Expansion for 2-complexes

Anna Gundert

ETH Zurich

Abstract

For graphs, there are two ways to define expansion: as a combinatorial or as a spectral property. By the Cheeger inequality these two definitions are very closely connected. In this talk, we will look at generalizations of expansion to 2-dimensional simplicial complexes. Both ways of defining graph expansion can be generalized in a pretty straightforward fashion using basic cohomological notions. But we will see that the close connection of the graph properties does not carry over to the higher dimension.