Analytic and Geometric Study of Stratified Spaces
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Markus J. Pflaum
Analytic and Geometric Study of Stratified Spaces
123
Author Markus J. Pflaum Department of Mathematics Humboldt University Rudower Chaussee 25 10099 Berlin, Germany E-mail: [email protected]
Cataloging-in-Publication Data applied for
Mathematics Subject Classification (2000): 58Axx, 32S60, 35S35, 16E40, 14B05, 13D03 ISSN 0075-8434 ISBN 3-540-42626-4 Springer-Verlag Berlin Heidelberg New York 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 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 version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10852611
41/3142-543210/du - Printed on acid-free paper
For
Stephanie and
Konstantin
Contents
1
Introduction
11
Notation 1
2
1.1
Spaces and Functional Structures Decomposed spaces
1.2
Stratifications
1.3
Smooth Structures
1.4
Local
1.5
The, sheaf of
1.6
Rectifiable
1.7
Extension
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and the
Triviality Whitney
conditions
Whitney
functions
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theory for
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63
on
regular
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Singular Spaces Whitney's condition (A)
Metrics and
2.5
Differential operators
2.6
Poisson structures
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space structures
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