Groups of Self-Equivalences and Related Topics Proceedings of a Conf
Since the subject of Groups of Self-Equivalences was first discussed in 1958 in a paper of Barcuss and Barratt, a good deal of progress has been achieved. This is reviewed in this volume, first by a long survey article and a presentation of 17 open proble
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1425 R.A. Piccinini (Ed.)
Groups of Self-Equivalences and Related Topics Proceedings of a Conference held in Montreal, Canada, Aug. 8-12, 1988
Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong
Editor
Renzo A. Piccinini Department of Mathematics and Statistics Memorial University of Newfoundland St. John's, Newfoundland, Canada A 1C 5S7
Mathematics Subject Classification (1980): 55P10, 55P50, 55R05, 55R20, 57MlO,57N10 ISBN 3-540-52658-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-52658-7 Springer-Verlag New York Berlin Heidelberg
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FOREWORD During the week of August 8, 1988, a conference on spaces of self-homotopy equivalences and related topics was held at the Centre de Recherches Mathematiques, Universit.e de Montreal, in Montreal, Canada. The conference was attended by some 30 mathematicians from Canada, Denmark, England, France, Germany, Japan and the United States. This volume contains the Proceedings thereof, covering most of the talks presented at the Centre. It also contains two specially written articles (a survey on groups of self-equivalences and a paper presenting seventeen open problems). The volume is completed by a list of papers on groups of selfequivalences and related areas. The conference was made possible thanks to a most generous contribution from the Centre des Recherches Mathematiques; their superb organization and most helpful staff were also a key point in the success of the conference. The organizers wish to take this opportunity to thank, both for themselves and also in the name of the participants, the Director of the Centre, Prof. Frank Clarke, and his staff, for their most gracious hospitality. Each paper in this volume was carefully refereed and sincere thanks are due to all those who helped in this. While the referees must, of course, remain unknown to the public, those who helped me on the technical side can be thanked and named; they are: Edgar Goodaire, Bruce Shawyer and Kathleen Stewart.
Renzo A.Piccinini
Contents Research Papers P. Booth: Equivalent Homotopy Theories and Groups of Self Equivalences 1 P. Booth and P. Heath: On the Groups C(X X Y) and cB(X XB Y) 17 G. Didierjean: Homotopie des Espaces d'Equivalences . 32 V. Hansen: The Space of Self Maps on the 2-sphere . 40 A. Hatcher and D. McCullough: Finite Presen
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