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Arithmetic groups and their generalizations : what, why, and how

Author: Lizhen Ji
Publisher: Providence (R.I.) : American Mathematical Society ; [Somerville (Mass.)] : International Press, cop. 2008.
Series: AMS/IP studies in advanced mathematics, 43.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

In one guise or another, mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n,\mathbf{Z})$. This work aims to explain what arithmetic groups and their  Read more...

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Document Type: Book
All Authors / Contributors: Lizhen Ji
ISBN: 9780821846759 0821846752
OCLC Number: 493566465
Notes: Informations sur l'ouvrage.
Description: 1 vol. (XVII-259 p.) ; 27 cm.
Contents: 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 References Index.
Series Title: AMS/IP studies in advanced mathematics, 43.
Responsibility: Lizhen Ji.
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