A sheaf-theoretic approach to homology manifolds and Poincaré/Atiyah duality

In this talk I will review the construction of the six functor formalism on locally compact Hausdorff spaces with coefficients in general stable infinity-categories, and explain how to interpret Poincaré and Atiyah duality through this language. As an application, I will show that any locally of constant shape integral homology manifold satisfies Poincaré and Atiyah duality.