An Introduction to Topological Groups

Author: P. J. Higgins
Publisher: Cambridge University Press
ISBN: 9780521205276
Format: PDF, ePub
Download Now
The book is based on lecture courses given for the London M.Sc. degree in 1969 and 1972, and the treatment is more algebraic than usual.

Introduction to the Representation Theory of Compact and Locally Compact Groups

Author: Alain Robert
Publisher: Cambridge University Press
ISBN: 0521289750
Format: PDF, ePub, Docs
Download Now
Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Author: Sidney A. Morris
Publisher: Cambridge University Press
ISBN: 0521215439
Format: PDF, ePub
Download Now
These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.

Introduction to Uniform Spaces

Author: I. M. James
Publisher: Cambridge University Press
ISBN: 9780521386203
Format: PDF
Download Now
This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

The Topology of Stiefel Manifolds

Author: I. M. James
Publisher: Cambridge University Press
ISBN: 0521213347
Format: PDF, ePub, Docs
Download Now
Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard University, describe the state of knowledge of the subject, as well as the outstanding problems. The emphasis throughout is on applications (within the subject) rather than on theory. However, such theory as is required is summarized and references to the literature are given, thus making the book accessible to non-specialists and particularly graduate students. Many examples are given and further problems suggested.

Topological Groups and Related Structures An Introduction to Topological Algebra

Author: Alexander Arhangel’skii
Publisher: Springer Science & Business Media
ISBN: 949121635X
Format: PDF, ePub, Docs
Download Now
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.

Interaction Models

Author: Norman Biggs
Publisher: Cambridge University Press
ISBN: 0521217709
Format: PDF, ePub, Docs
Download Now
This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

Lie Groups and Compact Groups

Author: John F. Price
Publisher: Cambridge University Press
ISBN: 0521213401
Format: PDF, ePub, Docs
Download Now
Provides a self-contained introduction to Lie groups and makes results about the structure of Lie groups and compact groups available to a wide audience.