Seminar series
Date
Mon, 13 May 2024
15:30
15:30
Location
L5
Speaker
Ashot Minasyan
Organisation
Southampton University
Given a finite simplicial graph $\Gamma$, the right angled Artin group (RAAG) $A(\Gamma)$ is generated by the vertices of $\Gamma$ subject to the relations that two vertices commute if and only if they are adjacent in $\Gamma$. RAAGs play an important role in Geometric Group Theory and in Low Dimensional Topology.
Given a group $G$, a finite graph $\Gamma$ and a homomorphism $\phi: A(\Gamma) \to G$ one can ask for conditions ensuring that this homomorphism can be "promoted" to an injective one. In my talk I will discuss such criteria in the case when $G$ is a one-relator group and $\Gamma$ is a forest. In particular, I will sketch an argument showing that it is sufficient for $\phi$ to be injective on the positive sub-monoid of $A(\Gamma)$.
The talk will be based on joint work with Motiejus Valiunas (University of Wroclaw, Poland).