Arithmetic aspects of hyperbolic knots and their Dehn surgeries
A consequence of Mostow-Prasad rigidity is that the trace-field of an orientable finite volume hyperbolic 3-manifold M is a number field. In addition, there is a quaternion algebra over this number field that is a natural invariant associated to M. This talk will review this background, and survey recent advances in trying to understand the trace-field and this quaternion algebra, especially in the setting of Dehn surgery on a hyperbolic knot.
