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Introduction to Arithmetic Groups

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Dave Witte Morris

Copyright Year: 2015

ISBN 13: 9780986571602

Publisher: Deductive Press

Language: English

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Table of Contents


  • 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

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  • About the Book

    Introduction to Arithmetic Groups

    About the Contributors


    Dave Witte Morris, University of Lethbridge

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