Topics in Algebraic and Topological K-Theory (Lecture Notes in Mathematics Book 2008)

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories. Front Matter....Pages i-xvi K -Theory for Group C ∗-algebras....Pages 1-43 Universal Coefficient Theorems and Assembly Maps in KK-Theory....Pages 45-102 Algebraic v. Topological K -Theory: A Friendly Match....Pages 103-165 Higher Algebraic K -Theory (After Quillen, Thomason and Others)....Pages 167-241 Lectures on DG-Categories....Pages 243-302 Back Matter....Pages 303-308 Annotation This volume offers a thorough introduction to K-theory, both algebraic and topological, and to current research topics including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the K-theory of schemes, the theory of dg-categories, and more