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| Softcover ISBN: | 978-0-8218-4866-1 |
| Product Code: | AMSIP/43.S |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $58.40 |
| eBook ISBN: | 978-1-4704-3833-3 |
| Product Code: | AMSIP/43.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Softcover ISBN: | 978-0-8218-4866-1 |
| eBook ISBN: | 978-1-4704-3833-3 |
| Product Code: | AMSIP/43.S.B |
| List Price: | $142.00 $107.50 |
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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 co-published with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students interested in arithmetic groups and their applications to number theory, geometry and topology.
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Table of Contents
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Chapters
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Introduction
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General comments on references
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Examples of basic arithmetic groups
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General arithmetic subgroups and locally symmetric spaces
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Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups
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Different completions of $\mathbb {Q}$ and $S$-arithmetic groups over number fields
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Global fields and $S$-arithmetic groups over function fields
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Finiteness properties of arithmetic and $S$-arithmetic groups
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Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients
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Compactifications of locally symmetric spaces
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Rigidity of locally symmetric spaces
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Automorphic forms and automorphic representations for general arithmetic groups
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Cohomology of arithmetic groups
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$K$-groups of rings of integers and $K$-groups of group rings
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Locally homogeneous manifolds and period domains
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Non-cofinite discrete groups, geometrically finite groups
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Large scale geometry of discrete groups
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Tree lattices
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Hyperbolic groups
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Mapping class groups and outer automorphism groups of free groups
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Outer automorphism group of free groups and the outer spaces
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Additional Material
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Reviews
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...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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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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 co-published 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, Bruhat-Tits 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
-
Non-cofinite 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
