3 research outputs found
Limit groups over coherent right-angled Artin groups
A new class of groups , containing all coherent RAAGs and all
toral relatively hyperbolic groups, is defined. It is shown that, for a group
in the class , the -exponential group
may be constructed as an iterated centraliser extension.
Using this fact, it is proved that is fully residually
(i.e. it has the same universal theory as ) and so its finitely generated
subgroups are limit groups over . If is a coherent RAAG, then
the converse also holds - any limit group over embeds into
. Moreover, it is proved that limit groups over
are finitely presented, coherent and CAT, so in particular
have solvable word and conjugacy problems.Comment: 40 pages, 1 figur