The Geometry Of Four Manifolds
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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 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.
The Geometry Of Four Manifolds
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Author : S. K. Donaldson
language : en
Publisher:
Release Date : 2023
The Geometry Of Four Manifolds written by S. K. Donaldson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Four-manifolds (Topology) categories.
The Wild World Of 4 Manifolds
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Author : Alexandru Scorpan
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-26
The Wild World Of 4 Manifolds written by Alexandru Scorpan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-26 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.
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
Smooth Four Manifolds And Complex Surfaces
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Author : Robert Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Smooth Four Manifolds And Complex Surfaces written by Robert Friedman 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 2013-03-09 with Mathematics categories.
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.
Connections Definite Forms And Four Manifolds
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Author : Ted Petrie
language : en
Publisher: Oxford University Press on Demand
Release Date : 1990
Connections Definite Forms And Four Manifolds written by Ted Petrie and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Connections (Mathematics) categories.
The central theme of this book is the study of the relationship between the geometry and topology of four-manifolds. The authors adopt a topologists' perspective and present a lucid introduction to moduli space techniques, and then apply them to four-manifolds.
Gauge Theory And The Topology Of Four Manifolds
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Author : Robert Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman 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 1998 with Four-manifolds (Topology). categories.
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
The Topology Of 4 Manifolds
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Author : Robion C. Kirby
language : en
Publisher: Springer
Release Date : 2006-11-14
The Topology Of 4 Manifolds written by Robion C. Kirby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Smooth Four Manifolds And Complex Surfaces
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Author : Robert Friedman
language : en
Publisher:
Release Date : 2014-01-15
Smooth Four Manifolds And Complex Surfaces 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 2014-01-15 with categories.
Instantons And Four Manifolds
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Author : Daniel Freed
language : en
Publisher: Springer
Release Date : 1984-08-24
Instantons And Four Manifolds written by Daniel Freed and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-08-24 with Mathematics categories.
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.