Topological Stability of Smooth Mappings
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552 C. G. Gibson K. WirthmUller AA du Plessis E. J. N. Looijenga
Topological Stability of Smooth Mappings
,£,
Springer-Verlag Berlin' Heidelberg' NewYork 1976
Authors Christopher G. Gibson Department of Pure Mathematics University of Liverpool P. O. Box 147 Liverpool, L69 3BXlGreat Britain Klaus Wirthmuller Fachbereich Mathematik d. Universitat Postfach 397 8400 Regensburg/BRD Andrew A. du Plessis School of Mathematics and Computer Science University College of North Wales Bangor Gwynedd, LL57 2 UW, Wales/Great Britain Eduard J. N. Looijenga Mathematisch Instituut der Katholieke Universiteit Toernooiveld Nijmegen/The Netherlands
AMS Subject Classifications (1970): 57D45, 58C25 ISBN 3-540-07997-1 Springer-Verlag Berlin' Heidelberg· New York ISBN 0-387-07997-1 Springer-Verlag New York· Heidelberg' Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
Prefaoe During the aoademic year 1974 - 75 the Department of Pure Mathema tic s in the University of Liverpool held a seminar on the Topological Stability of Smooth Mappings:
the main objective was to piece together a oomplete proof of the
Topological Stability Theorem (conjectured already by Thorn in 1960, and proved by Mather ar-ound 1970) for which no published account existed.
This volume oomprises
a write-up of the seminar by four of its participants. There are several aoknowledgements which should be made.
mathematioian
working in this area is conscious of his debt to the inventiveness of Thom, and to the technical work of Mather which has plaoed much that was conjecture on a firm mathematical foWldation.
As far as the seminar is concerned I would like to
single out the special contribution of Eduard Looijenga, who showed us how to fill in gaps which otherwise might have remained open.
Also, I would like to
acknowledge the considerable help offered by Terry Wall, from the inception of the seminar to the production of the typescript.
Further acknowledgements are due
to the seminar audience (who frequently had good reason to appear confused) for their patience and in particular to Tim Ward who helped out with the talks;
to
the British Scientific Research Council who provided financial support for Eduard Looijenga, and the University of Wales whose financial assistance enabled Andrew du Plessis to participate in the seminar;
to Les Lander who was inveigled
into drawing the diagrams, and did an excellent job;
to Dirk Siersma and
Klaus Lamotke whose careful reading of parts of the manuscript removed
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