Rational Homotopy Theory and Differential Forms

Phillip Griffiths, John Morgan (auth.)3764330414, 9783764330415

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.

Table of contents :
Front Matter….Pages i-xi
Introduction….Pages 1-3
Basic Concepts….Pages 5-20
CW Homology Theorem….Pages 21-25
The Whitehead Theorem and the Hurewicz Theorem….Pages 27-40
Spectral Sequence of a Fibration….Pages 41-52
Obstruction Theory….Pages 53-61
Eilenberg–MacLane Spaces, Cohomology, and Principal Fibrations….Pages 63-67
Postnikov Towers and Rational Homotopy Theory….Pages 69-81
deRham’s Theorem for Simplicial Complexes….Pages 83-93
Differential Graded Algebras….Pages 95-102
Homotopy Theory of DGAs….Pages 103-111
DGAs and Rational Homotopy Theory….Pages 113-118
The Fundamental Group….Pages 119-126
Examples and Computations….Pages 127-140
Functorality….Pages 141-149
The Hirsch Lemma….Pages 151-163
Quillen’s Work on Rational Homotopy Theory….Pages 165-176
A ∞ -Structures and C ∞ -Structures….Pages 177-185
Exercises….Pages 187-221
Back Matter….Pages 223-227