Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

Refinement invariance of intersection (co)homologies

Pages: 311 – 340

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a17


Martintxo Saralegi-Aranguren (Laboratoire de Mathématiques de Lens, Université d’Artois, Lens, France)


We prove the refinement invariance of several intersection (co)homologies existing in the literature: Borel–Moore, Blownup, the classical one, … These (co)homologies have been introduced in order to establish the Poincaré Duality in various contexts. In particular, we retrieve the classical topological invariance of the intersection homology as well as several refinement invariance results already known.


intersection homology, intersection cohomology, invariance

2010 Mathematics Subject Classification


Received 16 November 2019

Received revised 17 June 2020

Accepted 28 July 2020

Published 4 November 2020