  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. In particular, prior to this work, the only known bounded degree
cosystolic expanders known were derived from the theory of buildings that is
far from being elementary.
  In this work we study high dimensional complexes which are {\em strongly
symmetric}. Namely, there is a group that acts transitively on top dimensional
cells of the simplicial complex [e.g., for graphs it corresponds to a group
that acts transitively on the edges]. Using the strong symmetry, we develop a
new machinery to prove coboundary and cosystolic expansion.
