Theoretical analysis demonstrates uniform waist inequalities in codimension two for finite covers of manifolds with Kazhdan fundamental groups, highlighting higher-dimensional expansion.
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.
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Bader et al. (2026) studied this question.
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