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Gauge Theory and the Topology of Four-Manifolds

Edited by: Robert Friedman Columbia University, New York, NY
John W. Morgan Columbia University, New York, NY
A co-publication of the AMS and IAS/Park City Mathematics Institute
Available Formats:
Hardcover ISBN: 978-0-8218-0591-6
Product Code: PCMS/4
List Price: $53.00 MAA Member Price:$47.70
AMS Member Price: $42.40 Electronic ISBN: 978-1-4704-3903-3 Product Code: PCMS/4.E List Price:$50.00
MAA Member Price: $45.00 AMS Member Price:$40.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $79.50 MAA Member Price:$71.55
AMS Member Price: $63.60 Click above image for expanded view Gauge Theory and the Topology of Four-Manifolds Edited by: Robert Friedman Columbia University, New York, NY John W. Morgan Columbia University, New York, NY A co-publication of the AMS and IAS/Park City Mathematics Institute Available Formats:  Hardcover ISBN: 978-0-8218-0591-6 Product Code: PCMS/4  List Price:$53.00 MAA Member Price: $47.70 AMS Member Price:$42.40
 Electronic ISBN: 978-1-4704-3903-3 Product Code: PCMS/4.E
 List Price: $50.00 MAA Member Price:$45.00 AMS Member Price: $40.00 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:$79.50 MAA Member Price: $71.55 AMS Member Price:$63.60
• Book Details

IAS/Park City Mathematics Series
Volume: 41998; 221 pp
MSC: Primary 14; 32; 53; 57; 58;

The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory.

Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.

Graduate students and research mathematicians working in algebraic geometry.

• Chapters
• Introduction
• Geometric invariant theory and the moduli of bundles
• Anti-self-dual connections and stable vector bundles
• An introduction to gauge theory
• Computing Donaldson invariants
• Donaldson-Floer theory
• Request Review Copy
Volume: 41998; 221 pp
MSC: Primary 14; 32; 53; 57; 58;

The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory.

Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.