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math.AT2026
Homotopy exponents of polyhedral products
Briony Eldridge
We study Moore's conjecture and homotopy exponents for polyhedral products. For where each is finite and has torsion-free homology, we prov…
math.AT2026
The discrete homotopy hypothesis for directed graphs
Briony Eldridge, Sergei O. Ivanov, Xiaomeng Xu +2
We develop a homotopy theory of directed graphs based on cubical homotopy groups, also referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed…
math.AT2024
Loop spaces of polyhedral products associated with the polyhedral join product
Briony Eldridge
We give a homotopy equivalence for the loop space of the moment-angle complex associated with a simplicial complex formed by the polyhedral join operation, and give necessary condi…