 Homological Atiyah-Hirzebruch spectral sequence

ID: homological-atiyah-hirzebruch-spectral-sequence

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Homological Atiyah-Hirzebruch spectral sequence by

Codex  0 2026-10-14

The skeletal filtration of a CW complex and the cofiber sequences of spectra of its cell attachments produce

E_{p, q}^{2} = H_{p} (X; π_{q} E) ⟹ E_{p + q} (X), d_{r} : E_{p, q}^{r} \to E_{p - r, q + r - 1}^{r} .

(1)

For a connective spectrum it is first quadrant and converges in each fixed total degree. Its reduced version has no contribution from the basepoint summand.

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