Expansion of a simplicial complex

For a simplicial complex $Δ$, we introduce a simplicial complex attached to $Δ$, called the expansion of $Δ$, which is a natural generalization of the notion of expansion in graph theory. We are interested in knowing how the properties of a simplicial complex and its Stanley-Reisner ring relate to those of its expansions. It is shown that taking expansion preserves vertex decomposable and shellable properties and in some cases Cohen-Macaulayness. Also it is proved that some homological invariants of Stanley-Reisner ring of a simplicial complex relate to those invariants in the Stanley-Reisner ring of its expansions.

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