The Seiberg-Witten Equations And Applications To The Topology Of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)

$45.31 New In stock Publisher: Princeton University Press
SKU: DADAX0691025975
ISBN : 9780691025971
Availability: Only 5 Left In-stock.

Price:
$45.31

Domestic Shipping: $3.99

Internation Shipping (Except United states): $16

Shipping & Tax will be calculated at Checkout.
Estimated delivery time 7-14 days.
International delivery time 2 to 4 weeks.

Qty:
   - OR -   
The Seiberg-Witten Equations And Applications To The Topology Of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)

The Seiberg-Witten Equations And Applications To The Topology Of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)

The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.Review"This book provides an excellent introduction to the recently discovered Seilberg-Witten invariants for smooth closed oriented 4-mainifolds.", Mathematical ReviewsFrom the Back CoverBeginning with the groundbreaking work of Donaldson in about 1980 it became clear that gauge-theoretic invariants of principal bundles and connections were an important tool in the study of smooth four-dimensional manifolds. Donaldson showed the importance of the moduli space of antiself-dual connections. The next fifteen years saw an explosion of work in this area leading to computations of Donaldson polynomial invariants for a wide class of four-dimensional manifolds, especially algebraic surfaces.About the AuthorJohn W. Morgan is Professor of Mathematics at Columbia University.

Specification of The Seiberg-Witten Equations And Applications To The Topology Of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)

GENERAL
AuthorMorgan, John W.
BindingPaperback
LanguageEnglish
Edition1st
ISBN-100691025975
ISBN-139780691025971
PublisherPrinceton University Press
Publication Year11-12-1995

Write a review


Your Name:


Your Email:


Your Review:

Note: HTML is not translated!

Rating: Bad           Good

Enter the code in the box below: