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Lectures On Seiberg Witten Invariants
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Book Synopsis Lectures on Seiberg-Witten Invariants by : John D. Moore
Download or read book Lectures on Seiberg-Witten Invariants written by John D. Moore and published by Springer. This book was released on 2006-11-14 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 by : John W. Morgan
Download or read book The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 written by John W. Morgan and published by Princeton University Press. This book was released on 2014-09-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Notes on Seiberg-Witten Theory by : Liviu I. Nicolaescu
Download or read book Notes on Seiberg-Witten Theory written by Liviu I. Nicolaescu and published by American Mathematical Soc.. This book was released on 2000 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lecture Notes on Chern-Simons-Witten Theory by : Sen Hu
Download or read book Lecture Notes on Chern-Simons-Witten Theory written by Sen Hu and published by World Scientific. This book was released on 2001 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on lectures on topological quantum field theory given in 1989 at Princeton University by E. Witten, in which he unified several important mathematical works in terms of the Donaldson polynomial, Gromov/Floer homology, and Jones polynomials. Witten explained his three-dimensional construction of Jones polynomials, "an elegant construction of a new polynomial invariant in three-dimensional space" (per the author), via quantization of Chern-Simons gauge theory. Hu (Princeton U.) adds missing details and some new developments in the field. Annotation copyrighted by Book News Inc., Portland, OR.
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :9780821838457 Total Pages :318 pages Book Rating :4.8/5 (384 download)
Book Synopsis Floer Homology, Gauge Theory, and Low-Dimensional Topology by : Clay Mathematics Institute. Summer School
Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis Geometric Analysis and Applications to Quantum Field Theory by : Peter Bouwknegt
Download or read book Geometric Analysis and Applications to Quantum Field Theory written by Peter Bouwknegt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Book Synopsis An Introduction to Invariants and Moduli by : Shigeru Mukai
Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text
Book Synopsis Seiberg Witten Gauge Theory by : Matilde Marcolli
Download or read book Seiberg Witten Gauge Theory written by Matilde Marcolli and published by Springer. This book was released on 1999-12-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Chern-Weil Theory and Witten Deformations by : Weiping Zhang
Download or read book Lectures on Chern-Weil Theory and Witten Deformations written by Weiping Zhang and published by World Scientific. This book was released on 2001 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to ShiingOCoshen Chern and Andr(r) Weil, as well as a proof of the GaussOCoBonnetOCoChern theorem based on the MathaiOCoQuillen construction of Thom forms; the second part presents analytic proofs of the Poincar(r)OCoHopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. Contents: ChernOCoWeil Theory for Characteristic Classes; Bott and DuistermaatOCoHeckman Formulas; GaussOCoBonnetOCoChern Theorem; Poincar(r)OCoHopf Index Formula: An Analytic Proof; Morse Inequalities: An Analytic Proof; ThomOCoSmale and Witten Complexes; Atiyah Theorem on Kervaire Semi-characteristic. Readership: Graduate students and researchers in differential geometry, topology and mathematical physics."
Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Book Synopsis Lectures on Choquet's Theorem by : Robert R. Phelps
Download or read book Lectures on Choquet's Theorem written by Robert R. Phelps and published by Springer. This book was released on 2003-07-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis Algebraic Surfaces and Holomorphic Vector Bundles by : Robert Friedman
Download or read book Algebraic Surfaces and Holomorphic Vector Bundles written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
Book Synopsis Lectures on the Geometry of Manifolds by :
Download or read book Lectures on the Geometry of Manifolds written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monopoles and Three-Manifolds by : Peter Kronheimer
Download or read book Monopoles and Three-Manifolds written by Peter Kronheimer and published by . This book was released on 2007-12-20 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.
Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory L. Naber
Download or read book Topology, Geometry, and Gauge Fields written by Gregory L. Naber and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Book Synopsis Introduction to Combinatorial Torsions by : Vladimir Turaev
Download or read book Introduction to Combinatorial Torsions written by Vladimir Turaev and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
