Rational Homotopy Theory and Differential Forms

• Main Authors: Griffiths, Phillip. (Author), Morgan, John. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhũser, 2013.
• Edition: 2nd ed. 2013.
• Series: Progress in Mathematics, 16
• Subjects: Mathematics.; Algebra.; Topology.; Algebraic topology.; Algebraic Topology.; Category Theory, Homological Algebra.; Commutative Rings and Algebras.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-8468-4

<U+001c>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 sa...

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.