Download or read book Instantons and Four Manifolds written by D. S. Freed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of a seminar organized by Michael Freedman and Karen Uhlenbeck (the senior author) at the Mathematical Sciences Research Institute in Berkeley during its first few months of existence. Dan Freed (the junior author) was originally appointed as notetaker. The express purpose of the seminar was to go through a proof of Simon Donaldson's Theorem, which had been announced the previous spring. Donaldson proved the nonsmoothability of certain topological four-manifolds; a year earlier Freedman had constructed these manifolds as part of his solution to the four dimensional ; Poincare conjecture. The spectacular application of Donaldson's and Freedman's theorems to the existence of fake 1R4,s made headlines (insofar as mathematics ever makes headlines). Moreover, Donaldson proved his theorem in topology by studying the solution space of equations the Yang-Mills equations which come from ultra-modern physics. The philosophical implications are unavoidable: we mathematicians need physics! The seminar was initially very well attended. Unfortunately, we found after three months that we had covered most of the published material, but had made little real progress towards giving a complete, detailed proof. Mter joint work extending over three cities and 3000 miles, this book now provides such a proof. The seminar bogged down in the hard analysis (56 59), which also takes up most of Donaldson's paper (in less detail). As we proceeded it became clear to us that the techniques in partial differential equations used in the proof differ strikingly from the geometric and topological material.
Download or read book Instantons and Four Manifolds written by Daniel S Freed and published by . This book was released on 1990-12-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Instantons and Four Manifolds written by D. S Freed and published by . This book was released on 1984-08-24 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Instanton and Four manifolds written by Daniel S. Freed and published by . This book was released on 1984 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geometry of Four manifolds written by S. K. Donaldson and published by Oxford University Press. This book was released on 1997 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.
Download or read book The Wild World of 4 Manifolds written by Alexandru Scorpan and published by American Mathematical Society. This book was released on 2022-01-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.
Download or read book Uhlenbeck Compactness written by Katrin Wehrheim and published by European Mathematical Society. This book was released on 2004 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed account of the analytic foundations of gauge theory, namely, Uhlenbeck's compactness theorems for general connections and for Yang-Mills connections. It guides graduate students into the analysis of Yang-Mills theory as well as serves as a reference for researchers in the field. Largely self contained, the book contains a number of appendices (e.g., on Sobolev spaces of maps between manifolds) and an introductory part covering the $L^p$-regularity theory for the inhomogenous Neumann problem.
Download or read book Instantons and Large N written by Marcos Mariño and published by Cambridge University Press. This book was released on 2015-09-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A highly pedagogical textbook for graduate students, exploring advanced topics of quantum field theory with detailed derivations and worked examples.
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.
Download or read book The Floer Memorial Volume written by Helmut Hofer and published by Birkhäuser. This book was released on 2012-12-06 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder.
Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.
Download or read book Floer Homology Groups in Yang Mills Theory written by S. K. Donaldson and published by Cambridge University Press. This book was released on 2002-01-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
Download or read book Geometry of Low Dimensional Manifolds Volume 1 Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.
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).
Download or read book Exotic Smoothness and Physics written by Torsten Asselmeyer-Maluga and published by World Scientific. This book was released on 2007 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many Christians have an easier time being saved by grace than they do living in grace every day. But grace is at the center of the life God calls us to--and reflects the heart of the One who calls.These studies in Grace will help you make the connection between grace as a remote biblical concept and grace as a lifestyle--a reality you experience day in, day out. Through an unfolding study of Psalm 23, you'll learn how God--our Good Shepherd--is for you, how he longs to walk with you through temptation, sorrow, and even deep regret. You'll discover God's desire to make his joy your joy. Throughout, you'll learn how enduring, powerful, and life-affirming God's work in your life can be---and rediscover why it's called amazing grace.Leader's guide included!Grace group sessions are:Living in GraceGrace for RegretsSustaining GraceDelighting in GraceA Legacy of GraceGrace ForeverGrace to Share
Download or read book Instanton Counting Quantum Geometry and Algebra written by Taro Kimura and published by Springer Nature. This book was released on 2021-07-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.
Download or read book The Topology of 4 Manifolds written by Robion C. Kirby and published by Springer. This book was released on 2006-11-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.
