Minimal Finite Models

Jonathan Ariel Barmak and Elias Gabriel Minian

We characterize the smallest finite spaces with the same homotopy groups as the spheres. Similarly, we describe the minimal finite models of any finite graph.We also develop new combinatorial techniques based on finite spaces to study classical invariants of general topological spaces.

Journal of Homotopy and Related Structures, Vol. 2(2007), No. 1, pp. 127-140