Compactifications of Symmetric and Locally Symmetric Spaces
Authors: Borel, Armand, Ji, Lizhen
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 About this book

Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures.
The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces.
Familiarity with the theory of semisimple Lie groups is assumed, as is familiarity with algebraic groups defined over the rational numbers in later parts of the book, although most of the pertinent material is recalled as presented. Otherwise, the book is a selfcontained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics.
 Reviews

From the reviews:
"In the book under review the authors pursue three chief goals: to give a comprehensive overview of existing compactifications … to explain the relations among them and to provide a uniform construction. … The style is userfriendly … . It can be highly recommended and will be very useful to anyone, graduate student or research mathematician, interested in the geometry and topology of (locally) symmetric spaces."(Enrico Leuzinger, Mathematical Reviews, Issue 2007 d)
 Table of contents (14 chapters)


Introduction
Pages 122

Review of Classical Compactifications of Symmetric Spaces
Pages 27105

Uniform Construction of Compactifications of Symmetric Spaces
Pages 107164

Properties of Compactifications of Symmetric Spaces
Pages 165197

Smooth Compactifications of Riemannian Symmetric Spaces G/K
Pages 203213

Table of contents (14 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Compactifications of Symmetric and Locally Symmetric Spaces
 Authors

 Armand Borel
 Lizhen Ji
 Series Title
 Mathematics: Theory & Applications
 Copyright
 2006
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9780817644666
 DOI
 10.1007/0817644660
 Hardcover ISBN
 9780817632472
 Edition Number
 1
 Number of Pages
 XV, 479
 Topics