Resumen de Limit groups over coherent right-angled Artin groups

Montserrat Casals Ruiz , Andrew B. Duncan, Ilya Kazachkov

• A new class of groups C, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group G in the class C, the Z[t]-exponential group GZ[t] may be constructed as an iterated centraliser extension. Using this fact, it is proved that GZ[t] is fully residually G (i.e. it has the same universal theory as G) and so its finitely generated subgroups are limit groups over G. If G is a coherent RAAG, then the converse also holds – any limit group over G embeds into GZ[t] . Moreover, it is proved that limit groups over G are finitely presented, coherent and CAT(0), so in particular have solvable word and conjugacy problems