Algebraic Topology

Allen Hatcher

544 pages, parution le 07/02/2002

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Résumé

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

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Allen Hatcher
Parution	07/02/2002
Nb. de pages	544
Couverture	Broché
Poids	969g
Intérieur	Noir et Blanc
EAN13	9780521795401
ISBN13	978-0-521-79540-1