Extending simplicial complexes: Topological and combinatorial properties

Given an arbitrary hypergraph H, we may glue to H a family of hypergraphs to get a new hypergraph H' having H as an induced subhypergraph. In this paper, we introduce three gluing techniques for which the topological and combinatorial properties (such as CohenMacaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph 3L' 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. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.