Cosmetic surgeries on homology spheres

Geometry Topology Seminar
Monday, January 9, 2017 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
University of Georgia
Dehn surgery is a fundamental tool for constructing oriented 3-Manifolds. If we fix a knot K in an oriented 3-manifold Y and do surgeries with distinct slopes r and s, we can ask under which conditions the resulting oriented manifold Y(r) and Y(s) might be orientation preserving homeomorphic. The cosmetic surgery conjecture state that if the knot exterior is boundary irreducible  then this can't happen. My talk will be about the case where Y is an homology sphere and K is an hyperbolic knot.