Abstract
In the first two parts of the series, we constructed stabilizer subtorsors of a ‘twisted Magnus’ torsor, studied their relations with the associator and double shuffle torsors, and explained their ‘de Rham’ nature. In this paper, we make the associated bitorsor structures explicit and explain the ‘Betti’ nature of the corresponding right torsors; we thereby complete one aim of the series. We study the discrete and pro-p versions of the ‘Betti’ group of the double shuffle bitorsor.
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Acknowledgements
The collaboration of both authors has been supported by Grants JSPS KAKENHI JP18H01110 and HighAGT ANR-20-CE40-0016.
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Enriquez, B., Furusho, H. The Betti side of the double shuffle theory. III. Bitorsor structures. Sel. Math. New Ser. 29, 27 (2023). https://doi.org/10.1007/s00029-023-00825-2
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DOI: https://doi.org/10.1007/s00029-023-00825-2