Table of Contents – Volume 2 III. K-Theory and Geometric Topology III.1 Witt Groups Paul Balmer ............................................................539 III.2 K-Theory and Geometric Topology Jonathan Rosenberg .....................................................577 III.3 Quadratic K-Theory and Geometric Topology Bruce Williams..........................................................611 IV. K-Theory and Operator Algebras IV.1 Bivariant K- and Cyclic Theories Joachim Cuntz ..........................................................655 IV.2 The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory Wolfgang Lück, Holger Reich .............................................703 IV.3 Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C∗-Algebras Jonathan Rosenberg .....................................................843 V. Other Forms of K-Theory V.1 Semi-topological K-Theory Eric M. Friedlander, Mark E. Walker ......................................877 V.2 Equivariant K-Theory Alexander S. Merkurjev ..................................................925 VI Table of Contents – Volume 2 V.3 K(1)-Local Homotopy, Iwasawa Theory and Algebraic K-Theory Stephen A. Mitchell ......................................................955 V.4 The K-Theory of Triangulated Categories Amnon Neeman ........................................................1011 Appendix: Bourbaki Articles on the Milnor Conjecture A Motivic Complexes of Suslin and Voevodsky Eric M. Friedlander ....................................................1081 B La conjecture de Milnor (d’après V. Voevodsky) Bruno Kahn ...........................................................1105 Index .................................................................1151 Table of Contents – Volume 1 I. Foundations and Computations I.1 Deloopings in Algebraic K-Theory Gunnar Carlsson ..........................................................3 I.2 The Motivic Spectral Sequence Daniel R. Grayson ........................................................39 I.3 K-Theory of Truncated Polynomial Algebras Lars Hesselholt ...........................................................71 I.4 Bott Periodicity in Topological, Algebraic and Hermitian K-Theory Max Karoubi ...........................................................111 I.5 Algebraic K-Theory of Rings of Integers in Local and Global Fields Charles Weibel ..........................................................139 II. K-Theory and Algebraic Geometry II.1 Motivic Cohomology, K-Theory and Topological Cyclic Homology Thomas Geisser .........................................................193 II.2 K-Theory and Intersection Theory Henri Gillet .............................................................235 II.3 Regulators Alexander B. Goncharov .................................................295 II.4 Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry Bruno Kahn ............................................................351 II.5 Mixed Motives Marc Levine ............................................................429 Index ..................................................................523 List of Contributors Paul Balmer University of Southern California Department of Mathematics Los Angeles, CA 90089-2532 ETH Zentrum USA 8092 Zürich [email protected] Switzerland [email protected] Henri Gillet Department of Mathematics, Statistics, Gunnar Carlsson and Computer Science Department of Mathematics University of Illinois at Chicago Stanford University 322 Science and Engineering Offices Stanford, California 94305 (M/C 249) USA Chicago, IL 60607-7045 [email protected] USA [email protected] Joachim Cuntz Mathematisches Institut Alexander B. Goncharov Universität Münster 48149 Münster Department of Mathematics Germany Brown University [email protected] Providence, RI 02906 USA Eric M. Friedlander [email protected] Department of Mathematics Northwestern University Daniel R. Grayson Evanston, IL 60208 Department of Mathematics USA University of Illinois [email protected] at Urbana-Champaign Urbana, Illinois 61801 Thomas H. Geisser USA Department of Mathematics [email protected] X List of Contributors Lars Hesselholt Seattle, WA 98195 Department of Mathematics USA Massachusetts Institute of Technology [email protected] Cambridge, Massachusetts 02139 USA Amnon Neeman [email protected] Centre for Mathematics and its Applications Bruno Kahn Mathematical Sciences Institute Institut de Mathématiques de Jussieu John Dedman Building Equipe Théories Géométriques The Australian National University Université Paris 7 Canberra, ACT 0200 Case 7012 Australia 75251 Paris Cedex 05 [email protected] France [email protected] Holger Reich Fachbereich Mathematik Max Karoubi Universität Münster Department of Mathematics 48149 Münster University Paris 7 Germany 75251 Paris [email protected] France [email protected] Jonathan Rosenberg University of Maryland Marc Levine College Park, MD 20742 Department of Mathematics USA Northeastern University [email protected] Boston, MA 02115 USA Mark E. Walker [email protected] Department of Mathematics Wolfgang Lück University of Nebraska – Lincoln Fachbereich Mathematik Lincoln, NE 68588-0323 Universität Münster [email protected] 48149 Münster Charles Weibel Germany Department of Mathematics [email protected] Rutgers University Alexander S. Merkurjev New Brunswick, NJ 08903 Department of Mathematics USA University of California [email protected] Los Angeles, CA 90095-1555 USA Bruce Williams [email protected] Department of Mathematics University of Notre Dame Stephen A. Mitchell Notre Dame, IN 46556-4618 Department of Mathematics USA University of Washington [email protected].