Homotopy Theory and Models

1. Front Matter

   Pages i-ix

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2. Basic Homotopy Theory

   • Marc Aubry

   Pages 1-13

3. Homology and Homotopy Decomposition of Simply Connected Spaces

   • Marc Aubry

   Pages 14-32

4. Cofibration Categories

   • Marc Aubry

   Pages 33-44

5. Algebraic Examples of Cofibration Categories

   • Marc Aubry

   Pages 45-60

6. The Rational Homotopy Category of Simply Connected Spaces

   • Marc Aubry

   Pages 61-77

7. Attaching Cells in Topology and Algebra

   • Marc Aubry

   Pages 78-84

8. Elliptic Spaces

   • Marc Aubry

   Pages 85-93

9. Non Elliptic Finite C.W.-Complexes

   • Marc Aubry

   Pages 94-103

10. Towards Integral Algebraic Models of Homotopy Types

    • Marc Aubry

    Pages 104-110

11. Back Matter

    Pages 111-118

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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].

• Algebraic models
• Algebraic topology
• Homotopy
• cofibration
• fibrations
• homology
• homotopy theory

• Laboratoire de Mathématiques Faculté des Sciences, Université de Nice, Nice Cedex 2, France

  Marc Aubry

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