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Low Dimensional Topology
 
Edited by: Tomasz S. Mrowka Massachusetts Institute of Technology, Cambridge, MA
Peter S. Ozsváth Columbia University, New York, NY
A co-publication of the AMS and IAS/Park City Mathematics Institute
Front Cover for Low Dimensional Topology
Available Formats:
Hardcover ISBN: 978-0-8218-4766-4
Product Code: PCMS/15
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN: 978-1-4704-1629-4
Product Code: PCMS/15.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
Front Cover for Low Dimensional Topology
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  • Front Cover for Low Dimensional Topology
  • Back Cover for Low Dimensional Topology
Low Dimensional Topology
Edited by: Tomasz S. Mrowka Massachusetts Institute of Technology, Cambridge, MA
Peter S. Ozsváth Columbia University, New York, NY
A co-publication of the AMS and IAS/Park City Mathematics Institute
Available Formats:
Hardcover ISBN:  978-0-8218-4766-4
Product Code:  PCMS/15
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN:  978-1-4704-1629-4
Product Code:  PCMS/15.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 152009; 315 pp
    MSC: Primary 53; 57; 58;

    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.

    Readership

    Graduate students and research mathematicians interested in low dimensional topology.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Fifty years ago: Topology of manifolds in the 50’s and 60’s
    • Dehn surgery and 3-manifolds
    • Hyperbolic geometry and 3-manifold topology
    • Ricci flow and Thurston’s geometrization conjecture (with notes by Max Lipyanskiy)
    • Notes on link homology
    • Lecture notes on Heegard Floer homology
    • Contact geometry in low dimensional topology
    • Six lectures on four 4-manifolds
  • Additional Material
     
     
  • Request Review Copy
Volume: 152009; 315 pp
MSC: Primary 53; 57; 58;

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.

Readership

Graduate students and research mathematicians interested in low dimensional topology.

  • Chapters
  • Introduction
  • Fifty years ago: Topology of manifolds in the 50’s and 60’s
  • Dehn surgery and 3-manifolds
  • Hyperbolic geometry and 3-manifold topology
  • Ricci flow and Thurston’s geometrization conjecture (with notes by Max Lipyanskiy)
  • Notes on link homology
  • Lecture notes on Heegard Floer homology
  • Contact geometry in low dimensional topology
  • Six lectures on four 4-manifolds
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