Speaker
Gabriele Viaggi
(Università di Pisa)
Description
There are two important operations that one can perform on a finite volume hyperbolic 3-manifold. One can drill out a simple closed geodesic and one can Dehn fill a cusp. It is a well-known phenomenon that all drillings and most fillings give back a hyperbolizable 3-manifold whose volume is larger for the first operation and smaller for the second. How can we bound the volume change in terms of the relevant geometric parameters (such as the lengths of the geodesic or of the filling slope)? After reviewing the global picture and the known results, I will describe some new (completely local) linear bounds.
Author
Gabriele Viaggi
(Università di Pisa)