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Generalized Cohomology
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Generalized Cohomology

Generalized Cohomology

Akira Kono, Dai Tamaki - Collection Iwanami Series in Modern Mathematics

272 pages, parution le 20/08/2006

Résumé

In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all except the condition on the "homology" of the point), one can obtain many other interesting systems of algebraic invariants of topological manifolds, such as $K$-theory, cobordisms, and others. These theories come under the common name of generalized homology (or cohomology) theories.

The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. Then the authors discuss various types of generalized cohomology theories, such as complex-oriented cohomology theories and Chern classes, K-theory, complex cobordisms, and formal group laws. A separate chapter is devoted to spectral sequences and their use in generalized cohomology theories.

The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced knowledge of algebraic topology. Prerequisites include standard graduate courses in algebra and topology, with some knowledge of ordinary homology theory and homotopy theory.

Sommaire

  • Preliminaries
  • Generalized Cohomology
  • Characteristic Classes of Vector Bundles
  • K-theory
  • The Spectral Sequence
  • Complex Cobordism and its Applications
  • Simplicial Techniques
  • Limits
  • Spectrum
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Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Akira Kono, Dai Tamaki
Collection Iwanami Series in Modern Mathematics
Parution 20/08/2006
Nb. de pages 272
Format 14 x 21,5
Couverture Broché
Poids 320g
Intérieur Noir et Blanc
EAN13 9780821835142
ISBN13 978-0-8218-3514-2

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