An intrinsic homotopy theory for simplicial complexes, with applications to image analysis (Q1610272)

This paper contains a description of the homotopy theory of simplicial complexes. The description is given directly in terms of combinatorial structures, without reference to geometric realizations. In particular, there are results intended for application to image analysis, using discrete approximations \(t_\epsilon X\) to metric spaces \(X\). The simplexes in \(t_\epsilon X\) are the finite sets in \(X\) of diameter at most \(\epsilon\).