We introduce a new model of random groups, in which the random group is
(but
not hyperbolic). The definition relies on a surgery type construction for
Möbius–Kantor complexes; it depends on the existence of a sufficiently large
semigroup of group cobordisms, which can be composed in a random way to define a
group. By construction, the local geometry in this model is preassigned. We aim to
study the asymptotic geometry of the random group, in particular to prove that it is
not hyperbolic in a strong sense.
Keywords
nonpositive curvature, discrete groups, random groups
