Cyclic Symmetries of Chord Diagrams
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915917867253760 |
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| author | Singh, Chandan |
| author_facet | Singh, Chandan |
| contents | We give a direct proof that the proalgebraic graded Grothendieck-Teichmüller group $\mathsf{GRT}_{\mathbb{K}}$ is isomorphic to the group of automorphisms of the prounipotent cyclic operad of parenthesized ribbon chord diagrams based on Furusho's $5$-cycle reformulation of the pentagon equation. As an application, we describe a $\mathsf{GRT}_{\mathbb{K}}$-action on the category of framed chord diagrams with self-dual objects, which is closely related to the target category of the Kontsevich integral for framed tangles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cyclic Symmetries of Chord Diagrams Singh, Chandan Algebraic Topology Category Theory Quantum Algebra 55, 18, 18M05, 18M60 We give a direct proof that the proalgebraic graded Grothendieck-Teichmüller group $\mathsf{GRT}_{\mathbb{K}}$ is isomorphic to the group of automorphisms of the prounipotent cyclic operad of parenthesized ribbon chord diagrams based on Furusho's $5$-cycle reformulation of the pentagon equation. As an application, we describe a $\mathsf{GRT}_{\mathbb{K}}$-action on the category of framed chord diagrams with self-dual objects, which is closely related to the target category of the Kontsevich integral for framed tangles. |
| title | Cyclic Symmetries of Chord Diagrams |
| topic | Algebraic Topology Category Theory Quantum Algebra 55, 18, 18M05, 18M60 |
| url | https://arxiv.org/abs/2604.04688 |