Notices of the American Mathematical Society

Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization. rnoti-mar10-cov1 rtx10030cov2p rtx100300329p rtx100300330p rtx100300331p rtx100300333p rtx100300334p rtx100300343p rtx100300357p rtx100300366p rtx100300375p rtx100300378p rtx100300380p rtx100300385p rtx100300391p rtx100300404p rtx100300406p rtx100300407p rtx100300410p rtx100300416p rtx100300418p rtx100300420p rtx100300421p rtx100300422p rtx100300426p rtx100300427p rtx100300435p rtx100300440p rtx100300442p rtx100300443p rtx100300455p rtx100300456p rtx10030cov3p rnoti-mar10-cov4