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arXiv · 2507.18250

A note on Duality and the Atiyah-Hirzebruch spectral sequence

Maximilian David Hans
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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 Poincar\'e duality for a Poincar\'e duality complex that is oriented over a ring spectrum $R$ induces an isomorphism between the two spectral sequences.

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Maximilian David Hans. 2025-07-24. A note on Duality and the Atiyah-Hirzebruch spectral sequence. https://arxiv.org/abs/2507.18250

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