3 papers
math.GR2026
Kazhdan groups of dimension with prescribed second -Betti number
Francesco Fournier-Facio, Roman Sauer
We construct a family of simple, lacunary hyperbolic groups with property that have rational cohomological dimension~ and whose second -Betti number can be prescr…
math.GR2025
Higher property T and below-rank phenomena of lattices
Uri Bader, Roman Sauer
The purpose of this paper is twofold. We explore higher property T as an abstract group-theoretic property. In particular, we provide new operator-algebraic characterizations of hi…
math.DG2024
Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group
Uri Bader, Roman Sauer
Let M be a closed Riemannian manifold with Kazhdan fundamental group. It is well known that the Cheeger inequality yields a uniform waist inequality in codimension one for the fini…