**IAS/Park City Mathematics Series**

Volume: 4;
1998;
221 pp;
Hardcover

MSC: Primary 14; 32; 53; 57; 58;

Print ISBN: 978-0-8218-0591-6

Product Code: PCMS/4

List Price: $50.00

Individual Member Price: $40.00

**Electronic ISBN: 978-1-4704-3903-3
Product Code: PCMS/4.E**

List Price: $50.00

Individual Member Price: $40.00

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# Gauge Theory and the Topology of Four-Manifolds

Share this page *Edited by *
*Robert Friedman; John W. Morgan*

A co-publication of the AMS and IAS/Park City Mathematics Institute

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.

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. *NOTE: This discount does not apply to volumes in this
series co-published with the Society for Industrial and Applied
Mathematics (SIAM).*

#### Table of Contents

# Table of Contents

## Gauge Theory and the Topology of Four-Manifolds

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Introduction 112
- Geometric invariant theory and the moduli of bundles 516
- Anti-self-dual connections and stable vector bundles 2334
- An introduction to gauge theory 5162
- Computing Donaldson invariants 145156
- Donaldson-Floer theory 195206
- Back Cover Back Cover1233

#### Readership

Graduate students and research mathematicians working in algebraic geometry.