Rational Homotopy Theory and Differential Forms
Reduzierte Artikel in dieser Kategorie
0,99 €
| Verlag | Springer |
| Auflage | 2013 |
| Seiten | 227 |
| Format | 15,9 x 23,8 x 1,9 cm |
| Gewicht | 512 g |
| Artikeltyp | Englisches Buch |
| Reihe | Progress in Mathematics 16 |
| EAN | 9781461484677 |
| Bestell-Nr | 46148467UA |
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 topo logy, differential forms, and homotopy theory.
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.
Rezension:
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)