Lectures on Hilbert Cube Manifolds

Lectures on Hilbert Cube Manifolds
Title Lectures on Hilbert Cube Manifolds PDF eBook
Author Thomas A. Chapman
Publisher American Mathematical Soc.
Pages 148
Release 1976-12-31
Genre Mathematics
ISBN 9780821888742

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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.

Lectures on Hilbert Cube Manifolds

Lectures on Hilbert Cube Manifolds
Title Lectures on Hilbert Cube Manifolds PDF eBook
Author Thomas A. Chapman
Publisher American Mathematical Soc.
Pages 145
Release 1976
Genre Mathematics
ISBN 0821816780

Download Lectures on Hilbert Cube Manifolds Book in PDF, Epub and Kindle

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.

Euler Products and Eisenstein Series

Euler Products and Eisenstein Series
Title Euler Products and Eisenstein Series PDF eBook
Author Gorō Shimura
Publisher American Mathematical Soc.
Pages 282
Release 1997
Genre Mathematics
ISBN 0821805746

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This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called well-known. In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.

Single Orbit Dynamics

Single Orbit Dynamics
Title Single Orbit Dynamics PDF eBook
Author Benjamin Weiss
Publisher American Mathematical Soc.
Pages 127
Release 2000
Genre Mathematics
ISBN 0821804146

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This book presents the expanded notes from ten lectures given by the author at the NSF/CBMS conference held at California State University (Bakersfield). The author describes what he calls single orbit dynamics, which is an approach to the analysis of dynamical systems via the study of single orbits, rather than the study of a system as a whole. He presents single orbit interpretations of several areas of topological dynamics and ergodic theory and some new applications of dynamics to graph theory. In the concluding lectures, single orbit approaches to generalizations of the Shannon-Breiman-McMillan theorem and related problems of compression and universal coding are presented. Complete proofs and illuminating discussions are included and references for further study are given. Some of the material appears here for the first time in print.

Topological Degree Methods in Nonlinear Boundary Value Problems

Topological Degree Methods in Nonlinear Boundary Value Problems
Title Topological Degree Methods in Nonlinear Boundary Value Problems PDF eBook
Author J. Mawhin
Publisher American Mathematical Soc.
Pages 130
Release 1979
Genre Mathematics
ISBN 082181690X

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Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.

Some Recent Developments in Operator Theory

Some Recent Developments in Operator Theory
Title Some Recent Developments in Operator Theory PDF eBook
Author Carl M. Pearcy
Publisher American Mathematical Soc.
Pages 82
Release 1978
Genre Business & Economics
ISBN 0821816861

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Surveys some of the remarkable developments that have taken place in operator theory over the years. This monograph is largely expository and should be accessible to those who have had a course in functional analysis and operator theory.

Topics in the Homological Theory of Modules Over Commutative Rings

Topics in the Homological Theory of Modules Over Commutative Rings
Title Topics in the Homological Theory of Modules Over Commutative Rings PDF eBook
Author Melvin Hochster
Publisher American Mathematical Soc.
Pages 88
Release 1975-12-31
Genre Mathematics
ISBN 9780821888711

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This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.