CBMS Regional Conference Series in Mathematics
Volume: 89;
1996;
90 pp;
Softcover
MSC: Primary 53;
Secondary 58
Print ISBN: 978-0-8218-0323-3
Product Code: CBMS/89
List Price: $20.00
Individual Price: $16.00
Electronic ISBN: 978-1-4704-2449-7
Product Code: CBMS/89.E
List Price: $20.00
Individual Price: $16.00
Metrics, Connections and Gluing Theorems
Share this pageClifford Henry Taubes
A co-publication of the AMS and CBMS
In this book, the author's goal is to provide an
introduction to some of the analytic underpinnings for the geometry of
anti-self duality in 4-dimensions. Anti-self duality is rather special
to 4-dimensions 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.
Readership
Graduate students and research mathematicians interested in differential geometry.
Reviews & Endorsements
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
Table of Contents
Table of Contents
Metrics, Connections and Gluing Theorems
- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- 1. Introduction 18 free
- 2. The anti-self dual equations 1017 free
- 3. Grafting theorems 2532
- 4. Deformations to anti-self duality I 3441
- 5. Deformations to anti-self duality II 4653
- 6. Metrics with W[sub(+)] ≡ 0 5562
- 7. Grafting metrics 6168
- 8. Deforming the metric 7077
- 9. Strategy for connect sums 7683
- 10. Open questions 8491
- References 8895
- Back Cover 9198