Hyperbolic and relatively hyperbolic groups with 2-sphere boundary

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• Genevieve Walsh (Tufts University)
• Tuesday 15 July 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

We define a “drilling” of a hyperbolic group along a maximal infinite cyclic subgroup, which results in a relatively hyperbolic group pair.  This procedure is inspired by drilling a hyperbolic 3-manifold along an embedded geodesic.  We show that, under suitable circumstances, drilling a hyperbolic group with 2-sphere hyperbolic boundary results in a relatively hyperbolic group with 2-sphere relatively hyperbolic boundary.  This is joint work with D. Groves, P. Haissinsky, D. Osajda, and A. Sisto. If time permits, I will discuss a somewhat related result with E. Stark which implies that a hyperbolic space which admits a geometric action and admits a relatively hyperbolic action with rank -2 abelian peripheral subgroups is quasi-isometric to $H^3$. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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