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.
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.
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:
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.
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 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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 113 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.
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.
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:
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.
Download or read book Topology of Infinite Dimensional Manifolds written by Katsuro Sakai and published by Springer Nature. This book was released on 2020-11-21 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology). This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book. Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.
Download or read book Index Theory Coarse Geometry and Topology of Manifolds written by John Roe and published by American Mathematical Soc.. This book was released on 1996 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes from the conference held Aug. 1995 in Boulder, Colo.
Download or read book Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in nu.
Download or read book Decompositions of Manifolds written by and published by Academic Press. This book was released on 1986-12-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decompositions of Manifolds
Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Download or read book Geometric Topology written by James C. Cantrell and published by Elsevier. This book was released on 2014-05-10 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on the Differential Topology of Infinite Dimensional Manifolds written by Richard S. Palais and published by . This book was released on 1965 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
