| eBook ISBN: | 978-0-8218-3392-6 |
| Product Code: | CBMS/58.E |
| List Price: | $32.00 |
| MAA Member Price: | $28.80 |
| AMS Member Price: | $25.60 |
| eBook ISBN: | 978-0-8218-3392-6 |
| Product Code: | CBMS/58.E |
| List Price: | $32.00 |
| MAA Member Price: | $28.80 |
| AMS Member Price: | $25.60 |
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Book DetailsCBMS Regional Conference Series in MathematicsVolume: 58; 1985; 101 ppMSC: Primary 58; Secondary 53; 57; 81
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.
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Table of Contents
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Chapters
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Chapter I. Introduction
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Chapter II. The Geometry of Connections
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Chapter III. The Self-dual Yang–Mills Equations
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Chapter IV. The Moduli Space
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Chapter V. Fundamental Results of K. Uhlenbeck
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Chapter VI. The Taubes Existence Theorem
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Chapter VII. Final Arguments
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Appendix I. The Sobolev Embedding Theorems
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Appendix II. Bochner-Weitzenböck Formulas
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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.
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Chapters
-
Chapter I. Introduction
-
Chapter II. The Geometry of Connections
-
Chapter III. The Self-dual Yang–Mills Equations
-
Chapter IV. The Moduli Space
-
Chapter V. Fundamental Results of K. Uhlenbeck
-
Chapter VI. The Taubes Existence Theorem
-
Chapter VII. Final Arguments
-
Appendix I. The Sobolev Embedding Theorems
-
Appendix II. Bochner-Weitzenböck Formulas
