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Arithmetic Groups and Their Generalizations: What, Why, and How
About this Title
Lizhen Ji, University of Michigan, Ann Arbor, Ann Arbor, MI
Publication: AMS/IP Studies in Advanced Mathematics
Publication Year:
2008; Volume 43
ISBNs: 978-0-8218-4866-1 (print); 978-1-4704-3833-3 (online)
DOI: https://doi.org/10.1090/amsip/043
MathSciNet review: MR2410298
MSC: Primary 22E40; Secondary 11F06
ReadershipTable of Contents
Front/Back Matter
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