Lectures on Hilbert Cube Manifolds PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures on Hilbert Cube Manifolds PDF full book. Access full book title Lectures on Hilbert Cube Manifolds by Thomas A. Chapman. Download full books in PDF and EPUB format.
Author: Thomas A. Chapman
Publisher: American Mathematical Soc.
ISBN: 0821816780
Category : Mathematics
Languages : en
Pages : 145
Get Book
Book Description
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: 0821816780
Category : Mathematics
Languages : en
Pages : 145
Get Book
Book Description
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: 9780821888742
Category : Mathematics
Languages : en
Pages : 148
Get Book
Book Description
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: 9781470408299
Category : Fiber bundles
Languages : en
Pages : 75
Get Book
Book Description
Author: R. Daniel Mauldin
Publisher: Birkhäuser
ISBN: 3319228978
Category : Mathematics
Languages : en
Pages : 322
Get Book
Book Description
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: 0821816799
Category : Mathematics
Languages : en
Pages : 58
Get Book
Book Description
Features notes with sections containing a description of some of the basic constructions and results on symplectic manifolds and lagrangian submanifolds. This title also includes sections dealing with various aspects of the quantization problem, as wel as those giving a feedback of ideas from quantization theory into symplectic geometry itslef.
Author: R. James Milgram
Publisher: American Mathematical Soc.
ISBN: 082181432X
Category : Mathematics
Languages : en
Pages : 422
Get Book
Book Description
Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Author: Bruce Hughes
Publisher: American Mathematical Soc.
ISBN: 0821820699
Category : Mathematics
Languages : en
Pages : 113
Get Book
Book Description
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: 0521576253
Category : Mathematics
Languages : en
Pages : 384
Get Book
Book Description
A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.
Author: Alan Kenneth Jones
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 156
Get Book
Book Description
Author: Eric Friedlander
Publisher: Springer Science & Business Media
ISBN: 354023019X
Category : Mathematics
Languages : en
Pages : 1148
Get Book
Book Description
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.
