Rational Homotopy Theory and Differential Forms

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. 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. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.  

New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch lemma

*Presentation of a natural proof of a Serre spectral sequence result

*Updated content throughout the book, reflecting advances in the area of homotopy theory

With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

• Brouwer's theorem
• algebraic topology
• cohomology
• differential forms
• homotopy
• obstruction theory
• rational homotopy theory
• the Serre spectral sequence

From the book reviews:

“This book is a second, augmented version of one of the famous books on rational homotopy. … The topological intuition throughout the book, the recollections of the necessary elementary homotopy theory and the list of exercises make this book an excellent introduction to Sullivan’s theory. … this book is highly recommended to anyone who wants to understand Sullivan’s theory of rational homotopy theory.” (Daniel Tanré, Mathematical Reviews, February, 2015)

• School of Mathematics, Princeton University Institute for Advanced Study, Princeton, USA

  Phillip Griffiths

• Simons Center for Geometry and Physics, Stonybrook University, Stonybrook, USA

  John Morgan

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