Alternating Quotients of Twist Knot Groups

Neil Hoffman (Minnesota)

Abstract: A 3-manifold M has a finitely presented group G. For all types of 3-manifolds, there are natural constructions of Abelian quotients and quotients of the form PSL(2,F) where F is a finite field. I will talk about constructing quotients from a class of 3-manifold groups, the twist knot groups, to alternating groups {A_n} for various values of n, which are seemingly less natural, but nonetheless interesting. This is joint work with Chloe George and Kate Petersen.