26 citations · 58 across the 14 of their papers we have counts for
20 papers
Sequential parametrized topological complexity and related invariants
Michael Farber, John Oprea
Parametrized motion planning algorithms \cite{CFW} have a high degree of universality and flexibility; they generate the motion of a robotic system under a variety of external cond…
Right-angled Artin groups, polyhedral products and the TC-generating function
Jorge Aguilar-Guzman, Jesus Gonzalez, John Oprea
For a graph , let denote the Eilenberg-Mac Lane space associated to the right-angled Artin (RAA) group defined by . We use the relationship between the combi…
The Digital Hopf Construction
Gregory Lupton, John Oprea, Nicholas A. Scoville
Various concepts and constructions in homotopy theory have been defined in the digital setting. Although there have been several attempts at a definition of a fibration in the digi…
Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
Andrés Angel, Hellen Colman, Mark Grant +1
We use the homotopy invariance of equivariant principal bundles to prove that the equivariant -category of Clapp and Puppe is invariant under Morita equivalence. As a…
A Fundamental Group for Digital Images
Gregory Lupton, John Oprea, Nicholas Scoville
We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebrai…
Subdivision of Maps of Digital Images
Gregory Lupton, John Oprea, Nicholas A. Scoville
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topol…