4 papers
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…
Fundamental groups of reduced suspensions are locally free
Jeremy Brazas, Patrick Gillespie
In this paper, we analyze the fundamental group of the reduced suspension where is an arbitrary based Hausdorff space. We show that $π_1(ΣX,…
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…
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…