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: C. T. C. Wall
Publisher: American Mathematical Society
ISBN: 1470479133
Category : Mathematics
Languages : en
Pages : 321
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Book Description
The publication of this book in 1970 marked the culmination of a particularly exciting period in the history of the topology of manifolds. The world of high-dimensional manifolds had been opened up to the classification methods of algebraic topology by Thom's work in 1952 on transversality and cobordism, the signature theorem of Hirzebruch in 1954, and by the discovery of exotic spheres by Milnor in 1956. In the 1960s, there had been an explosive growth of interest in the surgery method of understanding the homotopy types of manifolds (initially in the differentiable category), including results such as the $h$-cobordism theory of Smale (1960), the classification of exotic spheres by Kervaire and Milnor (1962), Browder's converse to the Hirzebruch signature theorem for the existence of a manifold in a simply connected homotopy type (1962), the $s$-cobordism theorem of Barden, Mazur, and Stallings (1964), Novikov's proof of the topological invariance of the rational Pontrjagin classes of differentiable manifolds (1965), the fibering theorems of Browder and Levine (1966) and Farrell (1967), Sullivan's exact sequence for the set of manifold structures within a simply connected homotopy type (1966), Casson and Sullivan's disproof of the Hauptvermutung for piecewise linear manifolds (1967), Wall's classification of homotopy tori (1969), and Kirby and Siebenmann's classification theory of topological manifolds (1970). The original edition of the book fulfilled five purposes by providing: • a coherent framework for relating the homotopy theory of manifolds to the algebraic theory of quadratic forms, unifying many of the previous results; • a surgery obstruction theory for manifolds with arbitrary fundamental group, including the exact sequence for the set of manifold structures within a homotopy type, and many computations; • the extension of surgery theory from the differentiable and piecewise linear categories to the topological category; • a survey of most of the activity in surgery up to 1970; • a setting for the subsequent development and applications of the surgery classification of manifolds. This new edition of this classic book is supplemented by notes on subsequent developments. References have been updated and numerous commentaries have been added. The volume remains the single most important book on surgery theory.
Author: Stanley Chang
Publisher: Princeton University Press
ISBN: 069116049X
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and respected series in science published, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. Book jacket.
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: Christopher Lawrence
Publisher: Routledge
ISBN: 0429670710
Category : History
Languages : en
Pages : 437
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Book Description
Originally published in 1992, Medical Theory, Surgical Practice examines medical and surgical concepts of disease and their relation to the practice of surgery, in particular historical settings. It emphasises that understanding concepts of disease does not just include recounting explicit accounts of disease given by medical men. It needs an analysis of the social relations embedded in such concepts. In doing this, the contributors illustrate how surgery rose from a relatively humble place in seventeenth century life to being seen as one of the great achievements of late Victorian culture. They examine how medical theory and surgical practices relate to social contexts, how physical diagnosis entered medicine and whether anaesthesia and Lister’s antiseptic techniques really did cause a revolution in surgical practice.
Author: Stanley Chang
Publisher: Princeton University Press
ISBN: 0691200351
Category : Mathematics
Languages : en
Pages : 443
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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: Andrew Ranicki
Publisher: Springer Science & Business Media
ISBN: 3662120119
Category : Mathematics
Languages : en
Pages : 669
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Book Description
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.
Author: Frederick S. Brightbill
Publisher:
ISBN:
Category : Medical
Languages : en
Pages : 1016
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Book Description
The latest surgical techniques in ophthalmology today are presented in this comprehensive, clinically relevant overview of cornea surgery. CORNEAL SURGERY covers every aspect of diagnosis and surgical management of the diseased cornea--with special emphasis on refractive surgery. A 48-page color insert illustrates diagnostic topography, surgical procedures and disease entities with 180 superb photographs. An additional section on eye-banking makes this book the complete reference for the practicing ophthalmologist as well as the corneal specialist. * Provides state of the art coverage and complete clinical information on corneal surgery. * Includes information from more than 180 recognized experts writing on the most frequently used corneal surgery techniques. * Provides a 48-page color insert which feature 180 photographs that clearly show topography, surgical procedures and disease entities. * Features unique, comprehensive eye-banking section.
Author: Nobuhiko Isshiki
Publisher: Springer Science & Business Media
ISBN: 4431683585
Category : Medical
Languages : en
Pages : 236
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Book Description
"Phonosurgery: theory and practice" is a book that makes an impor tant contribution to the literature in laryngology. Professor Isshiki has been a driving force in the investigation and correction of certain conditions of the voice. His leadership in this field over two decades has proved to be an inspiration to those interested in the diagnosis and correction of the abnormal voice. His unique background and training in both otolaryngology and plastic surgery has provided him with fundamental knowledge and experience in the study of the voice and larynx and has given him an opportunity to utilize innovative surgical techniques in the correction of some of these problems. Professor Isshiki's name is indelibly linked with laryngeal framework surgery, and those who read this book will not be dis appointed. The book provides very adequate information on the phy siology and pathology of the voice. Emphasis is given to diagnostic aspects of abnormalities of the voice which have been made easier with the development of high technology, such as the use of the com puter and improved laryngoscopes, which include brighter lights, higher resolution lenses, and, when combined with stroboscopy and high-speed filming videolaryngoscopy, provide a valuable tool in faci litating communication between the patient, the physician, and the voice therapist.
Author: Frederick S. Brightbill
Publisher: Elsevier Health Sciences
ISBN: 0323048358
Category : Medical
Languages : en
Pages : 970
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Book Description
Part. 1 Introduction to corneal function and surgery -- Part. 2 Testing and measuring corneal function -- Part. 3 Ocular surface surgery and reconstruction -- Part. 4 Techniques in corneal transplantation -- Part. 5 Special situations in corneal surgery -- Part. 6 Surgical correction of refractive errors.
