Expansion of a simplicial complex
Commutative Algebra
2016-01-05 v1
Abstract
For a simplicial complex , we introduce a simplicial complex attached to , called the expansion of , 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.
Cite
@article{arxiv.1601.00456,
title = {Expansion of a simplicial complex},
author = {Somayeh Moradi and Fahimeh Khosh-Ahang},
journal= {arXiv preprint arXiv:1601.00456},
year = {2016}
}