Distinguishing hyperbolic knots using finite quotients

Geometry Topology Seminar
Monday, February 6, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Tam Cheetham-West – Rice University – tcw@rice.edu
Miriam Kuzbary

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 as well as recent work of Baldwin-Sivek to show that there are infinitely many hyperbolic knots distinguished (up to isotopy and mirroring) by finite quotients.