Homotopical decompositions of Vietoris-Rips complexes

In this talk we will investigate the idea of decomposing a simplicial complex and we will study it from a homotopical point of view. Since in general the initial simplicial complex and its decompositions do not have the same homotopy type, a natural question that might arise is under which conditions they are weakly equivalent. Furthermore, we will use the general machinery developed in the context of Vietoris-Rips complexes and their decompositions.