Grothendieck--Teichmüller Symmetries of Cyclic Operads and Tangles
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912775420248064 |
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| author | Robertson, Marcy Singh, Chandan |
| author_facet | Robertson, Marcy Singh, Chandan |
| contents | We characterise the profinite Grothendieck-Teichmüller group $\widehat{\mathsf{GT}}$ as the group of automorphisms of the profinite completion of a cyclic operad of parenthesised ribbon braids. This operad generates a symmetric monoidal category which is equivalent to the category of framed, oriented tangles, thereby providing an operadic model for profinite tangles and their arithmetic symmetries. As applications, we show that $\widehat{\mathsf{GT}}$ acts naturally on tangles and provide an alternative proof of the formality of the cyclic framed little disks operad. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grothendieck--Teichmüller Symmetries of Cyclic Operads and Tangles Robertson, Marcy Singh, Chandan Algebraic Topology Category Theory Quantum Algebra 55, 18, 18M05, 18M60, 18M75 We characterise the profinite Grothendieck-Teichmüller group $\widehat{\mathsf{GT}}$ as the group of automorphisms of the profinite completion of a cyclic operad of parenthesised ribbon braids. This operad generates a symmetric monoidal category which is equivalent to the category of framed, oriented tangles, thereby providing an operadic model for profinite tangles and their arithmetic symmetries. As applications, we show that $\widehat{\mathsf{GT}}$ acts naturally on tangles and provide an alternative proof of the formality of the cyclic framed little disks operad. |
| title | Grothendieck--Teichmüller Symmetries of Cyclic Operads and Tangles |
| topic | Algebraic Topology Category Theory Quantum Algebra 55, 18, 18M05, 18M60, 18M75 |
| url | https://arxiv.org/abs/2511.05911 |