Uniform Waist Inequalities in Codimension Two for Manifolds with Kazhdan Fundamental Group

Abstract Let $M$ M be a closed Riemannian manifold with Kazhdan fundamental group. It is well known that the Buser-Cheeger inequality yields a uniform waist inequality in codimension 1 for the finite covers of $M$ M , which is basically another way of saying that the finite covers form an expander family. We show that the finite covers of $M$ M also satisfy a uniform waist inequality in codimension 2.