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Briony Eldridge

Publications and source records attributed to Briony Eldridge.

3 recordsLinked to original sources
arXiv2026

The discrete homotopy hypothesis for directed graphs

We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as $A$-groups or reduced GLMY homotopy groups. Localizing the category of directed graphs at morphisms that induce isomorphisms on these groups yields an $\infty$-category, denoted by ${\sf DGra}_\infty$. We prove that ${\sf DGra}_\infty$ is equivalent to the $\infty$-category of spaces, establishing a directed version of the discrete homotopy hypothesis of Carranza and Kapulkin.

math.AT↗
arXiv2026

Homotopy exponents of polyhedral products

We study Moore's conjecture and homotopy exponents for polyhedral products. For $(\underline{CA},\underline{A})^K$ where each $A_i$ is finite and has torsion-free homology, we prove that if $(\underline{CA},\underline{A})^K$ is rationally hyperbolic, then it has no homotopy exponent at any odd prime. Under the additional hypothesis $ΣA_i$ is homotopy equivalent to a finite-type wedge of simply-connected spheres, we show Moore's conjecture holds for $(\underline{CA},\underline{A})^K$. We also give criteria such that, for a large family of polyhedral join products, the associated polyhedral products are rationally hyperbolic, mod-$p^r$ hyperbolic for all but finitely many primes, and have no homotopy exponent at all but finitely many primes.

math.AT↗