Download or read book High dimensional Manifold Topology written by R. T. Farrell and published by World Scientific. This book was released on 2003 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.
Download or read book High dimensional Manifold Topology Proceedings Of The School written by F Thomas Farrell and published by World Scientific. This book was released on 2003-10-17 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.)Equivariant Cellular Homology and Its Applications (B Chorny)Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.)Chain Complex Invariants for Group Actions (L E Jones)The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.)The Surgery Exact Sequence Revisited (E K Pedersen)K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer)Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz)and other papers Readership: Graduate students and researchers in geometry and topology. Keywords:High-Dimensional Manifold Topology;Operator Algebras;K-Theory;L-Theory;Foliated Control Theory
Download or read book High dimensional Manifold Topology written by Abdus Salam International Centre for Theoretical Physics and published by World Scientific. This book was released on 2003 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.); Equivariant Cellular Homology and Its Applications (B Chorny); Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.); Chain Complex Invariants for Group Actions (L E Jones); The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.); The Surgery Exact Sequence Revisited (E K Pedersen); K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer); Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schütz); and other papers;
Download or read book Higher dimensional Generalized Manifolds written by Alberto Cavicchioli and published by . This book was released on 2016 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces. (This is now called the manifold recognition problem.) As such, generalized manifolds have served to enhance our understanding of the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself. A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful. Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds. This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on the authors' graduate courses and seminars, as well as their talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology.
Download or read book 2019 20 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2021-02-10 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Download or read book Topology of Infinite Dimensional Manifolds written by Katsuro Sakai and published by Springer Nature. This book was released on 2020-11-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.
Download or read book Introductory Lectures on Manifold Topology written by Thomas Farrell and published by . This book was released on 2014-04-25 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1950s, many new ideas and tools from algebra, and algebraic and geometric topology, have been applied to study the structure of high-dimensional differential and topological manifolds, and so today it can be difficult for beginners to delve through the literature. This volume is a helpful guide to the basic concepts and results of topology of manifolds -- including the h- and s-cobordism theorems, topological invariance of rational Pontryagin classes, surgery theory, and algebraic K-theory
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 Algebraic and Geometric Surgery written by Andrew Ranicki and published by Oxford University Press. This book was released on 2002 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
Download or read book Topology of High dimensional Manifolds written by F. Thomas Farrell and published by . This book was released on 2002 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.
Download or read book How Surfaces Intersect in Space written by J. Scott Carter and published by World Scientific. This book was released on 1995 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
Download or read book High dimensional Knot Theory written by Andrew Ranicki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
Download or read book Topology of Low Dimensional Manifolds written by R. Fenn and published by Springer. This book was released on 2006-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surgery on Simply Connected Manifolds written by William Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of the technique of surgery on simply-connected smooth manifolds. Systematic study of differentiable manifolds using these ideas was begun by Milnor [45] and Wallace [68] and developed extensively in the last ten years. It is now possible to give a reasonably complete theory of simply-connected manifolds of dimension ~ 5 using this approach and that is what I will try to begin here. The emphasis has been placed on stating and proving the general results necessary to apply this method in various contexts. In Chapter II, these results are stated, and then applications are given to characterizing the homotopy type of differentiable manifolds and classifying manifolds within a given homotopy type. This theory was first extensively developed in Kervaire and Milnor [34] in the case of homotopy spheres, globalized by S. P. Novikov [49] and the author [6] for closed 1-connected manifolds, and extended to the bounded case by Wall [65] and Golo [23]. The thesis of Sullivan [62] reformed the theory in an elegant way in terms of classifying spaces.
Download or read book Smooth Four Manifolds and Complex Surfaces written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
