![School of Mathematics Event](/sites/default/files/styles/two_column_medium/public/2019-09/sm_default.jpg?itok=gMvWynkh)
Emerging Topics working group
Coherence, planar boundaries, and the geometry of subgroups
Abstract: This will be a broad talk about coherence of groups, and how it relates to conjectures about hyperbolic groups with planar boundaries. A group is coherent if every finitely generated subgroup is finitely presented. This is a property enjoyed by the fundamental groups of 3-manifolds. A natural stepping stone to proving that certain hyperbolic groups are 3-manifold groups is to prove that they are coherent. A stronger property that some hyperbolic groups possess is "local quasi-convexity", in that every finitely generated subgroup is quasi-convex. It is conjectured that a hyperbolic group whose Gromov boundary is a Sierpinski carpet is locally quasi-convex. I'll also discuss several examples of coherent and incoherent groups that have 3-manifold like properties.