This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Innehållsförteckning
Part I: Foundations and Computations: Deloopings in Algebraic K- theory.- The Motivic Spectral Sequence.- K-theory of truncated polynomial algebras.- Bott Periodicity in Topological, Algebraic and Hermitian K-theory.- Algebraic K-theory of Rings and Integers in Local and Global Fields.
Part II: K-theory and Algebraic Geometry: Motivic Cohomology, K-theory and topological cyclic Homology.- K-theory and Intersection Theory.- Regulators.- Algebraic K-theory, Algebraic Cycles and Arithmetic Geometry.- Mixed Motives.
Part III: K-theory and Geometric Topology: Witt Groups.- K-theory and Geometric Topology.- Quadratic K-theory and Geometric Topology.
Part IV: K-theory and Operator Algebras: Bivariant K-and Cyclic Theories.- The Baum-Connes and the Farrell-Jones Conjectures in K-and L-theory.- Comparison Between Algebraic and Topological K-theory for Banach Algebras and C*-Algebras.
Part V: Other Forms of K-theory: Semi-topological K-theory.- Equivariant K-theory.- K(1)-local Homotopy Theory, Iwasawa Theory and Algebraic K-theory.- The K-theory of Triangulated Categories.
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