S. Alexander: A History of Complex Dynamics Vol. E 25: A Tikhomirov/A Tyurin (Eds.): Algebraic Geometry and its Applications
*A Publication of the Max·Pianck·lnstitut fur Mathematik, Bonn Volumes of the German-language subseries "Aspekte der Mathematik" ore listed at the end of the book.
Friedrich Hirzebruch Thomas Berger Rainer jung
Manifolds and Modular Forms Translated by PeterS. Landweber A Publication from the Max-Pianck-lnstitut fur Mathematik, Bonn
Second Edition
II VJeweg
Professor Dr. Friedrich Hirzebruch, Thomas Berger, and Rainer Jung Max-Planck-Institut ftir Mathematik Gottfried-Claren-Str. 26 53225 Bonn Germany
First Edition 1992 Second Edition 1994
Appendix III: Elliptic genera of level N for complex manifolds reprinted with permission of Kluwer Academic Publishers Mathematics Subject Classification: 57-02, llFll, 33C45, 33E05, 55N22, 55R10, 57R20, 58G10 Ali rights reserved © Springer Fachmedien Wiesbaden 1994 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, in 1994
No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder.
Cover design: Wolfgang Nieger, Wiesbaden Typeset using ArborText Publisher and TEX
ISSN 0179-2156 ISBN 978-3-528-16414-0 ISBN 978-3-663-10726-2 (eBook) DOI 10.1007/978-3-663-10726-2
Preface During the winter term 1987/88 I gave a course at the University of Bo
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