Cohomology of group theoretic Dehn fillings. I: Cohen-Lyndon type theorems (Q2333354)

Dehn surgery is an operation in 3-dimensional topology which consists in modifying a 3-manifold by cutting off a solid torus and then gluing it back in a different way. A famous result in this direction is Thurston's hyperbolic Dehn filling theorem which asserts the existence of hyperbolic structures on a large class of manifolds obtained by Dehn filling. There is also a group theoretic settings for Dehn filling, which had many applications. For instance, the solution of the virtually Haken, by \textit{I. Agol} [Doc. Math. 18, 1045--1087 (2013; Zbl 1286.57019)] uses Dehn fillings of hyperbolic groups. In the paper under review, the author studies the cohomology of group theoretic Dehn fillings, in particular free product structure of Dehn filling kernels, which he calls the Cohen-Lyndon property. Using this, he describes the structure of relative relation modules of Dehn fillings.