Compactifications of Symmetric and Locally Symmetric Spaces

Armand Borel, Lizhen Ji - Collection Mathematics: Theory & Applications

492 pages, parution le 31/01/2006

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Résumé

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.

Written for: Graduate students, researchers, mathematicians, Lie theorists, representation theorists

Sommaire

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 R
- The DeConcini-Procesi Compactification of a Complex Symmetric Space and its Real Points
- The Oshima-Sekiguchi Compactification of G/K and Comparison with G/H^w (R)
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 Γ\G
- Metric Properties of Compactifications of Locally Symmetric Spaces Γ\X

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Armand Borel, Lizhen Ji
Collection	Mathematics: Theory & Applications
Parution	31/01/2006
Nb. de pages	492
Format	16 x 24
Couverture	Relié
Poids	810g
Intérieur	Noir et Blanc
EAN13	9780817632472
ISBN13	978-0-8176-3247-2