Department of Mathematics Calendar
Genevieve Walsh, Tufts University, Incoherent free-by-free groups
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A group G is called coherent if every finitely generated subgroup of G is finitely presented. This is a property enjoyed by the fundamental groups of 3-manifolds, and it is deeply related to the geometry of the group. We show that free-by-free groups satisfying a particular homological criterion are incoherent. This class is large in nature, including many examples of hyperbolic and non-hyperbolic free-by-free groups. We apply this criterion to finite index subgroups of $F_2\rtimes F_n$ to show incoherence of all such groups, and to other similar classes of groups. This is joint work with Rob Kropholler.