2-track algebras and the Adams spectral sequence
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866908840774074368 |
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| author | Baues, Hans-Joachim Frankland, Martin |
| author_facet | Baues, Hans-Joachim Frankland, Martin |
| contents | In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3$-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms $E_m$. In this paper, we introduce $2$-track algebras and tertiary chain complexes, and we show that the $E_4$-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1505_03885 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | 2-track algebras and the Adams spectral sequence Baues, Hans-Joachim Frankland, Martin Algebraic Topology 55T15 (Primary) 18G50, 55S20 (Secondary) In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3$-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms $E_m$. In this paper, we introduce $2$-track algebras and tertiary chain complexes, and we show that the $E_4$-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations. |
| title | 2-track algebras and the Adams spectral sequence |
| topic | Algebraic Topology 55T15 (Primary) 18G50, 55S20 (Secondary) |
| url | https://arxiv.org/abs/1505.03885 |