3 papers
math.AT2026
A colimit decomposition for the loop homology of polyhedral products
Lewis Stanton, Fedor Vylegzhanin
We show that the loop homology algebras of polyhedral products of the form can be written as a colimit over the flagification of $\mat…
math.AT2026
Anick's conjecture for polyhedral products
Lewis Stanton, Fedor Vylegzhanin
We develop a method for studying the pointed loop space of general polyhedral products, showing that many properties are determined by the moment-angle complex. To apply the method…
math.AT2025
Polyhedral coproducts
Steven Amelotte, William Hornslien, Lewis Stanton
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We be…