A note on Duality and the Atiyah-Hirzebruch spectral sequence

Published 24 Jul 2025 in math.AT and math.GT | (2507.18250v1)

Abstract: We show that, for a finite spectrum $X$, the Spanier-Whitehead duality isomorphism induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences. As an application, it follows that Poincar\'e duality for a Poincar\'e duality complex, which is oriented over a ring spectrum $E$, induces an isomorphism between the two spectral sequences.

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Maximilian Hans

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