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OverviewThis 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. Full Product DetailsAuthor: Phillip Griffiths , John MorganPublisher: Birkhauser Boston Inc Imprint: Birkhauser Boston Inc Edition: 2nd ed. 2013 Volume: 16 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 3.693kg ISBN: 9781493936991ISBN 10: 1493936999 Pages: 227 Publication Date: 02 October 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 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.ReviewsFrom 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 Tanre, Mathematical Reviews, February, 2015) 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 Tanre, Mathematical Reviews, February, 2015) 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 Tanre, Mathematical Reviews, February, 2015) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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