
Table of Contents 
IAS/Park City Mathematics Series 2009; 315 pp; hardcover Volume: 15 ISBN10: 082184766X ISBN13: 9780821847664 List Price: US$69 Member Price: US$55.20 Order Code: PCMS/15 See also: Gauge Theory and the Topology of FourManifolds  Robert Friedman and John W Morgan Hamilton's Ricci Flow  Bennett Chow, Peng Lu and Lei Ni LowDimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots  Francis Bonahon Ricci Flow and the Sphere Theorem  Simon Brendle Analytic and Algebraic Geometry: Common Problems, Different Methods  Jeffery McNeal and Mircea Mustata  Lowdimensional 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 lowdimensional topology. These notes give fresh, concise, and highlevel 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 lowdimensional 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 threemanifold 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 fourmanifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltán Szabó on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization. Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. Readership Graduate students and research mathematicians interested in low dimensional topology. 


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