Abstract
Buildings were originally introduced by Jacques Tits around the 1950s as a geometric tool to study the semisimple Lie (and algebraic) groups. By now, buildings have a very rich theory of their own; for instance, they possess a "non-positively curved" cellular complex structure, which makes them prominent objects of interest in geometric group theory. In this talk, I will investigate certain combinatorial analogues of geodesic rays in buildings (the "geodesic ray bundles") and give some intuition about how they look like. Using recent results of Huang, Sabok and Shinko, I will then derive some consequences on the topic of hyperfinite group actions.