Online Talk

Manifolds that are oriented with respect to a ring spectrum E satisfy a version of Poincaré duality in E-(co)homology. A standard tool for computing these (co)homology groups is the Atiyah–Hirzebruch spectral sequence, which comes in both homological and cohomological forms. We briefly discuss how the notion of E-orientability extends naturally to Poincaré duality complexes, and explain how Poincaré duality gives rise to an isomorphism between the homological and cohomological Atiyah–Hirzebruch spectral sequences.