On formality of diagrams of Eilenberg-MacLane spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908990992023552 |
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| author | Solomadin, Grigory Touzé, Antoine |
| author_facet | Solomadin, Grigory Touzé, Antoine |
| contents | In this paper, we establish formality (over $\mathbb{Q}$) for diagrams of Eilenberg-MacLane spaces of any height $n\geq 1$. This implies spectral sequence (over $\mathbb{Q}$) collapse at page $2$ for any diagram of EML spaces over any small category. We prove by functor calculus argument that formality does not hold over any fixed commutative ring $\mathbf{k}$ not containing $\mathbb{Q}$, where the category of diagrams is over the category generated by finite direct sums of a cyclic group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On formality of diagrams of Eilenberg-MacLane spaces Solomadin, Grigory Touzé, Antoine Algebraic Topology Category Theory K-Theory and Homology In this paper, we establish formality (over $\mathbb{Q}$) for diagrams of Eilenberg-MacLane spaces of any height $n\geq 1$. This implies spectral sequence (over $\mathbb{Q}$) collapse at page $2$ for any diagram of EML spaces over any small category. We prove by functor calculus argument that formality does not hold over any fixed commutative ring $\mathbf{k}$ not containing $\mathbb{Q}$, where the category of diagrams is over the category generated by finite direct sums of a cyclic group. |
| title | On formality of diagrams of Eilenberg-MacLane spaces |
| topic | Algebraic Topology Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2604.22435 |