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

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OGG - Operators, Graphs, Groups

Dehn filling is a fundamental tool in group theory, appearing in the solution of the Virtual Haken Conjecture, the study of the Farrell-Jones and Baum-Connes 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.

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

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