### Group theoretic Dehn fillings and their L^2-Betti numbers

Algebra Seminar

15th October 2024, 4:00 pm – 5:00 pm

Fry Building, 2.04

Dehn filling is a fundamental tool in group theory, appearing in the solution of the Virtual Haken Conjecture, the study of the Farrell-Jones Conjecture, the isomorphism problem of relatively hyperbolic groups, and the construction of purely pseudo-Anosov normal subgroups of mapping class groups. In this talk, I will discuss past joint work with Bin Sun on the cohomology of Dehn filling quotients and our recent results on their L^2-Betti numbers. The applications include the verification of the Singer Conjecture for certain Einstein manifolds, virtual fibering, and the construction of new examples of hyperbolic groups with exotic subgroups.

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