Loop spaces of polyhedral products associated with polyhedral join products
Loop spaces of polyhedral products associated with polyhedral join products
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Briony Eldridge, University of Southampton
Polyhedral products are a topological space formed by gluing together ingredient spaces in a manner governed by a simplicial complex. They appear in many areas of study, including toric topology, combinatorics, commutative algebra, complex geometry and geometric group theory. A fundamental problem is to determine how operations on simplicial complexes change the topology of the polyhedral product. In this talk, we obtain a description of the loop space of polyhedral products associated with polyhedral join complexes, and build a new family of simplicial complexes such that the homotopy type of the loop space of the moment angle complex is a product of spheres and loops on spheres.