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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

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Table of Contents

Front/Back Matter

• View this volume's front and 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

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