EMS Textbooks in Mathematics 2006; 312 pp; hardcover Volume: 3 ISBN10: 3037190167 ISBN13: 9783037190166 List Price: US$58 Member Price: US$46.40 Order Code: EMSTEXT/3
 Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the PeterWeyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for nonAbelian connected locally compact groups that can be derived using approximation by Lie groups. The book is selfcontained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for onesemester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Advanced undergraduate and graduate students interested in topology. Table of Contents  Preliminaries
 Topological groups
 Topological transformation groups
 The Haar integral
 Categories of topological groups
 Locally compact Abelian groups
 Locally compact semigroups
 Hilbert's fifth problem
 Bibliography
 Index of symbols
 Subject index
