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arXiv · 1601.00456

Expansion of a simplicial complex

Somayeh Moradi·Fahimeh Khosh-Ahang
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Abstract

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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Somayeh Moradi, Fahimeh Khosh-Ahang. 2016-01-04. Expansion of a simplicial complex. https://arxiv.org/abs/1601.00456

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