Refinement invariance of intersection (co)homologies

TL;DR

This paper investigates the invariance of various intersection (co)homologies under refinement, confirming classical topological invariance and presenting new refinement invariance results relevant for Poincaré Duality.

Contribution

It establishes the classical topological invariance of intersection homology and introduces new results on refinement invariance for different intersection (co)homologies.

Findings

Confirmed classical topological invariance of intersection homology.

Proved various refinement invariance results for intersection (co)homologies.

Enhanced understanding of invariance properties relevant for Poincaré Duality.

Abstract

We study the refinement invariance of several intersection (co)homologies existing in the literature. These (co)homologies have been introduced in order to establish the Poincar\'e Duality in variousl contexts. We found the classical topological invariance of the intersection homology and also various refinement invariance results already proved.