Rational Homotopy Theory and Differential Forms

2. Auflage 2013
ISBN: 978-1-4614-8467-7
Verlag: Springer

Buch, Englisch, Band 16, 227 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 4853 g

Reihe: Progress in Mathematics

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 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Morgan, John

Griffiths, Phillip

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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.

Über Autor(innen)

Phillip Griffiths is a professor at Princeton. John Morgan is a professor at Stony Brook University.