Why Arithmetic Sample Clauses

Why Arithmetic. Hyperbolic 3-Manifolds? Constructing hyperbolic 3-manifolds is hard in general. As previously mentioned, a good reason for studying arithmetic hyperbolic 3-manifolds is that they are easy to construct. Another motivation is that arithmetic data can tell you something about geometric qualities of the manifold. First, we will provide the volume formula for Kleinian groups arising from maximal orders. Then, a later theorem can be used to construct hyperbolic 3-manifolds in which all geodesics are simple. Note that the following two discussion points will not be used later, but are included to highlight the ease of working with arithmetic hyperbolic 3-manifolds and the utility of arithmetic data with respect to hyperbolic 3-manifolds.
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