Equivariant Framed Little Disk Operads are Additive
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910670987984896 |
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| author | Szczesny, Ben |
| author_facet | Szczesny, Ben |
| contents | In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence $\mathcal{C}_n \otimes \mathcal{C}_m \simeq \mathcal{C}_{n+m}$ for the little cubes operad $\mathcal{C}_n$. We introduce equivariant framed little disk operads, a new class of operads that simultaneously generalize the framed little disk operads and the little $V$-disk operads associated with a $G$-representation $V$. We prove that these operads satisfy an analogous additivity property, extending the classical theorem to settings involving group actions and framings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant Framed Little Disk Operads are Additive Szczesny, Ben Algebraic Topology 55P91 (Primary) 18M60, 55P48 (Secondary) In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence $\mathcal{C}_n \otimes \mathcal{C}_m \simeq \mathcal{C}_{n+m}$ for the little cubes operad $\mathcal{C}_n$. We introduce equivariant framed little disk operads, a new class of operads that simultaneously generalize the framed little disk operads and the little $V$-disk operads associated with a $G$-representation $V$. We prove that these operads satisfy an analogous additivity property, extending the classical theorem to settings involving group actions and framings. |
| title | Equivariant Framed Little Disk Operads are Additive |
| topic | Algebraic Topology 55P91 (Primary) 18M60, 55P48 (Secondary) |
| url | https://arxiv.org/abs/2410.20235 |