Seminar On Fiber Spaces

Lecture Notes in Mathematics An informal series of special lectures, seminars and reports on mathematical topics Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich 13 Emery Thomas University of California, Berkeley Forschungsinstitut for Mathematik, ETH, Z0rich Seminar on Fiber Spaces Lectures delivered in 1964 in Berkeley and 1965 in Z~irich Berkeley notes by J. F. Mc Clendon 1966 I~'iI, Springer-Verlag. Berlin. Heidelberg. New York Research supported in part by the U. S. Air Force Office of Scientific Research. All rights, especl~dlythat os transhtton into foreign ta.nguages, reserved. It is also forbidden to reproduce this book, either whole or in part, by photomechanic~d means (photostat, microfilm and/or microcard)or by other procedure without written permission from Springer Verlag. 9 by Springer-Verlag Berlin Heidelberg 1966. Library of Congress CatLlog Card Nurnbe~ 66--19122. Printed in Germany. Title No. 7333. Foreword These notes are divided into seven sections. the first five was given as a series of informal B e r k e l e y in the Summer of 1964. The material discussed in Professor Eckmann's The material lectures in at in the last two was seminar in Zurich during the Spring of 1965. Mr. J.F. Mc Clendon took m y lecture notes lectures and wrote them up in a p r e s e n t a b l e the formulation of Theorem 5 in section from the B e r k e l e y form. In p a r t i c u l a r five is due to him. The first five lectures develop the theory of the P o s t n i k o v resolution of a map. paper In particular [3] are covered. example - the universal V n,2" the m a i n results of M a h o w a l d ' s Section six applies the t h e o r y to a specific fibration