A note on Duality and the Atiyah-Hirzebruch spectral sequence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917402263945216 |
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| author | Hans, Maximilian David |
| author_facet | Hans, Maximilian David |
| contents | 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 $R$ induces an isomorphism between the two spectral sequences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Duality and the Atiyah-Hirzebruch spectral sequence Hans, Maximilian David Algebraic Topology Geometric Topology 57P10, 55P25, 55M05, 55T25 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 $R$ induces an isomorphism between the two spectral sequences. |
| title | A note on Duality and the Atiyah-Hirzebruch spectral sequence |
| topic | Algebraic Topology Geometric Topology 57P10, 55P25, 55M05, 55T25 |
| url | https://arxiv.org/abs/2507.18250 |