Homotopy Theory and Models: Based on Lectures held at a DMV Seminar in Blaubeuren by H.J. Baues, S. Halperin and J.-M. Lemaire: 24 (Oberwolfach Seminars, 24) - Softcover

Aubry, Marc

Softcover

ISBN 10: 3764351853 ISBN 13: 9783764351854

Publisher: Birkhäuser, 1995

Synopsis

In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi­ pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec­ tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW­ complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].

About this title

Synopsis

This text is based on notes taken by the author at the DMV Seminar on Algebraic Models of Homotopy Types. The work aims to provide an overview of homotopy theory from the point of view of algebraic models of homotopy types, leading the reader from basic definitions in algebraic topology to specific fields of research. The exposition is addressed towards graduate students as well as to researchers from other fields. Due to the scope and size of the book, only a few complete proofs can be given; however, the fundamental concepts and methods of the subject are pointed out, and a number of recent results are included together with the essential bibliographic references. The book begins with a recollection of the basic notions of homotopy theory. A discussion of rational homotopy theory, emphasizing both the Sullivan and the Quillen models, follows. Next, the Adams-Hilton and the Anick models are shown to yield some integral information. The last chapter provides an introduction to the integral classification of homotopy types, along the lines initiated by J.H.C. Whitehead and considerably developed by H. Baues during the last decade.

Edition details

• Publisher: Birkhäuser
• Publication date: 1995
• Language: English
• ISBN 10: 3764351853
• ISBN 13: 9783764351854
• Binding: Paperback
• Number of pages: 117