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Algebraic Topology - Homology and Homotopy
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Algebraic Topology - Homology and Homotopy

Algebraic Topology - Homology and Homotopy

Robert Switzer

526 pages, parution le 05/02/2002

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

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