A note on duality and the Atiyah–Hirzebruch spectral sequence
Abstract
Abstract We show that, for a finite spectrum $X$ , Spanier–Whitehead duality induces an isomorphism between the cohomological and homological Atiyah–Hirzebruch spectral sequences. As an application, it follows that Poincaré duality for a Poincaré duality complex that is oriented over a ring spectrum $\mathcal{R}$ induces an isomorphism between the two spectral sequences.
Fields of Study & Subjects
Mathematics and Applications
Spectral Theory in Mathematical Physics
Mathematical functions and polynomials
Publication details
- Journal / source
- Glasgow Mathematical Journal
- Pages
- 1–16
- Publication date
- 5 May 2026
- Language
- EN