Algebraic Topology - Homology and Homotopy

Robert Switzer

526 pages, parution le 05/02/2002

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Résumé

The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications. ... The author has sought to make his treatment complete and he has succeeded. The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. ... This book is, all in all, a very admirable work and a valuable addition to the literature...

This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book. ... (It is) suitable for specialists, or for those who already know what algebraic topology is for, and want a guide to the principal methods of stable homotopy theory.

Contents

Chapter 0 Some Facts from General Topology
Chapter 1 Categories, Functors and Natural Transformations
Chapter 2 Homotopy Sets and Groups
Chapter 3 Properties of the Homotopy Groups
Chapter 4 Fibrations
Chapter 5 CW-Complexes
Chapter 6 Homotopy Properties of CW-Complexes
Chapter 7 Homology and Cohomology Theories
Chapter 8 Spectra
Chapter 9 Representation Theorems
Chapter 10 Ordinary Homology Theory
Chapter 11 Vector Bundles and K-Theory
Chapter 12 Manifolds and Bordism
Chapter 13 Products
Chapter 14 Orientation and Duality
Chapter 15 Spectral Sequences
Chapter 16 Characteristic Classes
Chapter 17 Cohomology Operations and Homology Cooperations
Chapter 18 The Steenrod Algebra and its Dual
Chapter 19 The Adams Spectral Sequence and the e-Invariant
Chapter 20 Calculation of the Cobordism Groups
Bibliography
Subject Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Robert Switzer
Parution	05/02/2002
Nb. de pages	526
Format	15,5 x 23,5
Couverture	Broché
Poids	835g
Intérieur	Noir et Blanc
EAN13	9783540427506