IAS/Park City Mathematics Series
Volume: 15;
2009;
315 pp;
Hardcover
MSC: Primary 53; 57; 58;
Print ISBN: 978-0-8218-4766-4
Product Code: PCMS/15
List Price: $73.00
AMS Member Price: $58.40
MAA Member Price: $65.70
Electronic ISBN: 978-1-4704-1629-4
Product Code: PCMS/15.E
List Price: $73.00
AMS Member Price: $58.40
MAA Member Price: $65.70
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Low Dimensional Topology
Share this pageEdited by Tomasz S. Mrowka; Peter S. Ozsváth
A co-publication of the AMS and IAS/Park City Mathematics Institute
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.
Readership
Graduate students and research mathematicians interested in low dimensional topology.
Table of Contents
Low Dimensional Topology
- Cover Cover11
- Title page iv5
- Contents vi7
- Preface xii13
- Introduction 116
- Fifty years ago: Topology of manifolds in the 50’s and 60’s 722
- Dehn surgery and 3-manifolds 2136
- Hyperbolic geometry and 3-manifold topology 7388
- Ricci flow and Thurston’s geometrization conjecture (with notes by Max Lipyanskiy) 105120
- Notes on link homology 139154
- Lecture notes on Heegard Floer homology 197212
- Contact geometry in low dimensional topology 229244
- Six lectures on four 4-manifolds 265280
- Back Cover Back Cover1332