English

Extending simplicial complexes: Topological and combinatorial properties

Commutative Algebra 2021-10-28 v2 Combinatorics

Abstract

Given an arbitrary hypergraph H\mathcal{H}, we may glue to H\mathcal{H} a family of hypergraphs to get a new hypergraph H\mathcal{H}' having H\mathcal{H} as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph H\mathcal{H}' is under control in terms of the glued components. This enables us to construct broad classes of simplicial complexes containing a given simplicial complex as induced subcomplex satisfying nice topological and combinatorial properties. Our results will be accompanied with some interesting open problems.

Keywords

Cite

@article{arxiv.2110.12170,
  title  = {Extending simplicial complexes: Topological and combinatorial properties},
  author = {Mohammad Farrokhi Derakhshandeh Ghouchan and Alireza Shamsian and Ali Akbar Yazdan Pour},
  journal= {arXiv preprint arXiv:2110.12170},
  year   = {2021}
}

Comments

20 pages

R2 v1 2026-06-24T07:07:28.915Z