Finite Topological Spaces: Combinatorics and Topology

JONATHAN ARIEL BARMAK

Centro de Estruturas Lineares e Combinatórias, University of Lisbon, Lisboa, Portugal

Congreso; Summer School on Algebra and Combinatorics; 2007

In this talk I will recall the relationship between finite topological spaces and finite posets and show how their combinatorial and topological nature can be used to investigate homotopy theory of polyhedra and general spaces.I will show new results from a joint work with E.G. Minian concerning the minimal finite models of spaces, i.e. the smallest spaces with the same weak homotopy type of a given one. I will exhibit the minimal finite models of the spheres and of finite graphs and show new techniques based on finite spaces to compute algebraic invariants of general spaces.