### Dehn filling and drilling, and versions of Cannon's conjecture

Algebra and Geometry Seminar

24th October 2018, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

Thurston's Dehn filling theorem gives a way of constructing closed hyperbolic 3-manifolds starting from finite-volume ones, and it has an algebraic version for (relatively) hyperbolic groups. I will describe this operation, and the "inverse" operation of Dehn drilling, and explain how they can be used to relate versions of the so-called Cannon's Conjecture, one of the most important conjectures about hyperbolic groups. Based on joint work with Groves, Haissinsky, Manning, Osajda, Walsh.

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