Spectral sequences for the cyclic cohomology of differential graded algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915459680436224 |
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| author | Phimister, Andrew |
| author_facet | Phimister, Andrew |
| contents | We construct a number of new spectral sequences for calculating the cyclic cohomology $HC^*_{dg}(A)$ of a differential graded algebra (dga). With these spectral sequences we prove some results about the low dimensional cyclic cohomology and demonstrate the existence of various maps between $HC^*_{dg}(A)$ and $HH^*_{dg}(A)$. We also briefly introduce variations on Hochschild and cyclic cohomology of a dga, namely the $n$-th partial Hochschild cohomology and $n$-partial cyclic cohomology. Finally, we show how these results can be extended naturally to the dg-category setting. In particular we define the Hochschild and cyclic cohomolgy of dg-categories and show that the spectral sequences we have constructed can be used in this setting as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral sequences for the cyclic cohomology of differential graded algebras Phimister, Andrew K-Theory and Homology We construct a number of new spectral sequences for calculating the cyclic cohomology $HC^*_{dg}(A)$ of a differential graded algebra (dga). With these spectral sequences we prove some results about the low dimensional cyclic cohomology and demonstrate the existence of various maps between $HC^*_{dg}(A)$ and $HH^*_{dg}(A)$. We also briefly introduce variations on Hochschild and cyclic cohomology of a dga, namely the $n$-th partial Hochschild cohomology and $n$-partial cyclic cohomology. Finally, we show how these results can be extended naturally to the dg-category setting. In particular we define the Hochschild and cyclic cohomolgy of dg-categories and show that the spectral sequences we have constructed can be used in this setting as well. |
| title | Spectral sequences for the cyclic cohomology of differential graded algebras |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2508.16869 |