Coboundary Expansion of Coset Complexes

Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topological expansion, but nowadays a significant part of the motivation stems from its deep connection to problems in theoretical computer science such as agreement expansion in the low soundness regime. In this paper, we prove coboundary expansion with non-Abelian coefficients for the coset complex construction of Kaufman and Oppenheim. Our proof uses a novel global argument, as opposed to the local-to-global arguments that are used to prove cosystolic expansion. 1 When we refer to Ramanujan complexes below, any quotient of an affine An building with sufficiently large injectivity radius can be used.