On the Topology of Isolated Singularities in Analytic Spaces
The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singular
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Series Editors H. Bass J. Oesterlé A. Weinstein
José Seade Andrea Malchiodi
On the Topology of Isolated Singularities in Analytic Spaces
Birkhäuser Verlag Basel Boston Berlin
Author: José Seade Instituto de Matemáticas Unidad Cuernavaca Universidad Nacional Autónoma de México (UNAM) Av. Universidad s/n, col. Lomas de Chamilpa, Ciudad Universitaria C.P. 62210 Cuernavaca, Morelos México e-mail: [email protected]
2000 Mathematics Subject Classification Primary 14Bxx, 32Sxx, 53Cxx, 55A25, 57C45; Secondary 11Fxx, 32L30, 34Mxx, 37F75
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 3-7643-7322-9 Birkhäuser Verlag, Basel – Boston – Berlin 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, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained. © 2006 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ∞ Printed in Germany ISBN-10: 3-7643-7322-9 e-ISBN: 3-7643-7395-4 ISBN-13: 978-3-7643-7322-1 987654321
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To Swami Chidvilasananda and the Siddha lineage, whose light turned my life into a joyful path; and to Teresa, whose love is my everything.
Preface Singularity theory stands at a cross-road of mathematics, a meeting point where many areas of mathematics come together, such as geometry, topology and algebra, analysis, differential equations and dynamical systems, combinatorics and number theory, to mention some of them. Thus, one who would write a book about this fascinating topic necessarily faces the challenge of having to choose what to include and, most difficult, what not to include. A comprehensive treatment of singularities would have to consist of a collection of books, which would be beyond our present scope. Hence this work does not pretend to be comprehensive of the subject, neither is it a text book with a systematic approach to singularity theory as a core idea. This is rather a collection of essays on selected topics about the topology and geometry of real and complex analytic spaces around their isolated singularities. I have worked in the area of singularities since the late 1970s, and during this time have had the good fortune of encountering many gems of mathematics concerning the topology of singularities and related topics, masterpieces created by great mathematicians like Riemann, Klein and Poincar´e, then Milnor, Hirzebruch, Thom, Mumford, Brieskorn, Atiyah, Arnold, Wall, Lˆe D˜ ung Tr´ ang, Neumann, Looijenga, Teissier, and many more whose name
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