Distinguishing hyperbolic knots using finite quotients

Tam Cheetham-West, Yale University
Fine Hall 314

The fundamental groups of knot complements have lots of  finite quotients. We give a criterion for a hyperbolic knot in the  three-sphere to be distinguished (up to isotopy and mirroring) from  every other knot in the three-sphere by the set of finite quotients of  its fundamental group, and we use this criterion and work of Baldwin-Sivek to show that there are infinitely many hyperbolic knots distinguished (up to isotopy and mirroring) by finite quotients.