Aus den Besprechungen: "Although this volume appears as a set of "Lecture Notes", in fact it is a rather polished and complete text on homotopy theory, from the viewpoint of offering a very careful examination of the foundations.

Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs.

Homotopy Theory

The book will be of interest to researchers in rational homotopy theory and will provide them with new ideas and lines of research to develop further.

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.

The text pays particular attention to low-dimensional cases and trouble with the small primes. The book gives a complete treatment of some topics--such as Samelson products--with a view toward applications.

Readers will find within these pages a compilation of articles describing current research in the area, including classical stable and unstable homotopy theory, configuration spaces, group cohomology, K-theory, localization, p-compact ...

Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes.

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.