un 2 00 1 Arithmetic Groups and Locally Symmetric Spaces
نویسنده
چکیده
Permission to make copies of these lecture notes for educational or scientific use, including multiple copies for classroom or seminar teaching, is granted (without fee), provided that any fees charged for the copies are only sufficient to recover the reasonable copying costs, and that all copies include this title page and its copyright notice. Specific permission of the author is required to reproduce or distribute this book (in whole or in part) for profit or commercial advantage.
منابع مشابه
Introduction to arithmetic groups
Arithmetic groups are fundamental groups of locally symmetric spaces. We will see how they are constructed, and discuss some of their important properties. For example, although the Q-rank of an arithmetic group is usually defined in purely algebraic terms, we will see that it provides important information about the geometry and topology of the corresponding locally symmetric space. Algebraic ...
متن کاملA tale of two groups: arithmetic groups and mapping class groups
In this chapter, we discuss similarities, differences and interaction between two natural and important classes of groups: arithmetic subgroups Γ of Lie groups G and mapping class groups Modg,n of surfaces of genus g with n punctures. We also mention similar properties and problems for related groups such as outer automorphism groups Out(Fn), Coxeter groups and hyperbolic groups. Since groups a...
متن کاملBuildings and their applications in geometry and topology
In this paper, we briefly introduce different types of buildings such as spherical buildings, Euclidean buildings, twin buildings, R-buildings and describe some of their applications to many subjects: (1) differential geometry such as Mostow strong rigidity, rank rigidity of nonpositively curved manifolds, Margulis superrigidity, quasi-isometry rigidity, classification of isoparametric manifold...
متن کاملAlgebraic Groups with a Commuting Pair of Involutions and Semisimple Symmetric Spaces
Let G be a connected reductive algebraic group defined over an algebraically closed field F of characteristic not 2. Denote the Lie algebra of G by 9. In this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of G. This is shown to be independent of the characteristic of F and can be applied to describe all semisimple locally symmetric spac...
متن کاملL-Spectral theory of locally symmetric spaces with Q-rank one
We study the L-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M = Γ\X with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001