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]