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| Author | : Charles Terence Clegg Wall |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 321 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821809423 |
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 | : C. T. Wall |
| Publisher | : Academic Press |
| Total Pages | : 280 |
| Release | : 1970 |
| Genre | : Manifolds (Mathematics) |
| ISBN | : 9780127327501 |
| Author | : Charles T. C. Wall |
| Publisher | : |
| Total Pages | : 280 |
| Release | : 1976 |
| Genre | : Manifolds (Mathematics) |
| ISBN | : |
| Author | : William Browder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 141 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 364250020X |
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 | : Richard Walter Sharpe |
| Publisher | : |
| Total Pages | : 66 |
| Release | : 1971 |
| Genre | : Manifolds (Mathematics) |
| ISBN | : |
| Author | : Richard W. Sharpe |
| Publisher | : |
| Total Pages | : 64 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
| Author | : Stanley Chang |
| Publisher | : Princeton University Press |
| Total Pages | : 442 |
| Release | : 2021-01-26 |
| Genre | : MATHEMATICS |
| ISBN | : 069116049X |
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 | : Burak Ozbagci |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 279 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 366210167X |
This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.
| Author | : Andrew Ranicki |
| Publisher | : Oxford University Press |
| Total Pages | : 396 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780198509240 |
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 | : Andrew Ranicki |
| Publisher | : Cambridge University Press |
| Total Pages | : 372 |
| Release | : 1992-12-10 |
| Genre | : Mathematics |
| ISBN | : 9780521420242 |
Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
