Quantization of Singular Symplectic Quotients
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Series Editors H. Bass J. Oesterle A. Weinstein
Quantization
of Singular Symplectic Quotients
N. P. Landsman M. Pt1aum M. Schlichenmaier Editors
Springer Basel AG
Editors: N.P. Landsman Universiteit van Amsterdam Korteweg-de Vries Instituut voor Wiskunde Plantage Muidergracht 24 10 18 TV Amsterdam The Netherlands e-mail: [email protected] M. Schlichenmaier Universităt Mannheim Fakultăt fUr Mathematik und Informatik D7,27 68131 Mannheim Germany
M. Ptlaum Humboldt-Universităt zu Berlin Mathematisch-Naturwissenschaftliche Fakultăt II Institut fUr Mathematik Unter den Linden 6 10099 Berlin Germany
e-mail: [email protected]
e-mail: [email protected]
2000 Mathematics Subject Classification 53D20, 53D30, 81S1O, 35S35, 58A35
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Quantization of singular symplectic quotients / N. P. Landsman ... ed .. - Basel ; Boston; Berlin: Birkhăuser,2001
(Progress in mathematics ; VoI. 198) ISBN 978-3-0348-9535-4 ISBN 978-3-0348-8364-1 (eBook) DOI 10.1007/978-3-0348-8364-1
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind ofuse whatsoever, permission from the copyright owner must be obtained.
© 2001 Springer Basel AG Originally published by Birkhăuser Verlag in 2001 Softcover reprint ofthe hardcover Ist edition 2001 Printed on acid-free paper produced of chlorine-free pulp. TCF
00
ISBN 978-3-0348-9535-4 987654321
www.birkhauser-science.ch
Contents Preface ...................................................................
vii
J. E. Marsden and A. Weinstein Some comments on the history, theory, and applications of symplectic reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
M.- T. Benameur and V. Nistor Homology of complete symbols and non-commutative geometry
21
M. Braverman Cohomology of the Mumford quotient................................
47
A. Cattaneo and G. Felder Poisson sigma models and symplectic groupoids ......................
61
B. Fedosov Pseudo-differential operators and deformation quantization. . . . ... . . . .
95
J. Huebschmann Singularities and Poisson geometry of certain representation spaces ................................................
119
N.P. Landsman Quantized reduction as a tensor product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 R. Lauter and V. Nistor Analysis of geometric operator on open manifolds: a groupoid approach .................................................
181
M. Pflaum Smooth structures on stratified spaces.... ... . .. . . . ... . .. . ... . . .. .. . ..
231
M. Schlichenmaier Singular projective varieties and quantization ........................
259
V. Schomeru
