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Surgery Theory And Geometry Of Representations
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Book Synopsis Surgery Theory and Geometry of Representations by : T. tom Dieck
Download or read book Surgery Theory and Geometry of Representations written by T. tom Dieck and published by Birkhäuser. This book was released on 2012-12-06 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were prepared for the DMV-Seminar held in Dusseldorf, Schloss Mickeln from June 28 to July 5, 1987. They consist of two parts which can be read independently. The reader is presumed to have a basic education in differential and algebraic topology. Surgery theory is the basic tool for the investigation of differential and topological manifolds. A systematic development of the theory is a long and difficult task. The purpose of these notes is to describe simple examples and at the same time to give an introduction to some of the systematic parts of the theory. The first part is concerned with examples. They are related to representations of finite groups and group actions on spheres, and are considered as a generalisation of the spherical space form problem. The second part reviews the general setting of surgery theory and reports on the computation of the surgery abstraction groups. Both parts present material not covered in any textbook and also give an introduction to the literature and areas of research. 1. REPRESENTATION FORMS AND HOMOTOPY REPRESENTATIONS. Tammo tom Dieck Mathematical Institute Gottingen University Fed. Rep. of Germany Let G be a (finite) group. We consider group actions of G on spheres and spherelike spaces.
Book Synopsis A Course on Surgery Theory by : Stanley Chang
Download or read book A Course on Surgery Theory written by Stanley Chang and published by Princeton University Press. This book was released on 2021-01-26 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, A Course on Surgery Theory serves as an important resource for the mathematics community.
Book Synopsis Algebraic and Geometric Surgery by : Andrew Ranicki
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.
Book Synopsis Surgery on Compact Manifolds by : Charles Terence Clegg Wall
Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
Book Synopsis Geometry and Representation Theory of Real and P-Adic Groups by : Juan Tirao
Download or read book Geometry and Representation Theory of Real and P-Adic Groups written by Juan Tirao and published by . This book was released on 1997-11-18 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry and Topology of Coxeter Groups by : Michael Davis
Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis and published by Princeton University Press. This book was released on 2008 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
Book Synopsis Handbook of Geometric Topology by : R.B. Sher
Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Book Synopsis Geometry and Topology of Manifolds by : Hans U. Boden
Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on 2005 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Book Synopsis The Interaction of Geometry and Representation Theory. Exploring New Frontiers by :
Download or read book The Interaction of Geometry and Representation Theory. Exploring New Frontiers written by and published by . This book was released on 2014 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Surgery on Simply-Connected Manifolds by : William Browder
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.
Book Synopsis Lectures on Vanishing Theorems by : Esnault
Download or read book Lectures on Vanishing Theorems written by Esnault and published by Springer Science & Business Media. This book was released on 1992-12-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre's GAGA-theorems [56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p > 0 some additional assumptions were needed. This was the state of the art until P. Deligne and 1. Illusie [12J proved the degeneration of the Hodge to de Rham spectral sequence for projective manifolds X defined over a field k of characteristic p > 0 and liftable to the second Witt vectors W2(k). Standard degeneration arguments allow to deduce the degeneration of the Hodge to de Rham spectral sequence in characteristic zero, as well, a re sult which again could only be obtained by analytic and differential geometric methods beforehand. As a corollary of their methods M. Raynaud (loc. cit.) gave an easy proof of Kodaira vanishing in all characteristics, provided that X lifts to W2(k).
Book Synopsis The Topological Classification of Stratified Spaces by : Shmuel Weinberger
Download or read book The Topological Classification of Stratified Spaces written by Shmuel Weinberger and published by University of Chicago Press. This book was released on 1994 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Book Synopsis Introduction to Coding Theory and Algebraic Geometry by : J. van Lint
Download or read book Introduction to Coding Theory and Algebraic Geometry written by J. van Lint and published by Birkhäuser. This book was released on 2012-12-06 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Book Synopsis Nonlinear Methods in Riemannian and Kählerian Geometry by : Jürgen Jost
Download or read book Nonlinear Methods in Riemannian and Kählerian Geometry written by Jürgen Jost and published by Birkhäuser. This book was released on 2013-11-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps between Riemannian and Kählerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kähler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can Iead to very signifi cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones.
Book Synopsis Homotopy Theory and Models by : Marc Aubry
Download or read book Homotopy Theory and Models written by Marc Aubry and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].
Book Synopsis Current Trends in Transformation Groups by : Anthony Bak
Download or read book Current Trends in Transformation Groups written by Anthony Bak and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.
