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

Author: Lizhen Ji Providence, R.I. : American Mathematical Society ; [Somerville, MA] : International Press, ©2008. AMS/IP studies in advanced mathematics, v. 43. Print book : EnglishView all editions and formats WorldCat 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... (not yet rated) 0 with reviews - Be the first.

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Material Type: Internet resource Book, Internet Resource Lizhen Ji Find more information about: Lizhen Ji 9780821846759 0821846752 9780821848661 0821848666 212909009 xvii, 259 pages : illustrations ; 27 cm. 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 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 of free groups and the outer spaces. AMS/IP studies in advanced mathematics, v. 43. Lizhen Ji.

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