Genevieve Walsh, Tufts

Genevieve Walsh, Tufts University

Abstract: A group is coherent if every finitely generated subgroup is finitely presented, and incoherent otherwise. Many well-known groups are coherent: free groups, surface groups, and the fundamental groups of compact 3-manifolds. We consider groups of the form $F_m \by F_n$ or $S_g \by F_n$  where $S_g$ is the fundamental group of a closed surface of genus $g$. We show that all these groups are incoherent whenever $g, n$ are at least 2, answering a question of D. Wise. One possible alternative method to prove incoherence  would be to show that these groups virtually algebraically fiber. We additionally show that not all groups covered by our methods virtually algebraically fiber.

This is joint work with Robert Kropholler and Stefano Vidussi.

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