Cohomology of group theoretic Dehn fillings I: Cohen-Lyndon type theorems

TL;DR

This paper establishes a free product structure called the Cohen-Lyndon property for Dehn filling kernels in group theory, providing insights into the cohomology of group theoretic Dehn fillings.

Contribution

It introduces the Cohen-Lyndon property for Dehn filling kernels and describes the structure of related relative relation modules, advancing the understanding of cohomology in this context.

Findings

Proves the Cohen-Lyndon property for Dehn filling kernels

Describes the structure of relative relation modules in Dehn fillings

Provides foundational results for subsequent cohomological analysis

Abstract

This is the first paper of two papers in a row aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we prove a particular free product structure, which is termed the Cohen-Lyndon property, of Dehn filling kernels. As an application, we describe the structure of relative relation modules of Dehn fillings.