AnyBook4Less.com	Find the Best Price on the Web Order from a Major Online Bookstore
Home  |  Store List  |  FAQ  |  Contact Us  |
Ultimate Book Price Comparison Engine Save Your Time And Money Keyword AuthorISBN

Title: The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44) by John W. Morgan ISBN: 0-691-02597-5 Publisher: Princeton Univ Pr Pub. Date: 11 December, 1995 Format: Paperback Volumes: 1 List Price(USD): $29.95

Your Country USA Canada United Kingdom Australia Austria Belgium France Germany Italy Netherlands Switzerland Currency AutoUSD CAD GBP EUR AUD CHF Delivery Only cheapest delivery All delivery options Include Used Books Are you a club member of: Barnes and Noble Books A Million Chapters.Indigo.ca

Average Customer Rating: 3 (1 review)

Rating: 3
Summary: Fairly good book on the subject
Comment: This book is a pretty good introduction to the main results that caused a flurry of excitement in the mathematical community in the mid 1990's. The mathematical constructions involved here are interesting mostly to those in the area of the differential topology of 4-manifolds. The Seiberg-Witten invariants as they are now called, have been widely discussed since then, but mostly now in the context of symplectic geometry. After a brief overview of spin geometry and Clifford algebras, the author discusses the complex spin representation. This sets up the discussion of spin bundles in the next chapter, and, even though it is really not the place for it, the author does not prove that a principal SO(V) bundle lifts to a principal Spin(V) if and only if the second Stiefel-Whitney class is equal to zero. There are many different proofs of this in the literature, but I have not discovered in any of these proofs any real, sound insight as to why this result is true. The chapter continues its very formal treatment with an overview of spin bundles and the Dirac operator. The next chapter then moves immediately to the Seiberg-Witten equations and they are viewed as nonlinear generalizations of elliptic partial differential equations in the sense that the linearization of both the Seiberg-Witten equations and the gauge group action is shown to be an ellipic complex. The next chapter shows that the moduli space of solutions to the Seiberg-Witten equations is compact. This is the most technical of the chapters and requires attentive reading. The Seiberg-Witten invariant for complex spin structures is discussed in the next chapter. Again one must pay close attention to the details of the arguments. The actual calculation of a Seiberg-Witten invariant is performed in the context of Kahler manifolds in the last chapter of the book. This sets up the reader nicely for the current work on symplectic manifolds. The book will be of interest to mathematicians wanting an understanding of this area of four-dimensional topology and to high-energy physicists who are interested in the low energy behavior and duality in SU(2) supersymmetric gauge theories. The constructions of Seiberg and Witten in quantum field theory are what led to the invariants outlined in this book. All in all a fascinating area of mathematics and its consequences are sill being worked out with diligence.