A Course On Surgery Theory
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A Course On Surgery Theory
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Author : Stanley Chang
language : en
Publisher: Princeton University Press
Release Date : 2021-01-26
A Course On Surgery Theory written by Stanley Chang and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Mathematics categories.
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.
A Course On Surgery Theory
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Author : Stanley Chang
language : en
Publisher: Princeton University Press
Release Date : 2021-01-26
A Course On Surgery Theory written by Stanley Chang and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with MATHEMATICS categories.
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.
Algebraic And Geometric Surgery
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Author : Andrew Ranicki
language : en
Publisher: Oxford University Press
Release Date : 2002
Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
Surgery On Compact Manifolds
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Author : Charles Terence Clegg Wall
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Surgery On Compact Manifolds written by Charles Terence Clegg Wall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Manifolds (Mathematics). categories.
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.
A Course In Simple Homotopy Theory
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Author : M.M. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course In Simple Homotopy Theory written by M.M. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970. I wrote it because of a strong belief that there should be readily available a semi-historical and geo metrically motivated exposition of J. H. C. Whitehead's beautiful theory of simple-homotopy types; that the best way to understand this theory is to know how and why it was built. This belief is buttressed by the fact that the major uses of, and advances in, the theory in recent times-for example, the s-cobordism theorem (discussed in §25), the use of the theory in surgery, its extension to non-compact complexes (discussed at the end of §6) and the proof of topological invariance (given in the Appendix)-have come from just such an understanding. A second reason for writing the book is pedagogical. This is an excellent subject for a topology student to "grow up" on. The interplay between geometry and algebra in topology, each enriching the other, is beautifully illustrated in simple-homotopy theory. The subject is accessible (as in the courses mentioned at the outset) to students who have had a good one semester course in algebraic topology. I have tried to write proofs which meet the needs of such students. (When a proof was omitted and left as an exercise, it was done with the welfare of the student in mind. He should do such exercises zealously.
Algebraic And Geometric Surgery
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Author : Andrew Ranicki
language : en
Publisher: Clarendon Press
Release Date : 2002-09-26
Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-26 with Mathematics categories.
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, cobordism, 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.
Lectures On Surgical Methods In Rigidity
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Author : F. T. Farrell
language : en
Publisher: Springer Verlag
Release Date : 1996
Lectures On Surgical Methods In Rigidity written by F. T. Farrell and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book is an introduction to the topological rigidity theorem for compact non-positively curved Riemannian manifolds. It contains a quick informal account of the background material from surgery theory and controlled topology prerequesite to this result. It is intended for researchers and advanced graduate students in both differential geometry and topology. This book is the content of a course given by the author at TIFR in 1993.
Surgery On Simply Connected Manifolds
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Author : William Browder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Surgery On Simply Connected Manifolds written by William Browder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Exact Sequences In The Algebraic Theory Of Surgery
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Author : Andrew Ranicki
language : en
Publisher:
Release Date : 1981
Exact Sequences In The Algebraic Theory Of Surgery written by Andrew Ranicki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
The Description for this book, Exact Sequences in the Algebraic Theory of Surgery. (MN-26): , will be forthcoming.
The Knot Book
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Author : Colin Conrad Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Knot Book written by Colin Conrad Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.