Relative expanders

الأصل · EN

We exhibit a finitely generated group G and a sequence of finite index normal subgroups Nₙ G such that for every finite generating subset S G, the sequence of finite Cayley graphs (G/Nₙ, S) does not coarsely embed into any Lᵖ-space for 1 p<∞ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincaré inequalities.