Simplicial perturbation techniques and effective homology

Abstract

In this paper, we deal with the problem of the computation of the homology of a finite simplicial complex after an “elementary simplicial perturbation” process such as the inclusion or elimination of a maximal simplex or an edge contraction. To this aim we compute an algebraic topological model that is a special chain homotopy equivalence connecting the simplicial complex with its homology (working with a field as the ground ring).