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Compactifications of Symmetric and Locally Symmetric Spaces (Mathematics: Theory & Applications), by Armand Borel, Lizhen Ji
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Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures
Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology
- Sales Rank: #3869509 in Books
- Brand: Brand: Birkhäuser
- Published on: 2005-12-08
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.06" w x 6.14" l, 1.80 pounds
- Binding: Hardcover
- 479 pages
- Used Book in Good Condition
Review
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 user-friendly … . 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)
From the Back Cover
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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