Henry Adams

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20232025

most citedLower bounds on the homology of Vietoris-Rips complexes of hypercube graphs

1 citations · 1 across the 5 of their papers we have counts for

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math.AT2025

Anti-Vietoris--Rips metric thickenings and Borsuk graphs

Henry Adams, Alex Elchesen, Sucharita Mallick +1

For $X$ a metric space and $r \geq 0$ , the anti-Vietoris-Rips metric thickening $AV R^{m} (X; r)$ is the space of all finitely supported probability measures on $X$ whose support…

math.AT2025

Vietoris-Rips complexes of torus grids

Henry Adams, Adenike Yeside Adetowubo, Hector Barriga-Acosta +2

We study the topology of Vietoris--Rips complexes of finite grids on the torus. Let $T_{n, n}$ be the grid of $n \times n$ points on the flat torus $S^{1} \times S^{1}$ , equipped with the…

math.AT2025

Homotopy connectivity of Čech complexes of spheres

Henry Adams, Ekansh Jauhari, Sucharita Mallick

Let $S^{n}$ be the $n$ -sphere with the geodesic metric and of diameter $π$ . The intrinsic Čech complex of $S^{n}$ at scale $r$ is the nerve of all open balls of radius $r$ in $S^{n}$ . In…

math.AT2024

Persistent equivariant cohomology

Henry Adams, Evgeniya Lagoda, Michael Moy +2

This article has two goals. First, we hope to give an accessible introduction to persistent equivariant cohomology. Given a topological group $G$ acting on a filtered space, persis…

math.AT2024

The connectivity of Vietoris-Rips complexes of spheres

Henry Adams, Johnathan Bush, Žiga Virk

We survey what is known and unknown about Vietoris-Rips complexes and thickenings of spheres. Afterwards, we show how to control the homotopy connectivity of Vietoris-Rips complexe…