CBMS Regional Conference Series in Mathematics
Volume: 58;
1985;
101 pp;
Softcover
MSC: Primary 58;
Secondary 53; 57; 81
Print ISBN: 978-0-8218-0708-8
Product Code: CBMS/58
List Price: $30.00
Individual Price: $24.00
Electronic ISBN: 978-0-8218-3392-6
Product Code: CBMS/58.E
List Price: $30.00
AMS Member Price: $24.00
MAA Member Price: $27.00
The Theory of Gauge Fields in Four Dimensions
Share this pageH. Blaine Lawson, Jr.
A co-publication of the AMS and CBMS
Lawson's expository lectures, presented at a CBMS Regional Conference
held in Santa Barbara in August 1983, provide an in-depth examination
of the recent work of Simon Donaldson, and is of special interest to both
geometric topologists and differential geometers. This work has
excited particular interest, in light of Mike Freedman's recent
profound results: the complete classification, in the simply connected
case, of compact topological 4-manifolds. Arguing from deep results in
gauge field theory, Donaldson has proved the nonexistence of
differentiable structures on certain compact 4-manifolds. Together
with Freedman's results, Donaldson's work implies the existence of
exotic differentiable structures in \(\mathbb R^4\)–a wonderful example of the
results of one mathematical discipline yielding startling consequences
in another.
The lectures are aimed at mature mathematicians with some training in
both geometry and topology, but they do not assume any expert
knowledge. In addition to a close examination of Donaldson's
arguments, Lawson also presents, as background material, the foundation
work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et
al.) which underlies Donaldson's work.
Readership
Table of Contents
Table of Contents
The Theory of Gauge Fields in Four Dimensions
- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Chapter I. Introduction 110 free
- Chapter II. The Geometry of Connections 1726
- 1. Quaternion line bundles 1726
- 2. Connections 1928
- 3. Riemannian connections 2029
- 4. Sp[sub(1)]-connections 2130
- 5. Change of connections 2231
- 6. Automorphisms (the gauge group) 2332
- 7. Sobolev completions 2534
- 8. Reductions 2837
- 9. The action of g on Ω[sup(p)] ([omitted]E) 3140
- 10. Equivalence classes of connections 3342
- Chapter III. The Self-dual Yang-Mills Equations 3948
- Chapter IV. The Moduli Space 4756
- Chapter V. Fundamentai Results of K. Uhlenbeck 5968
- Chapter VI. The Taubes Existence Theorem 7180
- Chapter VII. Final Arguments 8594
- Appendix I. The Sobolev Embedding Theorems 91100
- Appendix II. Bochner-Weitzenbtick Formulas 93102
- References 99108
- Back Cover Back Cover1111