publiée le 3 mai 2024
Laminations and structure theorems for group actions on the line - Part 1
De Michele Triestino
Incoherence of free-by-free and surface-by-free groups
Apparaît dans la collection : Virtual Geometric Group Theory conference / Rencontre virtuelle en géométrie des groupes
A group is said to be coherent if every finitely generated subgroup is finitely presented. This property is enjoyed by free groups, and the fundamental groups of surfaces and 3-manifolds. A group that is not coherent is incoherent, and it is very interesting to try and understand which groups are coherent. We will discuss some of the geometric and topological aspects of this question, particularly quasi-convexité and algebraic fibers. We show that free-by-free and surface-by-free groups are incoherent, when the rank and genus are at least 2. The proof uses an understanding of fibers and also the RFRS property. this is joint work with Robert Kropholler and Stefano Vidussi.
