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.
