A note on Duality and the Atiyah-Hirzebruch spectral sequence
Algebraic Topology
2026-04-14 v3 Geometric Topology
Abstract
We show that, for a finite spectrum , 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 induces an isomorphism between the two spectral sequences.
Keywords
Cite
@article{arxiv.2507.18250,
title = {A note on Duality and the Atiyah-Hirzebruch spectral sequence},
author = {Maximilian David Hans},
journal= {arXiv preprint arXiv:2507.18250},
year = {2026}
}
Comments
15 pages; accepted version, to appear in Glasgow Mathematical Journal