Surgery Theory And Geometry Of Representations PDF Download
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| Author | : T. tom Dieck |
| Publisher | : Birkhäuser |
| Total Pages | : 121 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034891679 |
Download Surgery Theory and Geometry of Representations Book in PDF, ePub and Kindle
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.
| Author | : Stanley Chang |
| Publisher | : Princeton University Press |
| Total Pages | : 442 |
| Release | : 2021-01-26 |
| Genre | : MATHEMATICS |
| ISBN | : 069116049X |
Download A Course on Surgery Theory Book in PDF, ePub and Kindle
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.
| Author | : Andrew Ranicki |
| Publisher | : Oxford University Press |
| Total Pages | : 396 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780198509240 |
Download Algebraic and Geometric Surgery Book in PDF, ePub and Kindle
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.
| Author | : Charles Terence Clegg Wall |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 321 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821809423 |
Download Surgery on Compact Manifolds Book in PDF, ePub and Kindle
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.
| Author | : Michael Davis |
| Publisher | : Princeton University Press |
| Total Pages | : 601 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0691131384 |
Download The Geometry and Topology of Coxeter Groups Book in PDF, ePub and Kindle
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.
| Author | : R.B. Sher |
| Publisher | : Elsevier |
| Total Pages | : 1145 |
| Release | : 2001-12-20 |
| Genre | : Mathematics |
| ISBN | : 0080532853 |
Download Handbook of Geometric Topology Book in PDF, ePub and Kindle
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.
| Author | : Hans U. Boden |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821837249 |
Download Geometry and Topology of Manifolds Book in PDF, ePub and Kindle
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.
| Author | : William Browder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 141 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364250020X |
Download Surgery on Simply-Connected Manifolds Book in PDF, ePub and Kindle
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.
| Author | : Ana Cannas da Silva |
| Publisher | : Springer |
| Total Pages | : 240 |
| Release | : 2004-10-27 |
| Genre | : Mathematics |
| ISBN | : 354045330X |
Download Lectures on Symplectic Geometry Book in PDF, ePub and Kindle
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.
| Author | : |
| Publisher | : |
| Total Pages | : 298 |
| Release | : 2014 |
| Genre | : |
| ISBN | : |
Download The Interaction of Geometry and Representation Theory. Exploring New Frontiers Book in PDF, ePub and Kindle
