Expanders and torsion homology

We say that a Riemannian 3-manifold has good higher expansion if every rationally null-homologous i-cycle bounds a relatively small i+1 chain. In this talk, I’ll explain how to construct rational homology spheres which are good higher expanders. On the other hand, I will explain that higher expanders must be rather topologically complicated; in particular, they must have large torsion homology compared to their volume.

See webpage for more details: https://people.math.harvard.edu/~ctm/sem/