The Betti side of the double shuffle theory. III: Bitorsor structures. (English) Zbl 1533.11156
Summary: 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.
For Part II, see [the authors, ibid. 29, No. 1, Paper No. 3, 28 p. (2023; Zbl 1523.11153)].
For Part II, see [the authors, ibid. 29, No. 1, Paper No. 3, 28 p. (2023; Zbl 1523.11153)].
MSC:
| 11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
| 14G32 | Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) |
Citations:
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