Geometry/Topology Seminar
Edgar Bering
San José State University
Ascending chains of free groups in 3-manifold groups
Abstract: When does an ascending chain of free subgroups of a given group G stabilize? Without placing conditions on the rank of each entry in the chain not much can be said. The story is quite different for ascending chains of bounded rank. G. Higman and M. Takahashi independently proved that when G is a free group every such chain stabilizes. I. Kapovich and A. Miyasnikov re-phrased their proof in the language of Stallings’ folds. This proof can be generalized to graphs-of-groups where the free subgroups of the vertex groups satisfy the chain condition. As a result every ascending chain of bounded rank free subgroups of a surface group stabilizes. In this talk I will prove that every ascending chain of bounded rank free subgroups in a closed (or finite-volume hyperbolic) 3—manifold group. Hyperbolic geometry, geometrization, and the JSJ decomposition all play a role in the proof. This is joint work with N. Lazarovich.
(Note this is a geometry talk at the usual dynamics time/place)
Wednesday March 15, 2023 at 3:00 PM in 427 SEO