Ascending Chains of Free Groups in 3-Manifold Groups

Explore a 49-minute lecture on ascending chains of free groups in 3-manifold groups, presented by Edgar Bering at the Workshop on Groups around 3-Manifolds. Delve into the groundbreaking work of Takahasi and Higman, who independently proved that ascending chains of subgroups with constant rank in free groups must stabilize. Examine Kapovich and Myasnikov's proof using graphs and Stallings folds, and discover how Lazarovich and Bering developed two new proofs for the constant-rank ascending chain condition (cracc) in closed surface groups. Investigate the extension of these techniques to establish cracc for free subgroups of constant rank in closed or finite-volume hyperbolic 3-manifold groups. Gain insights into the crucial roles played by hyperbolic geometry, geometrization, and JSJ decompositions in these proofs, advancing your understanding of 3-manifold group theory.