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Author: William Browder
Publisher: Springer Science & Business Media
ISBN: 364250020X
Category : Mathematics
Languages : en
Pages : 141
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Book Description
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: William Browder
Publisher:
ISBN:
Category : Differential topology
Languages : en
Pages : 372
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Book Description
Author: William Browder
Publisher: Springer Science & Business Media
ISBN: 364250020X
Category : Mathematics
Languages : en
Pages : 141
Get Book Here
Book Description
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: Charles Terence Clegg Wall
Publisher: American Mathematical Soc.
ISBN: 0821809423
Category : Mathematics
Languages : en
Pages : 321
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Book Description
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: Stanley Chang
Publisher: Princeton University Press
ISBN: 0691200351
Category : Mathematics
Languages : en
Pages : 472
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Book Description
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: Peter Orlik
Publisher:
ISBN:
Category : Differential topology
Languages : en
Pages : 150
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Book Description
Author: Sylvain Cappell
Publisher: Princeton University Press
ISBN: 9780691088143
Category :
Languages : en
Pages : 452
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Book Description
Author: Ib Madsen
Publisher: Princeton University Press
ISBN: 9780691082264
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.
Author: Laurence R. Taylor
Publisher:
ISBN:
Category :
Languages : en
Pages : 514
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Book Description
Author: Andrew Ranicki
Publisher: Oxford University Press
ISBN: 9780198509240
Category : Mathematics
Languages : en
Pages : 396
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Book Description
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: Burak Ozbagci
Publisher: Springer Science & Business Media
ISBN: 9783540229445
Category : Surfaces
Languages : en
Pages : 292
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Book Description
This book is about an investigation of recent developments in the field of sympletic and contact structures on four and three dimensional manifolds, respectively, from a topologist's point of view. The level of the book is appropriate for advanced graduate students.
