标题： TO_BE_TRANSLATED: Expansion of a simplicial complex 显示英文标题

标题： Expansion of a simplicial complex

摘要： TO_BE_TRANSLATED: For a simplicial complex $\Delta$, we introduce a simplicial complex attached to $\Delta$, called the expansion of $\Delta$, 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. 显示英文摘要

摘要： For a simplicial complex $\Delta$, we introduce a simplicial complex attached to $\Delta$, called the expansion of $\Delta$, 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.