Preface Nine years after the first edition, the Third Arolla Conference on Algebraic Topology brought together around 80 mathematicians specialised in a broad range of topics in algebraic topology. Some of us have had the privilege to attend all three editions, and we felt almost at home up there in the Alps, at an altitude of 2000 meters. However, along with the more experienced and faithful participants, many PhD students and postdocs (altogether 30 younger mathematicians) attended the conference. This reveals the vigor of the subject, and is, hopefully, a good sign for the future of the Arolla conferences series ! These proceedings reflect the variety of topics discussed at the conference. Quite roughly, Monday and Tuesday were dedicated to geometry, unstable homo- topy theory and operads, Wednesday to algebraic K-theory and traces, Thursday to Goodwillie calculus and its applications, and Friday to field theories and moduli spaces. Saturday then offered conference participants a bouquet of these topics. We would like to thank the following institutions and organizations for their generous financial support and sponsorship of the Third Arolla Conference on Al- gebraic Topology : - Swiss National Science Foundation - Bonn International Graduate School, Hausdorff Center for Mathematics - Ministerio de Educaci´ on y Ciencia de Espa˜na - Institute of Geometry, Algebra and Topology, EPFL, Lausanne - Faculty of Basic Sciences, EPFL, Lausanne - III-` eme Cycle Romand de Math´ematiques - Swiss Mathematical Society We would like to warmly thank the owners and personnel of the otel Mont- Collon in Arolla. It is a pleasure to organize a conference with their help. Our thanks also go to the speakers and to all the participants, to the contribu- tors of the present volume, and of course to the anonymous referees without them this volume would not exist. We also thank Chris Thivierge at the AMS for her help and guidance. Finally J. Scherer would like to thank the MPI in Bonn and the IHES in Bures-sur-Yvette for their generous hospitality during the months where most of the editorial work on this volume has been done. Christian Ausoni, Kathryn Hess and erˆ ome Scherer ix
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