Effective geometry change under Dehn surgery
Dehn surgery is a way to obtain one 3-manifold from another. In the late 1970s, Thurston showed that if the original manifold admits a hyperbolic structure, then for "most" Dehn surgeries, the hyperbolic geometry changes "very little." However, it has been difficult to apply this theorem to concrete examples because "most" and "very little" have not been quantified in general. In this talk, I will describe results giving effective bounds on change in hyperbolic metric under Dehn surgery, and present some consequences. One consequence is that the verification of the cosmetic surgery conjecture for any given hyperbolic knot can be reduced to a finite computer search. Another consequence is to bounding Margulis numbers of closed hyperbolic manifolds. I will describe the necessary terms and background during the talk. This work is joint with David Futer and Saul Schleimer.
(Note the special time!)
Dr Jessica Purcell, Monash University