"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."--Book cover

lgli/dvd43/Kono A., Tamaki D. - Generalized Cohomology(2006)(272).djvu

nexusstc/Generalized Cohomology/e9435c6016099edbb7433bda74f4da7d.djvu

Ippan kohomorojī

Akira Kono and Dai Tamaki; translated by Dai Tamaki

Akira Kōno; Dai Tamaki

Akira Kåono

Education Development Center, Incorporated

Translations of mathematical monographs, 0065-9282 -- v. 230, Iwanami series in modern mathematics, Providence, R.I, Rhode Island, 2006

Translations of mathematical monographs, v. 230, English ed, Providence, R.I, ©2006

American Mathematical Society, [N.p.], 2018

United States, United States of America

mexmat -- 43

lg56838

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Includes bibliographical references (p. 241-249) and index.

Includes bibliographical references and index.

Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This work starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. It focuses on spectral sequences and their use in generalized cohomology theories.

2009-07-20