Rational Homotopy Theory and Differential Forms

• Main Authors: Griffiths, Phillip (Author), Morgan, John (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2013.
• Edition: 2nd ed. 2013.
• Series: Progress in Mathematics, 16
• Subjects: Mathematics.; Algebra.; Category theory (Mathematics).; Homological algebra.; Commutative algebra.; Commutative rings.; Topology.; Algebraic topology.; Algebraic Topology.; Category Theory, Homological Algebra.; Commutative Rings and Algebras.

“Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now… The appearance of the text in book form is highly welcome, since it will satisfy the need of...

Table of Contents:

• 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 A1-structures and C1-structures
• 19 Exercises.