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Algebraic Topology

Librairie Eyrolles - Paris 5e
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Algebraic Topology

Algebraic Topology

544 pages, parution le 07/02/2002

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 du livre "Algebraic Topology"

  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
Sélection de Noël

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