The Arithmetic of Hyperbolic 3-Manifolds

By Colin Maclachlan, Alan W. Reid. 2002

222 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28fbb8d7d35e6a76bad6e7f9f6fd7fe9836894e6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

1. Nathan M. Dunfield
2. Stavros Garoufalidis
3. A. Borel
4. Lizhen Ji
5. Frank Calegari

In Geometry and Topology

1. Frank Calegari
2. A. Borel
3. Lizhen Ji
4. Nathan M. Dunfield
5. Stavros Garoufalidis
6. Akshay Venkatesh
7. Tudor Dimofte
8. Sergei Gukov

In Mathematical Physics

1. Frank Calegari
2. A. Borel
3. Lizhen Ji
4. Nathan M. Dunfield
5. Stavros Garoufalidis
6. Akshay Venkatesh
7. Nicolas Bergeron
8. Jacob Rasmussen

Citations in the corpus

• Automorphic forms and rational homology 3--spheres (2005, methodology): “When trying to determine the topology of M0 , it is important to remember that the structure of a commensurability class of arithmetic 3–manifolds is quite complicated; in particular, it contains infinitely many minimal orbifolds (throughout this subsection, see Maclachlan–Reid [28] for details).”
• Chern-Simons theory, analytic continuation and arithmetic (2007, background): “It turns out that (a) the Ray-Singer torsion invariants associated to a GC-representation of π1(M) are also algebraic numbers (this is proven and discussed in detail in [DG]), (b) in case M is hyperbolic and G = SU(2) the geometric representation is defined over a number field; see [MR], (c) the per”
• Compactifications of Symmetric and Locally Symmetric Spaces (2005, methodology): “There are also co-compact arithmetic subgroups of SL(2,C) constructed via quaternion algebras over F (see [MR]).”