Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
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Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
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This review is from: Topological and Bivariant K-Theory (Oberwolfach Seminars) (Paperback)
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octahedral axiom, bornological algebras, bounded algebra homomorphisms, connections with index theory, isoradial subalgebra, mapping cone triangle, bornological analysis, fine bornology, bornological vector spaces, bounded linear section, homotopy invariance result, inner endomorphism, bornological isomorphism, bounded homomorphism, uniformly bounded representation, covariant pair, classifying map, smooth homotopy, exact triangles, thick subcategory, extension triangles, continuous homotopies, crossed products, smooth homotopies, morphism spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Thom Isomorphism Theorem, Takai Duality, K-theory Definition, Atiyah-Singer Index Theorem, Baum-Douglas-Taylor Index Theorem, Swan's Theorem, The Weyl, K-theory Proof, Some K-theory, Joachim Cuntz, Yoneda Lemma, Using Lemma Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
octahedral axiom, bornological algebras, bounded algebra homomorphisms, connections with index theory, isoradial subalgebra, mapping cone triangle, bornological analysis, fine bornology, bornological vector spaces, bounded linear section, homotopy invariance result, inner endomorphism, bornological isomorphism, bounded homomorphism, uniformly bounded representation, covariant pair, classifying map, smooth homotopy, exact triangles, thick subcategory, extension triangles, continuous homotopies, crossed products, smooth homotopies, morphism spaces Key Phrases - Capitalized Phrases (CAPs): (learn more)
Thom Isomorphism Theorem, Takai Duality, K-theory Definition, Atiyah-Singer Index Theorem, Baum-Douglas-Taylor Index Theorem, Swan's Theorem, The Weyl, K-theory Proof, Some K-theory, Joachim Cuntz, Yoneda Lemma, Using Lemma Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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