Coboundary and cosystolic expansion from strong symmetry

Understand

Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions.

• The classical Cheeger inequality implies that for graphs edge expansion is equivalent to spectral expansion.
• In higher dimensions this is not the case: a simplicial complex can be spectrally expanding but not have high dimensional edge-expansion.
• The phenomenon of high dimensional edge expansion in higher dimensions is much more involved than spectral expansion, and is far from being understood.