Discrete Subgroups of Semisimple Lie Groups

  title={Discrete Subgroups of Semisimple Lie Groups},
  author={G. A. Margulis},
1. Statement of Main Results.- 2. Synopsis of the Chapters.- 3. Remarks on the Structure of the Book, References and Notation.- 1. Preliminaries.- 0. Notation, Terminology and Some Basic Facts.- 1. Algebraic Groups Over Arbitrary Fields.- 2. Algebraic Groups Over Local Fields.- 3. Arithmetic Groups.- 4. Measure Theory and Ergodic Theory.- 5. Unitary Representations and Amenable Groups.- II. Density and Ergodicity Theorems.- 1. Iterations of Linear Transformations.- 2. Density Theorems for… 
Discrete Subgroups Generated by Lattices in Opposite Horospherical Subgroups
0. Introduction. 1. Preliminaries. 1.1. Notation and terminology. 1.2. Some known algebraic lemmas. 1.3. Adjoint representation and maximal subgroups. 1.4. Qforms of algebraic groups and Q-rational
Lectures on Spaces of Nonpositive Curvature
I. On the interior geometry of metric spaces.- 1. Preliminaries.- 2. The Hopf-Rinow Theorem.- 3. Spaces with curvature bounded from above.- 4. The Hadamard-Cartan Theorem.- 5. Hadamard spaces.- II.
Introduction to Arithmetic Groups
This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among
Groups : topological, combinatorial and arithmetic aspects
1. Reductive groups as metric spaces H. Abels 2. Finiteness properties of groups acting on twin buildings P. Abramenko 3. Higher finiteness properties of S-arithmetic groups in the function field
Lectures on the Geometric Group Theory
Preface The main goal of this book is to describe several tools of the quasi-isometric rigidity and to illustrate them by presenting (essentially self-contained) proofs of several fundamental
In this note we prove a noncommutative version of Margulis’ Normal Subgroup Theorem (NST) for irreducible lattices Γ in the product of higher rank simple Lie groups. More precisely, we prove a
This is the course note of an introductory course on discrete subgroups of Lie groups. The contents contains basic facts about discrete subgroups, Borel density theorem, arithmeticity theorem of
Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low
Factor and normal subgroup theorems for lattices in products of groups
A central result in the theory of semisimple groups and their lattices is Margulis’ normal subgroup theorem: any normal subgroup of an irreducible lattice in a center free, higher rank semisimple
Relative property (T) and linear groups
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However,