The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds write by John W. Morgan. This book was released on 1996. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds available in PDF, EPUB and Kindle. 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.
Lectures on Seiberg-Witten Invariants
Lectures on Seiberg-Witten Invariants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Seiberg-Witten Invariants write by John D. Moore. This book was released on 2009-01-20. Lectures on Seiberg-Witten Invariants available in PDF, EPUB and Kindle. Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.
Lectures on Seiberg-Witten Invariants
Lectures on Seiberg-Witten Invariants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Seiberg-Witten Invariants write by John Douglas Moore. This book was released on 1996. Lectures on Seiberg-Witten Invariants available in PDF, EPUB and Kindle. In the fall of 1994, Edward Witten proposed a set of equations which give the main results of Donaldson theory in a far simpler way than had been thought possible. The purpose of these notes is to provide an elementary introduction to the equations that Witten proposed. They are directed towards graduate students who have already taken a basic course in differential geometry and topology.
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44
The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 write by John W. Morgan. This book was released on 2014-09-08. The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 available in PDF, EPUB and Kindle. 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.
Notes on Seiberg-Witten Theory
Notes on Seiberg-Witten Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Seiberg-Witten Theory write by Liviu I. Nicolaescu. This book was released on 2000. Notes on Seiberg-Witten Theory available in PDF, EPUB and Kindle. After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations and the group of gauge transformations, then look at algebraic surfaces. A final chapter presents in great detail a cut-and-paste technique for computing Seiberg-Witten invariants, covering elliptic equations on manifolds with cylindrical ends, finite energy monopoles on cylindrical manifolds, local and global properties of the moduli spaces of finite energy monopoles, and the process of reconstructing the space of monopoles on a 4-manifold decomposed into several parts by a hypersurface. Annotation copyrighted by Book News, Inc., Portland, OR.
