Commensurability classes of 2-bridge knots

Genevieve Walsh

Two three-manifolds are said to be commensurable if they share a
common finite-sheeted cover.  We discuss commensurability classes of
knot complements, and prove that every hyperbolic two-bridge knot is
the unique knot complement in its commensurability class.  This does
not hold for a general knot complement.  For example, if a knot
complement admits a lens space filling, it is covered by another knot
complement. We speculate on and give a conjecture regarding the
general case.  This is joint work with Alan Reid.