The non-hyperbolic features of random Gromov's monsters

15.01.2019 15:00 - 17:00

Dominik Gruber (ETH Zürich)

Gromov's graphical model for random groups produced the first counterexamples to the Baum-Connes conjecture with coefficients. Gromov's graphical small cancellation theory lead to another closely related class of such counterexamples. Graphical small cancellation groups admit non-elementary acylindrical actions on Gromov hyperbolic spaces and, therefore, exhibit many features of hyperbolic groups. By contrast, as we will discuss in this talk, the random groups arising from Gromov's graphical model do not admit any non-elementary actions on hyperbolic spaces. Furthermore, they cannot be quasi-isometric to any acylindrically hyperbolic group, because their divergence functions are linear along a subsequence. These results show that the two types of counterexamples to the Baum-Connes conjecture with coefficients are in fact very different classes of groups.


This is based on joint works with Alessandro Sisto and Romain Tessera.


G. Arzhantseva, Ch. Cashen


SR 8, 2. OG, OMP 1