3 papers
math.AT2023
Vietoris thickenings and complexes are weakly homotopy equivalent
Patrick Gillespie
Characterizing the homotopy types of the Vietoris--Rips complexes of a metric space is in general a difficult problem. The Vietoris--Rips metric thickening, a metric space anal…
math.AT2022
A homological nerve theorem for open covers
Patrick Gillespie
In this note we show that a particular homological nerve theorem, which was originally proved for a finite cover of a simplicial complex by subcomplexes, also holds for an open cov…
math.AT2020
Infinitary commutativity and fundamental groups of topological monoids
Jeremy Brazas, Patrick Gillespie
The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of -spaces are commutative. In this paper, we identify an infinitary analogue of the Eckm…