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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.
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Book Description American Mathematical Society, 2006. Paperback. Condition: New. Seller Inventory # DADAX0821835149
Book Description Amer Mathematical Society, 2006. Condition: New. book. Seller Inventory # M0821835149
Book Description Amer Mathematical Society, 2006. Paperback. Condition: Brand New. illustrated edition. 256 pages. 8.50x5.50x0.50 inches. In Stock. Seller Inventory # 0821835149
Book Description American Mathematical Society, 2006. Paperback. Condition: New. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. Buy with confidence, excellent customer service!. Seller Inventory # 0821835149n