We study a group theoretic analog of Dehn fillings of 3-manifolds and derive a spectral sequence to compute the cohomology of Dehn fillings of hyperbolically embedded subgroups. As applications, we generalize the results of Dahmani-Guirardel-Osin and Hull on SQ-universality and common quotients of acylindrically hyperbolic groups by adding cohomological finiteness conditions. This is a joint work with Nansen Petrosyan.
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- Topology Seminar