Poincar\'e duality for spaces with isolated singularities

TL;DR

This paper constructs rational Poincaré duality spaces for pseudomanifolds with isolated singularities using intersection space formalism, extending the understanding of duality in singular spaces.

Contribution

It introduces a method to assign rational Poincaré duality spaces to pseudomanifolds with isolated singularities, linking to Banagl's intersection spaces in even dimensions.

Findings

Construction of rational Poincaré duality spaces for singular pseudomanifolds

Relation established between these spaces and intersection spaces in even dimensions

Provides a framework for duality in spaces with isolated singularities

Abstract

In this paper we assign, under reasonable hypothesis, to each pseudomanifold with isolated singularities a rational Poincar\'e duality space. These spaces are constructed with the formalism of intersections spaces defined by Markus Banagl and are indeed related to them in the even dimensional case.