Title: Homotopy theory and models
Description: This book is based upon notes taken by the author at the DMV Seminar on Algebraic Models of Homotopy Types led by H.J. Baues, S. Halperin and J.-M. Lemaire in 1988. The notes have been substantially reorganized and expanded for this publication and now include some additional important proofs. The aim of the work is to provide an overview of homotopy theory from the point of view of algebraic models of homotopy types, leading the reader from the basic definitions in algebraic topology to specific fields of research. The exposition is directed towards graduate students as well as researchers from other fields. Due to the scope and size of this book, only a few complete proofs could be given. But 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 text begins with a review of the basic notions of homotopy theory. An extensive 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 gives 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.
Subjects: Homotopy theory, Mathematics, Algebraic topology