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IAS/Park City Mathematics Series
2009; 315 pp; hardcover
List Price: US$73
Member Price: US$58.40
Order Code: PCMS/15
Gauge Theory and the Topology of Four-Manifolds - Robert Friedman and John W Morgan
Hamilton's Ricci Flow - Bennett Chow, Peng Lu and Lei Ni
Low-Dimensional 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
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, 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 co-published 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.
Graduate students and research mathematicians interested in low dimensional topology.
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