Model Structures on Infinity-Categories of Filtrations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917599913181184 |
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| author | Aitken, Colin |
| author_facet | Aitken, Colin |
| contents | In 1974, Gugenheim and May showed that the cohomology $\text{Ext}_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of the $H\mathbb{F}_p$-based Adams spectral sequence. By studying a novel sequence of deformations of a presentably symmetric monoidal stable $\infty$-category $C$, we show that for a variety of spectral sequences coming from filtered spectra, the set of elements on the $E_2$ page surviving to the $E_k$ page is generated under matric Massey products by elements with degree $s < k.$ This work is the author's PhD thesis, completed under the supervision of Peter May. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model Structures on Infinity-Categories of Filtrations Aitken, Colin Algebraic Topology In 1974, Gugenheim and May showed that the cohomology $\text{Ext}_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of the $H\mathbb{F}_p$-based Adams spectral sequence. By studying a novel sequence of deformations of a presentably symmetric monoidal stable $\infty$-category $C$, we show that for a variety of spectral sequences coming from filtered spectra, the set of elements on the $E_2$ page surviving to the $E_k$ page is generated under matric Massey products by elements with degree $s < k.$ This work is the author's PhD thesis, completed under the supervision of Peter May. |
| title | Model Structures on Infinity-Categories of Filtrations |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2402.17921 |