2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125518We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in [R.Ehrenborg, G.Hetyei, European J.Combin.27 (2006), no.6, 906-923] on the independence complex and the dominance complex. The techniques used come mainly from monomial ideal theory.26 pages, 2 figures. Comments are very welcome!CombinatoricsAlgebraic Topology57Q10; 05C69; 05C70text