Homotopy equivalence reveals loop space structure of polyhedral products formed from simplicial complexes, suggesting finite-type characteristics.
We provide a homotopy equivalence for the loop space of the polyhedral product associated with a simplicial complex formed via the polyhedral join operation, and give sufficient conditions under which this loop space is a finite-type product of spheres and loops on spheres.
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Briony Eldridge (2025) studied this question.
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