Jone Lopez de Gamiz

Limit groups over coherent RAAGs and their subgroups.

Subgroups of direct products of free groups, and more generally, of limit groups have been extensively studied since the 1950's due to their interesting subgroup structure and their relevance in many areas of mathematics such as algebraic geometry over groups. Finitely presented subgroups of direct products of limit groups have a tame structure and the main algorithmic problems are decidable in this class. Nevertheless, Bridson showed that this is not necessarily true for RAAGs, that is, there are finitely presented subgroups of direct products of RAAGs with undecidable decision problems. This leads to the question of identifying the class of RAAGs for which finitely presented subgroups of the direct product of groups in this class have a rigid structure.

In this talk, we introduce limit groups over coherent RAAGs, we motivate the study of subgroups of direct products of limit groups over coherent RAAGs and we give partial answers to the previous question.