Softcover ISBN:  9780821803233 
Product Code:  CBMS/89 
List Price:  $22.00 
Individual Price:  $17.60 
Electronic ISBN:  9781470424497 
Product Code:  CBMS/89.E 
List Price:  $20.00 
Individual Price:  $16.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 89; 1996; 90 ppMSC: Primary 53; Secondary 58;
In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of antiself duality in 4dimensions. Antiself duality is rather special to 4dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics.
The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.ReadershipGraduate students and research mathematicians interested in differential geometry.

Table of Contents

Chapters

1. Introduction

2. The antiself dual equations

3. Grafting theorems

4. Deformations to antiself duality I

5. Deformations to antiself duality II

6. Metrics with $W_+ \equiv 0$

7. Grafting metrics

8. Deforming the metric

9. Strategy for connect sums

10. Open questions


Reviews

Provides an excellent introduction to the application of certain analytic techniques to problems in differential geometry … the casual style in which this book is written together with the straightforward explanations of the key ideas underlying the theory makes it an excellent source for those wishing to learn about these basic techniques … a perfect balance seems to have been struck in the choice between what to include and what to refer the reader elsewhere for.
Mathematical Reviews 
Easy to read … well written in a pleasant, informal style, with occasional humour … should be accessible to graduate students in differential geometry and others.
Bulletin of the LMS


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In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of antiself duality in 4dimensions. Antiself duality is rather special to 4dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics.
The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.
Graduate students and research mathematicians interested in differential geometry.

Chapters

1. Introduction

2. The antiself dual equations

3. Grafting theorems

4. Deformations to antiself duality I

5. Deformations to antiself duality II

6. Metrics with $W_+ \equiv 0$

7. Grafting metrics

8. Deforming the metric

9. Strategy for connect sums

10. Open questions

Provides an excellent introduction to the application of certain analytic techniques to problems in differential geometry … the casual style in which this book is written together with the straightforward explanations of the key ideas underlying the theory makes it an excellent source for those wishing to learn about these basic techniques … a perfect balance seems to have been struck in the choice between what to include and what to refer the reader elsewhere for.
Mathematical Reviews 
Easy to read … well written in a pleasant, informal style, with occasional humour … should be accessible to graduate students in differential geometry and others.
Bulletin of the LMS