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Author : Steve Armentrout
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 47,6 Mb
Release : 1971
Category : Decomposition (Mathematics)
ISBN : 9780821818077
Author : Anonim
Publisher : Academic Press
Page : 316 pages
File Size : 51,6 Mb
Release : 1986-12-22
Category : Mathematics
ISBN : 0080874436
Decompositions of Manifolds
Author : A Banyaga,H Movahedi-Lankarani,R Wells
Publisher : World Scientific
Page : 136 pages
File Size : 52,7 Mb
Release : 1999-10-15
Category : Electronic
ISBN : 9789814543439
Recent success with the four-dimensional Poincaré conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincaré conjecture and other aspects of the problems of classifying three-dimensional manifolds. These problems have a driving force, and have generated a great body of research, as well as insight. The main topics treated in this book include a paper by V Poenaru on the Poincaré conjecture and its ramifications, giving an insight into the herculean work of the author on the subject. Steve Armentrout's paper on “Bing's dogbone space” belongs to the topics in three-dimensional topology motivated by the Poincaré conjecture. S Singh gives a nice synthesis of Armentrout's work. Also included in the volume are shorter original papers, dealing with somewhat different aspects of geometry, and dedicated to Armentrout by his colleagues — Augustin Banyaga (and Jean-Pierre Ezin), David Hurtubise, Hossein Movahedi-Lankarani and Robert Wells. Contents: Mathematics of Steve Armentrout: A Review (S Singh)Bing's Dogbone Space Is Not Strongly Locally Simply Connected (S Armentrout)A Program for the Poincaré Conjecture and Some of Its Ramifications (V Poénaru)On the Foundation of Geometry, Analysis, and the Differentiable Structure for Manifolds (D Sullivan)A Conformal Invariant Characterizing the Sphere (A Banyaga & J-P Ezin)Spaces of Holomorphic Maps from ∀P1 to Complex Grassmann Manifolds (D E Hurtubise)Sets with Lie Isometry Groups (H Movahedi-Lankarani & R Wells) Readership: Researchers in mathematics and physics. Keywords:Poincare Conjecture;Topology;Holomorphic Maps;Complex Grassmann Manifolds;Lie Isometry Groups
Author : Robert J. Daverman,Gerard Venema
Publisher : American Mathematical Soc.
Page : 496 pages
File Size : 48,7 Mb
Release : 2009-10-14
Category : Mathematics
ISBN : 9780821836972
A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.
Author : CAMERON AUTOR GORDON,Cameron Gordon
Publisher : American Mathematical Soc.
Page : 528 pages
File Size : 49,6 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821850336
These are the proceedings of the Summer Research Conference on 4-manifolds held at Durham, New Hampshire, July 1982, under the auspices of the American Mathematical Society and National Science Foundation. The conference was highlighted by the breakthroughs of Michael Freedman and S. K. Donaldson and by Frank Quinn's completion at the conference of the proof of the annulus conjecture. (We commend the AMS committee, particularly Julius Shaneson, who had the foresight in Spring 1981 to choose the subject, 4-manifolds, in which such remarkable activity was imminent.) Freedman and several others spoke on his work; some of their talks are represented by papers in this volume. Donaldson and Clifford H. Taubes gave surveys of their work on gauge theory and 4-manifolds and their papers are also included herein. There were a variety of other lectures, including Quinn's surprise, and a couple of problem sessions which led to the problem list. A background of basic differential topology is adequate for potential readers.
Author : R. H. Bing,Ralph J. Bean
Publisher : Princeton University Press
Page : 256 pages
File Size : 47,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882076
During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincaré on the Poincaré conjectures, and sketching a proof of Haken's main result.
Author : Anonim
Publisher : Unknown
Page : 1032 pages
File Size : 49,5 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:49015003188381
Author : L.C. Glaser,T.B. Rushing
Publisher : Springer
Page : 472 pages
File Size : 49,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540374121
Author : K.P. Hart,Jun-iti Nagata,J.E. Vaughan
Publisher : Elsevier
Page : 536 pages
File Size : 45,8 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 0080530869
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published • Short and informative articles • Authors include the majority of top researchers in the field • Extensive indexing of terms
Author : R. Daniel Mauldin
Publisher : Birkhäuser
Page : 322 pages
File Size : 43,5 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319228976
The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of Wrocław’s New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read.
Author : American Mathematical Society
Publisher : Unknown
Page : 1646 pages
File Size : 49,6 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B3970570
Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.
Author : James C. Cantrell
Publisher : Elsevier
Page : 712 pages
File Size : 55,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483271316
Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.
Author : Anonim
Publisher : Academic Press
Page : 315 pages
File Size : 50,5 Mb
Release : 1973-03-30
Category : Mathematics
ISBN : 0080873677
Topological Embeddings
Author : Library of Congress. Copyright Office
Publisher : Copyright Office, Library of Congress
Page : 1040 pages
File Size : 50,9 Mb
Release : 1973
Category : Copyright
ISBN : STANFORD:36105119497647
Author : R. H. Bing
Publisher : American Mathematical Soc.
Page : 1702 pages
File Size : 46,5 Mb
Release : 1988
Category : Mathematics
ISBN : 0821810472
A powerful mathematician and a great problem solver, R. H. Bing laid the foundation for a number of areas of topology. Many of his papers have continued to serve as a source of major theoretical developments and concrete applications in recent years. One outstanding example was Michael H. Freedman's use of Bing's Shrinking Criterion to solve the four-dimensional Poincaré Conjecture. This two-volume set brings together over one hundred of Bing's research, expository, andmiscellaneous papers. These works range over a great variety of topics in topology, including the topology of manifolds, decomposition spaces, continua, metrization, general topology, and geometric topology. In addition, there are a number of papers in the areas of convex functions, linearity, and conformalvarieties. The introductory section in the first volume provides historical background on Bing's life and achievements. This collection will appeal to mathematicians in all areas, and especially those in topology, as well as students, historians, and educators in the mathematical sciences, for it provides a complete historical summary of the mathematical events in the life of the man and the mathematician, R. H. Bing.