Grothendieck-Teichmüller Symmetries of Cyclic Operads and Tangles

Marcy Robertson; Chandan Singh

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arXiv · 2511.05911

Grothendieck-Teichmüller Symmetries of Cyclic Operads and Tangles

Marcy Robertson·Chandan Singh

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Abstract

We identify the profinite Grothendieck-Teichmüller group $\widehat{\mathsf{GT}}$ with the group of homotopy automorphisms of the profinite completion of the cyclic operad of parenthesised ribbon braids. We transport this action to a profinite cyclic $\infty$-operad of framed configuration spaces. Using the metric prop associated to the cyclic ribbon-braid operad, we also obtain a $\widehat{\mathsf{GT}}$-action on a category of framed unoriented profinite tangles, and compare its prounipotent analogue with the action of Kassel and Turaev. Finally, the rational cyclic Grothendieck-Teichmüller action gives an alternative proof of the rational formality of the cyclic framed little-disks operad.

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BibTeX RIS

Marcy Robertson, Chandan Singh. 2026-09-14. Grothendieck-Teichmüller Symmetries of Cyclic Operads and Tangles. https://arxiv.org/abs/2511.05911

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