North British Geometric Group Theory Seminar

Dario Ascari: JSJ decomposition and generalized Baumslag-Solitar groups

The theory of JSJ decomposition plays a key role in the classification of hyperbolic groups, in analogy with the case of 3-manifolds. While this theory can be extended to larger families of groups, the JSJ decomposition displays significant flexibility in general, making a complete understanding of its behaviour more challenging. In this talk, we explore this flexibility, with an emphasis on the case of generalized Baumslag-Solitar groups.

Federica Gavazzi: On decomposability of Artin and virtual Artin groups.

Abstract: A group is said to be decomposable if it can be written as a direct product of two proper subgroups, and indecomposable otherwise. In this talk, we investigate this property in the context of Artin groups and virtual Artin groups, and we show how this question provides useful insights into related topics such as rigidity, the isomorphism problem, and the determination of automorphism groups. Irreducible Artin groups of spherical type are known to be indecomposable, but for general irreducible Artin groups, indecomposability remains a conjecture. Virtual Artin groups are a recent generalization of Artin groups introduced by Bellingeri, Paris, and Thiel, which contain the classical Artin groups as subgroups. More precisely, we show that irreducible virtual Artin groups are always indecomposable. As a consequence, we demonstrate that understanding the automorphism group of a (reducible) virtual Artin group reduces to analyzing the automorphism groups of its irreducible components.

Ian Leary: Groups of type FP via graphical small cancellation

We give a construction of uncountably many groups of type FP that does not involve Morse theory and is independent from the work of Bestvina-Brady, although there is some overlap between the groups constructed.  The main tool used is graphical small cancellation.  This is partially joint work with Tom Brown.