Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download On The Smooth Structures Of Elliptic Surfaces And Irreducible Four Manifolds PDF full book. Access full book title On The Smooth Structures Of Elliptic Surfaces And Irreducible Four Manifolds.
| Author | : Zoltán Szabó |
| Publisher | : |
| Total Pages | : 116 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : Robert Friedman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 532 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662030284 |
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
| Author | : Robert E. Gompf |
| Publisher | : American Mathematical Society |
| Total Pages | : 576 |
| Release | : 2023-08-10 |
| Genre | : Mathematics |
| ISBN | : 1470474557 |
Since the early 1980s, there has been an explosive growth in 4-manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. This book offers an exposition of the subject from the topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature. Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research. Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in-depth treatments of a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. The authors present many important applications. The text is supplemented with over 300 illustrations and numerous exercises, with solutions given in the book. I greatly recommend this wonderful book to any researcher in 4-manifold topology for the novel ideas, techniques, constructions, and computations on the topic, presented in a very fascinating way. I think really that every student, mathematician, and researcher interested in 4-manifold topology, should own a copy of this beautiful book. —Zentralblatt MATH This book gives an excellent introduction into the theory of 4-manifolds and can be strongly recommended to beginners in this field … carefully and clearly written; the authors have evidently paid great attention to the presentation of the material … contains many really pretty and interesting examples and a great number of exercises; the final chapter is then devoted to solutions of some of these … this type of presentation makes the subject more attractive and its study easier. —European Mathematical Society Newsletter
| Author | : Robert Friedman, John W. Morgan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 236 |
| Release | : |
| Genre | : Four-manifolds (Topology). |
| ISBN | : 9780821886861 |
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
| Author | : Alexandru Scorpan |
| Publisher | : American Mathematical Society |
| Total Pages | : 614 |
| Release | : 2022-01-26 |
| Genre | : Mathematics |
| ISBN | : 1470468611 |
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 | : Robert Friedman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 233 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821805916 |
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
| Author | : Robert Friedman |
| Publisher | : |
| Total Pages | : 536 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662030295 |
| Author | : John W. Morgan |
| Publisher | : Princeton University Press |
| Total Pages | : 140 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 9780691025971 |
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.
| Author | : Robion C. Kirby |
| Publisher | : Springer |
| Total Pages | : 114 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354046171X |
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.
| Author | : Tolga Etgü |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 2002 |
| Genre | : |
| ISBN | : |
