A Toda bracket convergence theorem for multiplicative spectral sequences
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866913468781690880 |
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| author | Belmont, Eva Kong, Hana Jia |
| author_facet | Belmont, Eva Kong, Hana Jia |
| contents | Moss' theorem, which relates Massey products in the $E_r$-page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric monoidal stable topological model category, we prove a general version of Moss' theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. The theorem has broad applications, e.g. to the computation of the motivic slice and motivic Adams spectral sequences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_08689 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Toda bracket convergence theorem for multiplicative spectral sequences Belmont, Eva Kong, Hana Jia Algebraic Topology 55T05 (Primary) 55S20, 55S30, 14F42 (Secondary) Moss' theorem, which relates Massey products in the $E_r$-page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric monoidal stable topological model category, we prove a general version of Moss' theorem which applies to spectral sequences that arise from filtrations compatible with the monoidal structure. The theorem has broad applications, e.g. to the computation of the motivic slice and motivic Adams spectral sequences. |
| title | A Toda bracket convergence theorem for multiplicative spectral sequences |
| topic | Algebraic Topology 55T05 (Primary) 55S20, 55S30, 14F42 (Secondary) |
| url | https://arxiv.org/abs/2112.08689 |