Ebook: Compactifications of Symmetric and Locally Symmetric Spaces

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 self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics.

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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 self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics.

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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 self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics.

Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-22
Front Matter....Pages 23-25
Review of Classical Compactifications of Symmetric Spaces....Pages 27-105
Uniform Construction of Compactifications of Symmetric Spaces....Pages 107-164
Properties of Compactifications of Symmetric Spaces....Pages 165-197
Front Matter....Pages 199-201
Smooth Compactifications of Riemannian Symmetric Spaces G/K ....Pages 203-213
Semisimple Symmetric Spaces G/H ....Pages 215-219
The Real Points of Complex Symmetric Spaces Defined over ?....Pages 221-231
The DeConcini-Procesi Compactification of a Complex Symmetric Space and Its Real Points....Pages 233-247
The Oshima-Sekiguchi Compactification of G/K and Comparison with $ overline {G/H} ^W $ (?)....Pages 249-262
Front Matter....Pages 263-265
Classical Compactifications of Locally Symmetric Spaces....Pages 267-322
Uniform Construction of Compactifications of Locally Symmetric Spaces....Pages 323-363
Properties of Compactifications of Locally Symmetric Spaces....Pages 365-374
Subgroup Compactifications of ??G ....Pages 375-398
Metric Properties of Compactifications of Locally Symmetric Spaces ??X ....Pages 399-422
Back Matter....Pages 423-479

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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 self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics.

Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-22
Front Matter....Pages 23-25
Review of Classical Compactifications of Symmetric Spaces....Pages 27-105
Uniform Construction of Compactifications of Symmetric Spaces....Pages 107-164
Properties of Compactifications of Symmetric Spaces....Pages 165-197
Front Matter....Pages 199-201
Smooth Compactifications of Riemannian Symmetric Spaces G/K ....Pages 203-213
Semisimple Symmetric Spaces G/H ....Pages 215-219
The Real Points of Complex Symmetric Spaces Defined over ?....Pages 221-231
The DeConcini-Procesi Compactification of a Complex Symmetric Space and Its Real Points....Pages 233-247
The Oshima-Sekiguchi Compactification of G/K and Comparison with $ overline {G/H} ^W $ (?)....Pages 249-262
Front Matter....Pages 263-265
Classical Compactifications of Locally Symmetric Spaces....Pages 267-322
Uniform Construction of Compactifications of Locally Symmetric Spaces....Pages 323-363
Properties of Compactifications of Locally Symmetric Spaces....Pages 365-374
Subgroup Compactifications of ??G ....Pages 375-398
Metric Properties of Compactifications of Locally Symmetric Spaces ??X ....Pages 399-422
Back Matter....Pages 423-479
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