7 citations · 10 across the 19 of their papers we have counts for
6 papers · 2 filters
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…
On the homotopy and strong homotopy type of complexes of discrete Morse functions
Connor Donovan, Maxwell Lin, Nicholas A. Scoville
In this paper, we determine the homotopy type of the Morse complex of certain collections of simplicial complexes by studying dominating vertices or strong collapses. We show that…
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…
On the automorphism group of the Morse complex
Maxwell Lin, Nicholas A. Scoville
Let be a finite, connected, abstract simplicial complex. The Morse complex of , first introduced by Chari and Joswig, is the simplicial complex constructed from all gradient…