3 citations · 7 across the 6 of their papers we have counts for
5 papers · 1 filter
Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
Spherical Coordinates from Persistent Cohomology
Nikolas C. Schonsheck, Stefan C. Schonsheck
We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second…
On the chromatic localization of the homotopy completion tower for -algebras
Crichton Ogle, Nikolas Schonsheck
The completion tower of a nonunital commutative ring is a classical construction in commutative algebra. In the setting of structured ring spectra as modeled by algebras over a spe…
TQ-completion and the Taylor tower of the identity functor
Nikolas Schonsheck
The goal of this short paper is to study the convergence of the Taylor tower of the identity functor in the context of operadic algebras in spectra. Specifically, we show that if $…
Fibration theorems for TQ-completion of structured ring spectra
Nikolas Schonsheck
The aim of this short paper is to establish a spectral algebra analog of the Bousfield-Kan "fibration lemma" under appropriate conditions. We work in the context of algebraic struc…