Stability, approximable quotients, and higher property (T)

Abstract

We construct a wealth of groups that are finitely presented, Frobenius stable, have property (T), but are very far from having property (T${}_2$). Our method also shows that property (T${}_2$) does not pass to quotients. A post-scriptum relates and comments on an experience this paper had with an AI benchmark.

12 pages. v2: added post-scriptum on AI benchmarks