The Classifying Spaces for Surgery and Cobordism of Manifolds

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Publisher : Princeton University Press
ISBN 13 : 9780691082264
Total Pages : 300 pages
Book Rating : 4.0/5 (822 download)

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Book Synopsis The Classifying Spaces for Surgery and Cobordism of Manifolds by : Ib Madsen

Download or read book The Classifying Spaces for Surgery and Cobordism of Manifolds written by Ib Madsen and published by Princeton University Press. This book was released on 1979-11-21 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Surgery on Simply-Connected Manifolds

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Publisher : Springer Science & Business Media
ISBN 13 : 364250020X
Total Pages : 141 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Surgery on Simply-Connected Manifolds by : William Browder

Download or read book Surgery on Simply-Connected Manifolds written by William Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Surgery on Compact Manifolds

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Publisher : American Mathematical Soc.
ISBN 13 : 0821809423
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Surgery on Compact Manifolds by : Charles Terence Clegg Wall

Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92

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Publisher : Princeton University Press
ISBN 13 : 1400881471
Total Pages : 296 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 by : Ib Madsen

Download or read book Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 written by Ib Madsen and published by Princeton University Press. This book was released on 2016-03-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic and Geometric Surgery

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Publisher : Oxford University Press
ISBN 13 : 9780198509240
Total Pages : 396 pages
Book Rating : 4.5/5 (92 download)

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Book Synopsis Algebraic and Geometric Surgery by : Andrew Ranicki

Download or read book Algebraic and Geometric Surgery written by Andrew Ranicki and published by Oxford University Press. This book was released on 2002 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course on Surgery Theory

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Publisher : Princeton University Press
ISBN 13 : 069116049X
Total Pages : 442 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Course on Surgery Theory by : Stanley Chang

Download or read book A Course on Surgery Theory written by Stanley Chang and published by Princeton University Press. This book was released on 2021-01-26 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 L-theory and Topological Manifolds

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Publisher : Cambridge University Press
ISBN 13 : 9780521420242
Total Pages : 372 pages
Book Rating : 4.4/5 (22 download)

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Book Synopsis Algebraic L-theory and Topological Manifolds by : Andrew Ranicki

Download or read book Algebraic L-theory and Topological Manifolds written by Andrew Ranicki and published by Cambridge University Press. This book was released on 1992-12-10 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classifying Spaces of Sporadic Groups

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Publisher : American Mathematical Soc.
ISBN 13 : 0821844741
Total Pages : 310 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classifying Spaces of Sporadic Groups by : David J. Benson

Download or read book Classifying Spaces of Sporadic Groups written by David J. Benson and published by American Mathematical Soc.. This book was released on 2008 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology.

The Hauptvermutung Book

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Publisher : Springer Science & Business Media
ISBN 13 : 9401733430
Total Pages : 192 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis The Hauptvermutung Book by : A.A. Ranicki

Download or read book The Hauptvermutung Book written by A.A. Ranicki and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hauptvermutung is the conjecture that any two triangulations of a poly hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu tung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sulli van, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an intro duction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc.

Surveys on Surgery Theory (AM-145), Volume 1

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Publisher : Princeton University Press
ISBN 13 : 1400865190
Total Pages : 448 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Surveys on Surgery Theory (AM-145), Volume 1 by : Sylvain Cappell

Download or read book Surveys on Surgery Theory (AM-145), Volume 1 written by Sylvain Cappell and published by Princeton University Press. This book was released on 2014-09-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Equivariant Surgery and Classification of Finite Group Actions on Manifolds

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Publisher : American Mathematical Soc.
ISBN 13 : 0821824422
Total Pages : 132 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Equivariant Surgery and Classification of Finite Group Actions on Manifolds by : Karl Heinz Dovermann

Download or read book Equivariant Surgery and Classification of Finite Group Actions on Manifolds written by Karl Heinz Dovermann and published by American Mathematical Soc.. This book was released on 1988 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we develop an equivariant Sullivan-Wall surgery exact sequence in the category of smooth and locally linear actions of finite groups which satisfy the gap hypothesis. We then apply this machinery to various problems of classifying group actions on manifolds.

Group Actions on Manifolds

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Publisher : American Mathematical Soc.
ISBN 13 : 0821850385
Total Pages : 586 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Group Actions on Manifolds by : Reinhard Schultz

Download or read book Group Actions on Manifolds written by Reinhard Schultz and published by American Mathematical Soc.. This book was released on 1985 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.

Surveys on Surgery Theory (AM-149), Volume 2

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Publisher : Princeton University Press
ISBN 13 : 1400865212
Total Pages : 446 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Surveys on Surgery Theory (AM-149), Volume 2 by : Sylvain Cappell

Download or read book Surveys on Surgery Theory (AM-149), Volume 2 written by Sylvain Cappell and published by Princeton University Press. This book was released on 2014-09-08 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations

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Publisher : Princeton University Press
ISBN 13 : 9780691081915
Total Pages : 376 pages
Book Rating : 4.0/5 (819 download)

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Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations by : Robion C. Kirby

Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations written by Robion C. Kirby and published by Princeton University Press. This book was released on 1977-05-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Topological Invariants of Stratified Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3540385878
Total Pages : 266 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Topological Invariants of Stratified Spaces by : Markus Banagl

Download or read book Topological Invariants of Stratified Spaces written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2007-02-16 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.

The Classifyng Spaces for Surgery and Cobordism of Manifolds

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Publisher :
ISBN 13 :
Total Pages : 279 pages
Book Rating : 4.:/5 (82 download)

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Book Synopsis The Classifyng Spaces for Surgery and Cobordism of Manifolds by : Ib Madesn

Download or read book The Classifyng Spaces for Surgery and Cobordism of Manifolds written by Ib Madesn and published by . This book was released on 1979 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symposium on Algebraic Topology in Honor of Jose Adem

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Publisher : American Mathematical Soc.
ISBN 13 : 0821850105
Total Pages : 374 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Symposium on Algebraic Topology in Honor of Jose Adem by : Samuel Gitler

Download or read book Symposium on Algebraic Topology in Honor of Jose Adem written by Samuel Gitler and published by American Mathematical Soc.. This book was released on 1982 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: