Abstract The aim of this paper is to construct a chain complex for a singular 2-manifold X with n -sheet cone singularities, where n N n ∈ N with n 2 n ≥ 2, equipped with a Gutierrez-Sotomayor flow φ, that computes the intersection homology of X. By combining Morse theory and de Rham cohomology, we introduce a chain complex (C* (X, ; R), *) (C ∗ (X, φ ; R), ∂ ∗) whose generators consist of the regular singularities of φ and the representatives of the de Rham cohomology of the links of the n -sheet cone singularities. The differential * ∂ ∗ carries a dynamical aspect, tracking the flow trajectories between consecutive singularities. The relevance of this chain complex becomes clear when we prove that its homology is isomorphic to the intersection homology of the underlying pseudomanifold.
Lima et al. (Thu,) studied this question.
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