3 papers
math.AT2025
The Simplicial Loop Space of a Simplicial Complex
Gregory Lupton, Jonathan Scott
Given a simplicial complex , we construct a simplicial complex that may be regarded as a combinatorial version of the based loop space of a topological space. Our construct…
math.AT2025
The Face Group of a Simplicial Complex
Gregory Lupton, Nicholas A. Scoville, P. Christopher Staecker
The edge group of a simplicial complex is a well-known, combinatorial version of the fundamental group. It is a group associated to a simplicial complex that consists of equivalenc…
math.AT2023
A Second Homotopy Group for Digital Images
Gregory Lupton, Oleg Musin, Nicholas A. Scoville +2
We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second hom…