Lectures On Hilbert Cube Manifolds

Author : Thomas A. Chapman
Publisher : American Mathematical Soc.
ISBN 13 : 0821816780
Total Pages : 145 pages
Book Rating : 4.83/5 ( download)

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Download or read book Lectures on Hilbert Cube Manifolds written by Thomas A. Chapman and published by American Mathematical Soc.. This book was released on 1976 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these lectures is to present an introduction to the geometric topology of the Hilbert cube Q and separable metric manifolds modeled on Q, which are called here Hilbert cube manifolds or Q-manifolds. In the past ten years there has been a great deal of research on Q and Q-manifolds which is scattered throughout several papers in the literature. The author presents here a self-contained treatment of only a few of these results in the hope that it will stimulate further interest in this area. No new material is presented here and no attempt has been made to be complete. For example, the author has omitted the important theorem of Schori-West stating that the hyperspace of closed subsets of $[0,1]$ is homeomorphic to Q.In an appendix (prepared independently by R. D. Anderson, D. W. Curtis, R. Schori and G. Kozlowski) there is a list of problems which are of current interest. This includes problems on Q-manifolds as well as manifolds modeled on various linear spaces. The reader is referred to this for a much broader perspective of the field. In the first four chapters, the basic tools which are needed in all of the remaining chapters are presented. Beyond this there seem to be at least two possible courses of action. The reader who is interested only in the triangulation and classification of Q-manifolds should read straight through (avoiding only Chapter VI). In particular the topological invariance of Whitehead torsion appears in Section 38. The reader who is interested in R. D. Edwards' recent proof that every ANR is a Q-manifold factor should read the first four chapters and then (with the single exception of 26.1) skip over to Chapters XIII and XIV.

Author : Thomas A. Chapman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821888742
Total Pages : 148 pages
Book Rating : 4.49/5 ( download)

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Download or read book Lectures on Hilbert Cube Manifolds written by Thomas A. Chapman and published by American Mathematical Soc.. This book was released on 1976-12-31 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these lectures is to present an introduction to the geometric topology of the Hilbert cube Q and separable metric manifolds modeled on Q, which are called here Hilbert cube manifolds or Q-manifolds. In the past ten years there has been a great deal of research on Q and Q-manifolds which is scattered throughout several papers in the literature. The author presents here a self-contained treatment of only a few of these results in the hope that it will stimulate further interest in this area. No new material is presented here and no attempt has been made to be complete. For example, the author has omitted the important theorem of Schori-West stating that the hyperspace of closed subsets of $[0,1]$ is homeomorphic to Q. In an appendix (prepared independently by R. D. Anderson, D. W. Curtis, R. Schori and G. Kozlowski) there is a list of problems which are of current interest. This includes problems on Q-manifolds as well as manifolds modeled on various linear spaces. The reader is referred to this for a much broader perspective of the field. In the first four chapters, the basic tools which are needed in all of the remaining chapters are presented. Beyond this there seem to be at least two possible courses of action. The reader who is interested only in the triangulation and classification of Q-manifolds should read straight through (avoiding only Chapter VI). In particular the topological invariance of Whitehead torsion appears in Section 38. The reader who is interested in R. D. Edwards' recent proof that every ANR is a Q-manifold factor should read the first four chapters and then (with the single exception of 26.1) skip over to Chapters XIII and XIV.

Author : Henryk Toruńczyk
Publisher :
ISBN 13 : 9781470408299
Total Pages : 75 pages
Book Rating : 4.95/5 ( download)

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Download or read book Fibrations and Bundles with Hilbert Cube Manifold Fibers written by Henryk Toruńczyk and published by . This book was released on 1989 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : R. Daniel Mauldin
Publisher : Birkhäuser
ISBN 13 : 3319228978
Total Pages : 322 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Scottish Book written by R. Daniel Mauldin and published by Birkhäuser. This book was released on 2015-11-26 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alan Weinstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821816799
Total Pages : 48 pages
Book Rating : 4.90/5 ( download)

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Download or read book Lectures on Symplectic Manifolds written by Alan Weinstein and published by American Mathematical Soc.. This book was released on 1977 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first six sections of these notes contain a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. Section 7, on intersections of largrangian submanifolds, is still mostly internal to symplectic geometry, but it contains some applications to machanics and dynamical systems. Sections 8, 9, and 10 are devoted to various aspects of the quantization problem. In Section 10 there is a feedback of ideas from quantization theory into symplectic geometry itslef.

Author : R. James Milgram
Publisher : American Mathematical Soc.
ISBN 13 : 082181432X
Total Pages : 422 pages
Book Rating : 4.21/5 ( download)

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Download or read book Algebraic and Geometric Topology, Part 1 written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.

Author : Bruce Hughes
Publisher : American Mathematical Soc.
ISBN 13 : 0821820699
Total Pages : 96 pages
Book Rating : 4.98/5 ( download)

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Download or read book Control and Relaxation over the Circle written by Bruce Hughes and published by American Mathematical Soc.. This book was released on 2000 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work formulates and proves a geometric version of the fundamental theorem of algebraic K-theory which relates the K-theory of the Laurent polynomial extension of a ring to the K-theory of the ring. The geometric version relates the higher simple homotopy theory of the product of a finite complex and a circle with that of the complex. By using methods of controlled topology, we also obtain a geometric version of the fundamental theorem of lower algebraic K-theory. The main new innovation is a geometrically defined nil space.

Author : Bruce Hughes
Publisher : Cambridge University Press
ISBN 13 : 0521576253
Total Pages : 384 pages
Book Rating : 4.53/5 ( download)

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Download or read book Ends of Complexes written by Bruce Hughes and published by Cambridge University Press. This book was released on 1996-08-28 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.

Author : Alan Kenneth Jones
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.00/5 ( download)

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Download or read book Path Spaces which are Hilbert Cube Manifolds written by Alan Kenneth Jones and published by . This book was released on 1976 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Eric Friedlander
Publisher : Springer Science & Business Media
ISBN 13 : 354023019X
Total Pages : 1148 pages
Book Rating : 4.99/5 ( download)

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Download or read book Handbook of K-Theory written by Eric Friedlander and published by Springer Science & Business Media. This book was released on 2005-07-18 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.