Arithmetic of Hyperbolic 3-Manifolds

Includes index

Includes bibliographical references

0. Number-Theoretic Menagerie
1. Kleinian Groups and Hyperbolic Manifolds
2. Quaternion Algebras I
3. Invariant Trace Fields
4. Examples
5. Applications
6. Orders in Quaternion Algebras
7. Quaternion Algebras II
8. Arithmetic Kleinian Groups
9. Arithmetic Hyperbolic 3-Manifolds and Orbifolds
10. Discrete Arithmetic Groups
11. Commensurable Arithmetic Groups and Volumes
12. Length and Torsion in Arithmetic Hyperbolic Orbifolds
13. Appendices

For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them.