Geometry and Topology Seminar

We describe a novel scheme for creating integral surgeries from 3-manifolds with two torus boundary components to cable spaces. Using this scheme we recover the 22 examples of asymmetric, hyperbolic, 1-cusped, 3-manifolds with two lens space fillings of Dunfield-Hoffman-Licata and many, many more. This scheme also produced the recent family of tunnel number 2 knots in the Poincare homology sphere with lens space surgeries. Time permitting, we'll also discuss related constructions of new surgeries between pairs of reducible manifolds and between lens spaces and reducible manifolds. Portions of this work are in progress, some with Hoffman and Licata.