In most major universities one of the three or four basic firstyear graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

Contents

Preface

Ch. 1 The Fundamental Group

1.1 Basic Constructions
1.2 Van Kampen's Theorem
1.3 Covering Spaces

Ch. 2 Homology

2.1 Simplicial and Singular Homology
2.2 Computations and Applications
2.3 The Formal Viewpoint

Ch. 3 Cohomology

3.1 Cohomology Groups
3.2 Cup Product
3.3 Poincare Duality

Ch. 4 Homotopy Theory

4.1 Homotopy Groups
4.2 Elementary Methods of Calculation
4.3 Connections with Cohomology

Appendix

Bibliography

Index

Type produit : Ouvrage Langue : Anglais   Editeur(s) : Cambridge University Press Auteur(s) : Allen Hatcher   ISBN13 : 978-0-521-79540-1 EAN13 : 9780521795401 ISBN10 : 0-521-79540-0

Parution : 07/02/2002 Edition : 1ère édition   Nb de pages : 544 pages Couverture : Broché Poids : 969 g Intérieur : Noir et Blanc