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Unknotting Information For 4 Manifolds
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Book Synopsis Unknotting Information for 4-manifolds by : Mathematical Sciences Research Institute (Berkeley, Calif.).
Download or read book Unknotting Information for 4-manifolds written by Mathematical Sciences Research Institute (Berkeley, Calif.). and published by . This book was released on 1985 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Topology of 4-Manifolds by : Robion C. Kirby
Download or read book The Topology of 4-Manifolds written by Robion C. Kirby and published by Springer. This book was released on 2006-11-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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.
Download or read book 4-Manifolds written by Selman Akbulut and published by Oxford University Press. This book was released on 2016-09-22 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.
Book Synopsis The Algebraic Unknotting Number by : Micah Elton Fogel
Download or read book The Algebraic Unknotting Number written by Micah Elton Fogel and published by . This book was released on 1993 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 4-manifolds written by Selman Akbulut and published by Oxford University Press. This book was released on 2016 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.
Book Synopsis A Survey of Knot Theory by : Akio Kawauchi
Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Book Synopsis 4-Manifolds and Kirby Calculus by : Robert E. Gompf
Download or read book 4-Manifolds and Kirby Calculus written by Robert E. Gompf and published by American Mathematical Society. This book was released on 2023-08-10 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Chern-Simons Gauge Theory: 20 Years After by : Jørgen E. Andersen
Download or read book Chern-Simons Gauge Theory: 20 Years After written by Jørgen E. Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
Book Synopsis Low Dimensional Topology by : Hanna Nencka
Download or read book Low Dimensional Topology written by Hanna Nencka and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book has two main parts. The first is devoted to the Poincare conjecture, characterizations of PL-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory.
Download or read book Knots 90 written by Akio Kawauchi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsváth
Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Book Synopsis Aspects of Low Dimensional Manifolds by : Yukio Matsumoto
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.
Book Synopsis The Knot Book by : Colin Conrad Adams
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Book Synopsis Grids as Unknotting Operations by : Nikos Askitas
Download or read book Grids as Unknotting Operations written by Nikos Askitas and published by . This book was released on 1997 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Embeddings in Manifolds by : Robert J. Daverman
Download or read book Embeddings in Manifolds written by Robert J. Daverman and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.
Book Synopsis Bordered Heegaard Floer Homology by : Robert Lipshitz
Download or read book Bordered Heegaard Floer Homology written by Robert Lipshitz and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
