---
tag: FJB1WF2E6K
kind: concept
name: Arithmetic hyperbolic 3-manifold
aliases: [arithmetic-kleinian-group]
sources:
  - wikipedia: en:15239331@r1351989487
    locator: Arithmetic hyperbolic 3-manifold
    note: adopted
    mention: wikipedia://en/15239331
    sections: [Summary]
same_as:
  wikidata: Q4791128
  wikipedia: Arithmetic hyperbolic 3-manifold
inventory: [R0P0AV1AJ2]
---

## Summary

In mathematics, more precisely in group theory and hyperbolic geometry, **Arithmetic Kleinian groups** are a special class of Kleinian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. An **arithmetic hyperbolic three-manifold** is the quotient of hyperbolic space $\mathbb H^3$ by an arithmetic Kleinian group.