Distinguishing hyperbolic knots using finite quotients
Distinguishing hyperbolic knots using finite quotients
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Tam Cheetham-West, Yale University
The fundamental groups of knot complements have lots of听听finite quotients. We give a criterion for a hyperbolic knot in the听听three-sphere to be distinguished (up to isotopy and mirroring) from听听every other knot in the three-sphere by the set of finite quotients of听听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.