Introduction to Arithmetic Groups

• Part I. Introduction
• What is a Locally Symmetric Space?
• Geometric Meaning of R-rank and Q-rank
• Brief Summary
• Part II. Fundamentals
• Basic Properties of Lattices
• What is an Arithmetic Groups?
• Examples of Arithmetic Groups
• SL (n, Z) is a lattice in SL (n, R)
• Part III. Important Concepts
• Real Rank
• Q-Rank
• Quasi-Isometries
• Unitary Representations
• Amenable Groups
• Kazhdan's Property (T)
• Ergodic Theory
• Part IV. Major Results
• Mostow Rigidity Theorem
• Margulis Superrigidity Theorem
• Normal Subgroups of T
• Arithmetic Subgroups of Classical Groups
• Construction of a Coarse Fundamental Domain
• Ratner's Theorems of Unipotent Flows
• Appendices

Introduction to Arithmetic Groups