Instanton And Four Manifolds PDF Download
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Author | : D. S. Freed |
Publisher | : Springer Science & Business Media |
Total Pages | : 242 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468402587 |
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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.
Author | : Daniel S Freed |
Publisher | : |
Total Pages | : 220 |
Release | : 1990-12-03 |
Genre | : |
ISBN | : 9781461397045 |
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Author | : D. S Freed |
Publisher | : |
Total Pages | : 244 |
Release | : 1984-08-24 |
Genre | : |
ISBN | : 9781468402599 |
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Author | : Daniel S. Freed |
Publisher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461397030 |
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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
Author | : Daniel S. Freed |
Publisher | : |
Total Pages | : 232 |
Release | : 1984 |
Genre | : |
ISBN | : |
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Author | : S. K. Donaldson |
Publisher | : Oxford University Press |
Total Pages | : 464 |
Release | : 1997 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780198502692 |
Download The Geometry of Four-manifolds Book in PDF, ePub and Kindle
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.
Author | : Alexandru Scorpan |
Publisher | : American Mathematical Society |
Total Pages | : 614 |
Release | : 2022-01-26 |
Genre | : Mathematics |
ISBN | : 1470468611 |
Download The Wild World of 4-Manifolds Book in PDF, ePub and Kindle
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.
Author | : Marcos Mariño |
Publisher | : Cambridge University Press |
Total Pages | : 381 |
Release | : 2015-09-03 |
Genre | : Science |
ISBN | : 1107068525 |
Download Instantons and Large N Book in PDF, ePub and Kindle
A highly pedagogical textbook for graduate students, exploring advanced topics of quantum field theory with detailed derivations and worked examples.
Author | : Katrin Wehrheim |
Publisher | : European Mathematical Society |
Total Pages | : 228 |
Release | : 2004 |
Genre | : Compact groups |
ISBN | : 9783037190043 |
Download Uhlenbeck Compactness Book in PDF, ePub and Kindle
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.
Author | : Peter Kronheimer |
Publisher | : |
Total Pages | : 796 |
Release | : 2007-12-20 |
Genre | : Mathematics |
ISBN | : 9780521880220 |
Download Monopoles and Three-Manifolds Book in PDF, ePub and Kindle
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.