Cohomology of group theoretic Dehn fillings
Sun, Bin
:
2019-05-24
Abstract
This thesis aims to study cohomology of group theoretic Dehn fillings. For sufficiently deep Dehn fillings of hyperbically embedded subgroups, we first prove that Dehn filling kernels enjoy a particular free product structure, which is termed the Cohen-Lyndon property. We then combine the Cohen-Lyndon property with the Lyndon-Hochschild-Serre spectral sequence to compute cohomology of Dehn filling quotients. As applications, we estimate cohomological dimensions of Dehn fillings quotients, give criterions for Dehn fillings quotients to be of type $FP_{infty}$, and construct useful quotients of acylindrically hyperbolic groups with certain homological properties.