26 citations · 65 across the 25 of their papers we have counts for
35 papers
The structuring effect of a Gottlieb element on the Sullivan minimal model of a space
Gregory Lupton, Samuel Bruce Smith
We show a Gottlieb element in the rational homotopy of a simply connected space implies a structural result for the Sullivan minimal model, with different results depending on…
The universal fibration with fibre in rational homotopy theory
Gregory Lupton, Samuel Bruce Smith
Let be a simply connected space with finite-dimensional rational homotopy groups. Let be the universal fibration of simply connected…
Digital Fundamental Groups and Edge Groups of Clique Complexes
Gregory Lupton, Nicholas A. Scoville
In previous work, we have defined---intrinsically, entirely within the digital setting---a fundamental group for digital images. Here, we show that this group is isomorphic to the…
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…
Homotopy Theory in Digital Topology
Gregory Lupton, John Oprea, Nicholas Scoville
Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have be…