Surveys on Surgery Theory I-II
Author | : |
Publisher | : |
Total Pages | : 436 |
Release | : 2001 |
Genre | : |
ISBN | : |
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Publisher | : |
Total Pages | : 436 |
Release | : 2001 |
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Author | : Sylvain Cappell |
Publisher | : Princeton University Press |
Total Pages | : 445 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0691088152 |
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Author | : Sylvain Cappell |
Publisher | : Princeton University Press |
Total Pages | : 446 |
Release | : 2014-09-08 |
Genre | : Mathematics |
ISBN | : 1400865212 |
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Author | : Sylvain E. Cappell |
Publisher | : |
Total Pages | : 0 |
Release | : 2000 |
Genre | : Surgery (Topology) |
ISBN | : |
Author | : Sylvain E. Cappell |
Publisher | : |
Total Pages | : 436 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780691088143 |
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.
Author | : Sylvain Cappell |
Publisher | : Princeton University Press |
Total Pages | : 448 |
Release | : 2014-09-08 |
Genre | : Mathematics |
ISBN | : 1400865190 |
Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.
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 | : 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 | : Wolfgang Lück |
Publisher | : Springer Nature |
Total Pages | : 956 |
Release | : 2024 |
Genre | : Surgery (Topology) |
ISBN | : 3031563344 |
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
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.