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Author : Colin Patrick Rourke
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (127 download)
Download or read book The Hauptvermutung According to Sullivan written by Colin Patrick Rourke and published by . This book was released on 1968 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George E. Cooke
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (11 download)
Download or read book On the Hauptvermutung According to Sullivan written by George E. Cooke and published by . This book was released on 1968 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.A. Ranicki
Publisher : Springer Science & Business Media
ISBN 13 : 9401733430
Total Pages : 192 pages
Book Rating : 4.4/5 (17 download)
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.
Author : Robion C. Kirby
Publisher : Princeton University Press
ISBN 13 : 1400881501
Total Pages : 368 pages
Book Rating : 4.4/5 (8 download)
Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 written by Robion C. Kirby and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 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.
Author : Stanley Chang
Publisher : Princeton University Press
ISBN 13 : 0691200351
Total Pages : 472 pages
Book Rating : 4.6/5 (912 download)
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 472 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.
Author : N. H. Kuiper
Publisher : Springer
ISBN 13 : 3540366539
Total Pages : 240 pages
Book Rating : 4.5/5 (43 download)
Download or read book Manifolds - Amsterdam 1970 written by N. H. Kuiper and published by Springer. This book was released on 2006-11-15 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Frank Adams
Publisher : Cambridge University Press
ISBN 13 : 0521203546
Total Pages : 137 pages
Book Rating : 4.5/5 (212 download)
Download or read book New Developments in Topology written by John Frank Adams and published by Cambridge University Press. This book was released on 1974-02-28 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond with the original talks, as it was the intention of the volume editor to make this book of mathematical rather than historical interest. The contributions will be of value to workers in topology in universities and polytechnics.
Author : Dennis P. Sullivan
Publisher : Springer
ISBN 13 : 9789048103508
Total Pages : 286 pages
Book Rating : 4.1/5 (35 download)
Download or read book Geometric Topology: Localization, Periodicity and Galois Symmetry written by Dennis P. Sullivan and published by Springer. This book was released on 2009-09-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
Author : Charles Terence Clegg Wall
Publisher : American Mathematical Soc.
ISBN 13 : 0821809423
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)
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.
Author :
Publisher :
ISBN 13 :
Total Pages : 706 pages
Book Rating : 4.:/5 (318 download)
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1975 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sylvain Cappell
Publisher : Princeton University Press
ISBN 13 : 1400865190
Total Pages : 448 pages
Book Rating : 4.4/5 (8 download)
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.
Author : I.M. James
Publisher : Elsevier
ISBN 13 : 0080534074
Total Pages : 1067 pages
Book Rating : 4.0/5 (85 download)
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Author : J. L. Dupont
Publisher : Springer
ISBN 13 : 3540385207
Total Pages : 705 pages
Book Rating : 4.5/5 (43 download)
Download or read book Algebraic Topology, Aarhus 1978 written by J. L. Dupont and published by Springer. This book was released on 2006-11-15 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: University of Aarhus, 50. Anniversary, 11 September 1978
Author : Yuli RUDYAK
Publisher : World Scientific
ISBN 13 : 9814733792
Total Pages : 129 pages
Book Rating : 4.8/5 (147 download)
Download or read book Piecewise Linear Structures on Topological Manifolds written by Yuli RUDYAK and published by World Scientific. This book was released on 2015-12-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture. The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking."--
Author :
Publisher :
ISBN 13 :
Total Pages : 536 pages
Book Rating : 4.:/5 (36 download)
Download or read book Transactions of the American Mathematical Society written by and published by . This book was released on 1971 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Springer
ISBN 13 :
Total Pages : 476 pages
Book Rating : 4.3/5 (91 download)
Download or read book Proceedings of the Second Conference on Compact Transformation Groups written by and published by Springer. This book was released on 1972 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gerald A. Anderson
Publisher : Springer
ISBN 13 : 354037356X
Total Pages : 165 pages
Book Rating : 4.5/5 (43 download)
Download or read book Surgery with Coefficients written by Gerald A. Anderson and published by Springer. This book was released on 2006-11-14 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
