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4:00 pm Monday, October 30, 2017 Topology Seminar: Relatively hyperbolic groups vs 3-manifold groups.by Genevieve Walsh (Tufts) in HBH 227- Bowditch described the boundary of a relatively hyperbolic group pair $(G,P)$ as the boundary of any hyperbolic space that $G$ acts geometrically finitely upon, where the maximal parabolic subgroups are conjugates of the subgroups in $P$. For example, the fundamental group of a hyperbolic knot complement acts geometrically finitely on $\mathbb{H}^3$, where the maximal parabolic subgroups are the conjugates of $\mathbb{Z} \oplus \mathbb{Z}$. Here the Bowditch boundary is $S^2$. We show that torsion-free relatively hyperbolic groups whose Bowditch boundaries are $S^2$ are relative $PD(3)$ groups. This is joint work with Bena Tshishiku. If time permits, I'll show some examples of strange phenomena that can happen with boundaries of relatively hyperbolic groups, joint with Chris Hruska.
Submitted by neil.fullarton@rice.edu |