Rational Homotopy Theory and Differential Forms

AvPhillip Griffiths,John Morgan

Häftad, Engelska, 2013

Del 16 i serien Progress in Mathematics

1 483 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Inbunden

1 483 kr

Beskrivning

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.

Produktinformation

Utgivningsdatum:2013-10-02
Mått:155 x 235 x 14 mm
Vikt:371 g
Format:Häftad
Språk:Engelska
Serie:Progress in Mathematics
Antal sidor:227
Upplaga:2
Förlag:Birkhauser Boston Inc
ISBN:9781493936991

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Recensioner i media

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)

Innehållsförteckning

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.