Rational Homotopy Theory and Differential Forms, 2nd Edition

  • Published By:
  • ISBN-10: 1461484685
  • ISBN-13: 9781461484684
  • DDC: 514.24
  • Grade Level Range: College Freshman - College Senior
  • 227 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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 theoryWith 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 Cover.
Other Frontmatter.
Other Frontmatter.
Title Page.
Copyright Page.
Preface to the First Edition.
Preface to the Second Edition.
1: Introduction.
2: Basic Concepts.
3: CW Homology Theorem.
4: The Whitehead Theorem and the Hurewicz Theorem.
5: Spectral Sequence of a Fibration.
6: Obstruction Theory.
7: Eilenberg–MacLane Spaces, Cohomology, and Principal Fibrations.
8: Postnikov Towers and Rational Homotopy Theory.
9: deRham's Theorem for Simplicial Complexes.
10: Differential Graded Algebras.
11: Homotopy Theory of DGAs.
12: DGAs and Rational Homotopy Theory.
13: The Fundamental Group.
14: Examples and Computations.
15: Functorality.
16: The Hirsch Lemma.
17: Quillen's Work on Rational Homotopy Theory.
18: A∞-Structures and C∞-Structures.
19: Exercises.
20: References.
Other Backmatter.
Other Backmatter.