English

Expansion of a simplicial complex

Commutative Algebra 2016-01-05 v1

Abstract

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

Keywords

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}
}
R2 v1 2026-06-22T12:22:23.441Z