Download or read book Geometry of Low Dimensional Manifolds Volume 2 written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1991-01-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.
Download or read book Low Dimensional Geometry written by Francis Bonahon and published by American Mathematical Soc.. This book was released on 2009-07-14 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
Download or read book Geometry of Low Dimensional Manifolds Volume 1 Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.
Download or read book Flows on 2 dimensional Manifolds written by Igor Nikolaev and published by Springer Science & Business Media. This book was released on 1999-07-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Download or read book Selected Applications of Geometry to Low Dimensional Topology written by Michael H. Freedman and published by American Mathematical Soc.. This book was released on 1990 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.
Download or read book Flows on 2 dimensional Manifolds written by Igor Nikolaev and published by Springer. This book was released on 2006-11-14 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Download or read book Aspects of Low Dimensional Manifolds written by Yukio Matsumoto and published by . This book was released on 1992 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains ten original papers written by leading experts in various areas of low-dimensional topology. The topics covered here are among those showing the most rapid progress in topology today: knots and links, three-dimensional hyperbolic geometry, conformally flat structures on three-manifolds, Floer homology, and the geometry and topology of four-manifolds. Offering both original results and up-to-date survey papers, Aspects of Low Dimensional Manifolds will interest mathematicians, physicists, graduate students, and others seeking a good introduction to the field.
Download or read book Geometry of Low Dimensional Manifolds 2 written by Donaldson/Thomas and published by . This book was released on 2014-05-14 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.
Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Download or read book Geometry of Low Dimensional Manifolds written by S. K. Donaldson and published by . This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry and mathematical physics). The workshop brought together a number of distinguished figures to give lecture courses and seminars in these subjects; the volume that has resulted is the only expository source for much of the material, and will be essential for all research workers in geometry and mathematical physics.
Download or read book Geometry of Low Dimensional Manifolds Volume 1 Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1991-01-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.
Download or read book Topology of Low Dimensional Manifolds written by R. Fenn and published by . This book was released on 2014-01-15 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups St Andrews 1997 in Bath Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 1999-02-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book contains selected papers from the international conference "Groups St. Andrews 1997 in Bath". The articles are arranged in roughly alphabetical order and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier "Groups St. Andrews" conferences have had a major impact on the development of group theory and these volumes should be equally important.
Download or read book Low Dimensional Topology written by Tomasz Mrowka and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.
Download or read book Topics in Physical Mathematics written by Kishore Marathe and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.
Download or read book Floer Homology Gauge Theory and Low Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).
Download or read book Geometry of Low Dimensional Manifolds written by S. K. Donaldson and published by . This book was released on 2014-05-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.
