## The Theory of Gauge Fields in Four Dimensions

**Author**: H. Blaine Lawson

**Publisher:**American Mathematical Soc.

**ISBN:**0821807080

**Category:**Mathematics

**Page:**101

**View:**5696

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Lawson's expository lectures, presented at a CBMS Regional Conference held in Santa Barbara in August 1983, provide an indepth examination of the recent work of Simon Donaldson, and is of special interest to both geometric topologists and differential geometers. This work has excited particular interest, in light of Mike Freedman's recent profound results: the complete classification, in the simply connected case, of compact topological 4-manifolds.Arguing from deep results in gauge field theory, Donaldson has proved the nonexistence of differentiable structures on certain compact 4-manifolds. Together with Freedman's results, Donaldson's work implies the existence of exotic differentiable structures in $\mathbb R^4$-a wonderful example of the results of one mathematical discipline yielding startling consequences in another. The lectures are aimed at mature mathematicians with some training in both geometry and topology, but they do not assume any expert knowledge. In addition to a close examination of Donaldson's arguments, Lawson also presents, as background material, the foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work.

## The Geometry of Four-manifolds

**Author**: S. K. Donaldson,P. B. Kronheimer

**Publisher:**Oxford University Press

**ISBN:**9780198502692

**Category:**Fiction

**Page:**440

**View:**4993

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This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds. One of the many consquences of this theory is that 'exotic' smooth manifolds exist which are homeomorphic but not diffeomorphic to (4, and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These result have hadfar-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come.

## Frobenius Algebras and 2-D Topological Quantum Field Theories

**Author**: Joachim Kock

**Publisher:**Cambridge University Press

**ISBN:**9780521540315

**Category:**Mathematics

**Page:**240

**View:**9776

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This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

## The Wild World of 4-manifolds

**Author**: Alexandru Scorpan

**Publisher:**American Mathematical Soc.

**ISBN:**0821837494

**Category:**Mathematics

**Page:**609

**View:**6563

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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.

## Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics

**Author**: Coquereaux Robert,Dubois-violette Michel,Flad Patricia

**Publisher:**World Scientific

**ISBN:**9814549320

**Category:**

**Page:**412

**View:**614

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## Internationale mathematische Nachrichten

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**4402

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Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

## On the Convergence of Some Boundary Element Methods in the Plane

**Author**: Keijo Ruotsalainen

**Publisher:**N.A

**ISBN:**9789516797451

**Category:**Boundary element methods

**Page:**26

**View:**7739

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## Bericht

*Report*

**Author**: Jyväskylän yliopisto. Matematiikan laitos,Osmo Pekonen

**Publisher:**N.A

**ISBN:**9789516799608

**Category:**Mathematics

**Page:**46

**View:**7218

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## Proceedings of the XVII International Conference on Differential Geometric Methods in Theoretical Physics

*Chester, England 15-19 August 1988*

**Author**: Allan I. Solomon

**Publisher:**World Scientific Publishing Company

**ISBN:**9789971508364

**Category:**Mathematics

**Page:**367

**View:**2678

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## Abstracts of Papers Presented to the American Mathematical Society

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**4960

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## Bulletin (new series) of the American Mathematical Society

**Author**: American Mathematical Society

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**9117

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## Journal of the Korean Mathematical Society

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**1238

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## Bulletin of the American Mathematical Society

**Author**: American Mathematical Society

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**415

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## Notices of the American Mathematical Society

**Author**: American Mathematical Society

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**8019

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## A Splitting Formula for Spectral Flow on Closed 3-manifolds

**Author**: Benjamin Himpel

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**246

**View:**1935

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## Lectures on geometric variational problems

**Author**: Seiki Nishikawa,Richard M. Schoen

**Publisher:**Springer Verlag

**ISBN:**9784431701521

**Category:**Mathematics

**Page:**154

**View:**572

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The field of geometric variational problems, that is, nonlinear problems arising in geometry and topology from the point of view of global analysis, has developed very rapidly in the last decade. It was therefore felt timely to produce a set of presentations on this subject in which leading experts would provide general survey of current research from the fundamentals to the most recent results with a view to future research. This volume will interest both mature researchers and graduate students concerned with gauge theory and low dimensional topology, theory of harmonic maps, and minimal surfaces and minimal submanifolds in Riemannian manifolds.

## Mathematical Reviews

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**7251

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## Minimizing P-harmonic Maps Into Projective Space

**Author**: Preston Nichols

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**268

**View:**6869

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## Nonlinear Dispersive Equations

*Local and Global Analysis*

**Author**: Terence Tao

**Publisher:**American Mathematical Soc.

**ISBN:**9780821889503

**Category:**Mathematics

**Page:**373

**View:**1412

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"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

## Das BUCH der Beweise

**Author**: Martin Aigner,Günter M. Ziegler

**Publisher:**Springer-Verlag

**ISBN:**3642022596

**Category:**Mathematics

**Page:**312

**View:**1545

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Die Sammlung eleganter mathematischer Beweise wurde für die 3. Auflage deutlich erweitert: In fünf neuen Kapiteln präsentieren die Autoren Klassiker wie den Fundamentalsatz der Algebra, kombinatorisch-geometrische Zerlegungsprobleme, aber auch Beweise aus jüngster Zeit, etwa den für die Kneser-Vermutung in der Graphentheorie. Die Neuausgabe wartet noch mit weiteren Verbesserungen und Überraschungen auf - darunter einem neuen Beweis für Hilberts Drittes Problem.