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Selected Applications of Geometry to Low-Dimensional Topology
 
Michael H. Freedman University of California, San Diego, La Jolla, CA
Feng Luo Rutgers University, New Brunswick, New Brunswick, NJ
Selected Applications of Geometry to Low-Dimensional Topology
eBook ISBN:  978-1-4704-2154-0
Product Code:  ULECT/1.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Selected Applications of Geometry to Low-Dimensional Topology
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Selected Applications of Geometry to Low-Dimensional Topology
Michael H. Freedman University of California, San Diego, La Jolla, CA
Feng Luo Rutgers University, New Brunswick, New Brunswick, NJ
eBook ISBN:  978-1-4704-2154-0
Product Code:  ULECT/1.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
  • Book Details
     
     
    University Lecture Series
    Volume: 11989; 79 pp
    MSC: Primary 57; Secondary 53; 54;

    This book, the inaugural volume in the University Lecture Series, is based on lectures presented at Pennsylvania State University in February 1987. The lectures attempt to give a taste of the accomplishments of manifold topology over the last 30 years. By the late 1950s, algebra and topology had produced a successful and beautiful fusion. Geometric methods and insight, now vitally important in topology, encompass analytic objects such as instantons and minimal surfaces, as well as nondifferentiable constructions.

    Keeping technical details to a minimum, the authors lead the reader on a fascinating exploration of several developments in geometric topology. They begin with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceed to the topology and geometry of foliated 3-manifolds. They also explain, in terms of general position, why four-dimensional space has special attributes, and they examine the insight Donaldson theory brings. The book ends with a chapter on exotic structures on \(\mathbf R^4\), with a discussion of the two competing theories of four-dimensional manifolds, one topological and one smooth.

    Background material was added to clarify the discussions in the lectures, and references for more detailed study are included. Suitable for graduate students and researchers in mathematics and the physical sciences, the book requires only background in undergraduate mathematics. It should prove valuable for those wishing a not-too-technical introduction to this vital area of current research.

    Readership

    Graduate students and research mathematicians and physical scientists.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Manifolds and smooth structures
    • Chapter 2. The Euler number
    • Chapter 3. Foliations
    • Chapter 4. The topological classification of simply-connected 4-manifolds
    • Chapter 5. Donaldson’s theory
    • Chapter 6. Fake $\mathbf {R}^4$’s
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 11989; 79 pp
MSC: Primary 57; Secondary 53; 54;

This book, the inaugural volume in the University Lecture Series, is based on lectures presented at Pennsylvania State University in February 1987. The lectures attempt to give a taste of the accomplishments of manifold topology over the last 30 years. By the late 1950s, algebra and topology had produced a successful and beautiful fusion. Geometric methods and insight, now vitally important in topology, encompass analytic objects such as instantons and minimal surfaces, as well as nondifferentiable constructions.

Keeping technical details to a minimum, the authors lead the reader on a fascinating exploration of several developments in geometric topology. They begin with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceed to the topology and geometry of foliated 3-manifolds. They also explain, in terms of general position, why four-dimensional space has special attributes, and they examine the insight Donaldson theory brings. The book ends with a chapter on exotic structures on \(\mathbf R^4\), with a discussion of the two competing theories of four-dimensional manifolds, one topological and one smooth.

Background material was added to clarify the discussions in the lectures, and references for more detailed study are included. Suitable for graduate students and researchers in mathematics and the physical sciences, the book requires only background in undergraduate mathematics. It should prove valuable for those wishing a not-too-technical introduction to this vital area of current research.

Readership

Graduate students and research mathematicians and physical scientists.

  • Chapters
  • Chapter 1. Manifolds and smooth structures
  • Chapter 2. The Euler number
  • Chapter 3. Foliations
  • Chapter 4. The topological classification of simply-connected 4-manifolds
  • Chapter 5. Donaldson’s theory
  • Chapter 6. Fake $\mathbf {R}^4$’s
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.