The notion of a group theoretic Dehn filling generalizes that of a geometric
Dehn filling for 3-manifolds. In this talk, I will be interested in Dehn fillings of
hyperbolically embedded subgroups and computing cohomology of the quotient
arising from Dehn filling. By refining the Lyndon-Hochschild-Serre spectral
sequence, I find an upper bound on the cohomological dimension of the quotient.
As an application, I construct, for any two given finitely generated acylindrically
hyperbolic groups, a finitely generated, acylindrically hyperbolic quotient with
a nice bound on its cohomological dimension.