Extending simplicial complexes: Topological and combinatorial properties
Abstract
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 Cohen-Macaulayness, shellability, vertex-decomposability etc.) of the resulting hypergraph 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.
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