# Topological invariance of torsion sensitive intersection homology

## TL;DR

This paper establishes the topological invariance of torsion sensitive intersection homology, showing that its defining sheaf complexes are independent of stratification choices, extending classical results and providing new insights.

## Contribution

It proves topological invariance for torsion sensitive intersection homology and offers new results even in classical intersection homology.

## Key findings

- Proves independence of sheaf complexes from stratification choices.
- Extends classical invariance theorems to torsion sensitive intersection homology.
- Provides new invariance results in classical intersection homology.

## Abstract

Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no local cohomology conditions on the underlying space. In this paper we consider for torsion sensitive intersection homology analogues of another important property of classical intersection homology: topological invariance. In other words, we consider to what extent the defining sheaf complexes of the theory are independent (up to quasi-isomorphism) of choice of stratification. In addition to providing torsion sensitive versions of the existing invariance theorems for classical intersection homology, our techniques provide some new results even in the classical setting.