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Compactifications of Symmetric and Locally Symmetric Spaces

By: Borel, Armand [author.].
Contributor(s): Ji, Lizhen [author.2] | SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Mathematics: Theory & Applications0.Publisher: Boston, MA : Birkh�user Boston, 2006. Description: XV, 479 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817644666.Subject(s): Mathematics | Algebraic geometry | Topological groups | Lie groups | Applied mathematics | Engineering mathematics | Geometry | Number theory | Algebraic topology.1 | Mathematics.2 | Topological Groups, Lie Groups.2 | Algebraic Topology.2 | Number Theory.2 | Geometry.2 | Algebraic Geometry.2 | Applications of Mathematics.1DDC classification: 512.55 | 512.482 Online resources: Click here to access online
Contents:
Compactifications of Riemannian Symmetric Spaces -- Review of Classical Compactifications of Symmetric Spaces -- Uniform Construction of Compactifications of Symmetric Spaces -- Properties of Compactifications of Symmetric Spaces -- Smooth Compactifications of Semisimple Symmetric Spaces -- Smooth Compactifications of Riemannian Symmetric Spaces G/K -- Semisimple Symmetric Spaces G/H -- The Real Points of Complex Symmetric Spaces Defined over ? -- The DeConcini-Procesi Compactification of a Complex Symmetric Space and Its Real Points -- The Oshima-Sekiguchi Compactification of G/K and Comparison with (?) -- Compactifications of Locally Symmetric Spaces -- Classical Compactifications of Locally Symmetric Spaces -- Uniform Construction of Compactifications of Locally Symmetric Spaces -- Properties of Compactifications of Locally Symmetric Spaces -- Subgroup Compactifications of ??G -- Metric Properties of Compactifications of Locally Symmetric Spaces ??X.
In: Springer eBooks0Summary: 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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PK Kelkar Library, IIT Kanpur
Available EBK7805
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Compactifications of Riemannian Symmetric Spaces -- Review of Classical Compactifications of Symmetric Spaces -- Uniform Construction of Compactifications of Symmetric Spaces -- Properties of Compactifications of Symmetric Spaces -- Smooth Compactifications of Semisimple Symmetric Spaces -- Smooth Compactifications of Riemannian Symmetric Spaces G/K -- Semisimple Symmetric Spaces G/H -- The Real Points of Complex Symmetric Spaces Defined over ? -- The DeConcini-Procesi Compactification of a Complex Symmetric Space and Its Real Points -- The Oshima-Sekiguchi Compactification of G/K and Comparison with (?) -- Compactifications of Locally Symmetric Spaces -- Classical Compactifications of Locally Symmetric Spaces -- Uniform Construction of Compactifications of Locally Symmetric Spaces -- Properties of Compactifications of Locally Symmetric Spaces -- Subgroup Compactifications of ??G -- Metric Properties of Compactifications of Locally Symmetric Spaces ??X.

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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