A Chain Complex for Computing Intersection Homology of GS Manifolds with n-sheet Cone Singularities
Year: 2026
Type: article
Abstract: The aim of this paper is to construct a chain complex for a singular 2-manifold X with n -sheet cone singularities, where $$n \in \mathbb {N}$$ n ∈ N with $$n \ge 2$$ n ≥ 2 , equipped with a Gutierrez-Sotomayor flow $$\varphi $$ φ , that computes the intersection homology of X . By combining Morse theory and de Rham cohomology, we introduce a chain complex $$(C_{*}(X,\varphi ; \mathbb {R}), \partial _{*})$$ ( C ∗ ( X , φ ; R ) , ∂ ∗ ) whose generators consist of the regular singularities of $$\varphi $$ φ and the representatives of the de Rham cohomology of the links of the n -sheet cone singularities. The differential $$\partial _{*}$$ ∂ ∗ 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.
Institutions: Universidade Federal do ABC, Universidade de São Paulo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7154609501