Non-formality of Voronov's Swiss-Cheese operads
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909606509281280 |
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| author | Idrissi, Najib Vieira, Renato Vasconcellos |
| author_facet | Idrissi, Najib Vieira, Renato Vasconcellos |
| contents | The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n-1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction to formality that we find lies in arity $(2, 2^n)$, rather than $(2, 0)$ (Livernet) or $(4, 0)$ (Willwacher). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16979 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-formality of Voronov's Swiss-Cheese operads Idrissi, Najib Vieira, Renato Vasconcellos Algebraic Topology 18M60, 18M75 (Primary) 55S30, 55S35, 55P62 (Secondary) The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n-1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction to formality that we find lies in arity $(2, 2^n)$, rather than $(2, 0)$ (Livernet) or $(4, 0)$ (Willwacher). |
| title | Non-formality of Voronov's Swiss-Cheese operads |
| topic | Algebraic Topology 18M60, 18M75 (Primary) 55S30, 55S35, 55P62 (Secondary) |
| url | https://arxiv.org/abs/2303.16979 |