Proceedings of Liverpool Singularities Symposium II
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209 Proceedings of Liverpool Si ng ularities Symposium II
Edited by C. T. C. Wall, University of Liverpool, Liverpool/G. B.
Springer-Verlag Berlin' Heidelberg· New York 1971
AMS Subjekt Classifications (1970): 14D05, 14E 15, 26A54, 32B 10,53 C 10, 53C45, 53C65, 57D30, 57D40, 57D45, 57D50, 57D70, 57D95, 58A 10, 58A30, 34C20, 53A05, 53B25, 58C25, 81A 15, 83C99
ISBN 3-540-{)5511-8 Springer-Verlag Berlin . Heidelberg . New York ISBN 0-387-{)5511-g Springer-Verlag New York· Heidelberg· Berlin This work is subject to copyright. All rights are reserved, w hetber 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 data banks.
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Under § 54 of the German Copyright Law where copies are made for otber tban private use, a fee is payahle to tbe publisher, the amollnt of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin' Heidelberg 1971. Library of Co ogress Catalog Card Number 72-154306. Printed in Germany. Offsetdruck: Julius Beltz, Hemsbacb/Bergstr.
Introduction
The papers in this volume and its predecessor were submitted by participants the Symposium on Singularities o~ smooth mani~olds and maps, held at the Department o~ Pure Mathematics at the University o~ Liverpool ~rom September 1969 - August 1970, and supported by the Science Research Council. They include also the texts of the courses o~ lectures given at a Summer School held in July 1970 in connection the the Symposium. I have added some further notes to bring out the relations of the d~~erent papers in an attempt to make this volume as complete an exposition of the present state o~ knowledge in the subject as is possible within its scope. For this reason also we have reprinted the classic notes by Levine o~ lectures by Thom, which had become unavailable, and which represent the source o~ many of the ideas ~urther developed in these papers. o~
Volume 1 oontains the papers closely related to the problem o~ classification singularities o~ smooth maps and is thus fairly coherent. Volume 2 represents applications of these ideas (and others) to other branches of pure and applied mathematics, arranged in order of subject. The lack o~ coherence is perhaps compensated by the wealth o~ unsolved problems which are raised in these pages. o~
Thanks are due to the S.R.C. for financial support; to Mrs. Evelyn Quayle (nee Hastwell) and 1~s. Eileen Bratt for doing the typing; to members o~ the department ~or proo~reading it; and o~ course to the participants in the Symposium for oreating the body o~ mathematics here presented.
Liverpool, March 1971
CONTENTS
G. Glaeser,
L'Interpolation des Fonctions Differentiables de Plusieurs Variables ••••••••.••••.••• •••••. .•. .•• .••••••.•••••.. ••••.••••
Normal Forms for Analytic 1mtrix Valued S.A. Khabbaz and G. Stengle,
1
F~nctions
S.A. Khabbaz,
Geometric Aspects of the Singular Solutions of Certain Diff'erential Equations , ••• , •• ,
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