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Softcover ISBN:  9780821848661 
Product Code:  AMSIP/43.S 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $58.40 
eBook ISBN:  9781470438333 
Product Code:  AMSIP/43.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Softcover ISBN:  9780821848661 
eBook ISBN:  9781470438333 
Product Code:  AMSIP/43.S.B 
List Price:  $142.00 $107.50 
MAA Member Price:  $127.80 $96.75 
AMS Member Price:  $113.60 $86.00 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 43; 2008; 259 ppMSC: Primary 11; 22
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \(\mathbf{Z}\) or \(\mathrm{SL}(n,\mathbf{Z})\). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations.
The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry.
It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students interested in arithmetic groups and their applications to number theory, geometry and topology.

Table of Contents

Chapters

Introduction

General comments on references

Examples of basic arithmetic groups

General arithmetic subgroups and locally symmetric spaces

Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups

Different completions of $\mathbb {Q}$ and $S$arithmetic groups over number fields

Global fields and $S$arithmetic groups over function fields

Finiteness properties of arithmetic and $S$arithmetic groups

Symmetric spaces, BruhatTits buildings and their arithmetic quotients

Compactifications of locally symmetric spaces

Rigidity of locally symmetric spaces

Automorphic forms and automorphic representations for general arithmetic groups

Cohomology of arithmetic groups

$K$groups of rings of integers and $K$groups of group rings

Locally homogeneous manifolds and period domains

Noncofinite discrete groups, geometrically finite groups

Large scale geometry of discrete groups

Tree lattices

Hyperbolic groups

Mapping class groups and outer automorphism groups of free groups

Outer automorphism group of free groups and the outer spaces


Additional Material

Reviews

...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.
Mathematical Reviews


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In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \(\mathbf{Z}\) or \(\mathrm{SL}(n,\mathbf{Z})\). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations.
The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry.
It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
Graduate students interested in arithmetic groups and their applications to number theory, geometry and topology.

Chapters

Introduction

General comments on references

Examples of basic arithmetic groups

General arithmetic subgroups and locally symmetric spaces

Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups

Different completions of $\mathbb {Q}$ and $S$arithmetic groups over number fields

Global fields and $S$arithmetic groups over function fields

Finiteness properties of arithmetic and $S$arithmetic groups

Symmetric spaces, BruhatTits buildings and their arithmetic quotients

Compactifications of locally symmetric spaces

Rigidity of locally symmetric spaces

Automorphic forms and automorphic representations for general arithmetic groups

Cohomology of arithmetic groups

$K$groups of rings of integers and $K$groups of group rings

Locally homogeneous manifolds and period domains

Noncofinite discrete groups, geometrically finite groups

Large scale geometry of discrete groups

Tree lattices

Hyperbolic groups

Mapping class groups and outer automorphism groups of free groups

Outer automorphism group of free groups and the outer spaces

...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.
Mathematical Reviews