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Gauge Theory And The Topology Of Four Manifolds

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Gauge Theory And The Topology Of Four Manifolds

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Author : Robert Friedman, John W. Morgan
language : en
Publisher: American Mathematical Soc.
Release Date :

Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman, John W. Morgan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.

Topological Quantum Field Theory And Four Manifolds

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Author : Jose Labastida
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-18

Topological Quantum Field Theory And Four Manifolds written by Jose Labastida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Science categories.

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.

Instantons And Four Manifolds

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Author : Daniel S. Freed
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Instantons And Four Manifolds written by Daniel S. Freed and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2

Gauge Theory And The Topology Of Four Manifolds

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Author : ROBERT. FRIEDMAN
language : en
Publisher:
Release Date : 1999

Gauge Theory And The Topology Of Four Manifolds written by ROBERT. FRIEDMAN and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

The Seiberg Witten Equations And Applications To The Topology Of Smooth Four Manifolds

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Author : John W. Morgan
language : en
Publisher: Princeton University Press
Release Date : 1996

The Seiberg Witten Equations And Applications To The Topology Of Smooth Four Manifolds written by John W. Morgan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

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.

Gauge Theory And The Topology Of Four Manifolds

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Author : Robert Friedman
language : en
Publisher:
Release Date : 1997

Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Four-manifolds (Topology) categories.

Gauge Theory And The Topology Of Four Manifolds

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Author : Robert Friedman
language : en
Publisher: American Mathematical Society, IAS/Park City Mathematics Institute
Release Date : 2024-12-05

Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman and has been published by American Mathematical Society, IAS/Park City Mathematics Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-05 with Mathematics categories.

The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.

The Wild World Of 4 Manifolds

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Author : Alexandru Scorpan
language : en
Publisher: American Mathematical Soc.
Release Date : 2005-05-10

The Wild World Of 4 Manifolds written by Alexandru Scorpan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-10 with Mathematics categories.

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.

Fields Medallists Lectures

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Author : Michael Atiyah
language : en
Publisher: World Scientific
Release Date : 1997-10-13

Fields Medallists Lectures written by Michael Atiyah and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-13 with Mathematics categories.

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.

The Geometry Of Four Manifolds

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Author : S. K. Donaldson
language : en
Publisher: Oxford University Press
Release Date : 1997

The Geometry Of Four Manifolds written by S. K. Donaldson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Language Arts & Disciplines categories.

This book provides the first lucid and accessible account of the modern study of the geometry of four-manifolds. It presents both a thorough treatment of the main lines of the developments and also a wide-ranging treatment of relevant topics from geometry and global analysis.

Gauge Theory And The Topology Of Four Manifolds

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