15 citations · 40 across the 23 of their papers we have counts for
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math.AT2006
Simple Homotopy Types and Finite Spaces
Jonathan Ariel Barmak, Elias Gabriel Minian
We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion…
math.AT2006
Minimal Finite Models
Jonathan Ariel Barmak, Elias Gabriel Minian
We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new c…