Title: A combination theorem for combinatorially non-positively curved complexes of hyperbolic groups
Speaker: Damian Osajda (University of Wrocław & McGill University)
Abstract: This is joint work with Alexandre Martin (Heriot-Watt University). Let X be a complex of hyperbolic groups. In general the fundamental group of X need not to be hyperbolic. M. Bestvina and M. Feighn showed that if X is a graph of groups, and satisfies some natural `acylindricity' conditions then the fundamental group of X is hyperbolic. A. Martin extended this combination theorem to the case of X whose underlying complex carries a hyperbolic CAT(0) metric. I will present a combinatorial counterpart of Martin's result obtained recently. We introduce a weak nonpositive-curvature-like combinatorial property and show that fundamental groups of complexes of groups with underlying complex satisfying that property are hyperbolic. Our property holds for e.g. (weakly) systolic complexes and small cancellation complexes giving rise to new examples of complexes of groups with hyperbolic fundamental groups. The proof relies on constructing a potential Gromov boundary for the resulting groups and analyzing the dynamics of the action on the boundary in order to use Bowditch’s characterization of hyperbolicity.
Seminar URL: https://research.math.osu.edu/ggt/
