Rational Homotopy Theory and Differential Forms
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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)
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Content
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 1 -structures and C 1 -structures.- 19 Exercises.
