双洗牌理论的贝蒂方面：一项调查
The Betti side of the double shuffle theory: a survey
摘要：
这是H.古庄和作者。本文的目的是：（1）给出结合子关系蕴涵双重混洗关系的证明，替代Furusho的arXiv：0808.0319v3的证明;（2）明确双重混洗关系的Racinet torsor上的双torsor结构。主要的工具是根据模空间$\mathfrak M_{0,4}$和$\mathfrak M_{0,5}$的拓扑来解释调和余积，这在Deligne和Terasoma的2005年预印本中引入，并将其扩展到Betti设置。
英文摘要：
This is a survey of arXiv:1803.10151v4, arXiv:1807.07786v2 and arXiv:1908.00444v2 by H. Furusho and the author. The purpose of this series of papers is: (1) to give a proof that associator relations imply double shuffle relations, alternative to Furusho's paper arXiv:0808.0319v3; (2) to make explicit the bitorsor structure on Racinet's torsor of double shuffle relations. The main tool is the interpretation of the harmonic coproduct in terms of the topology of the moduli spaces $\mathfrak M_{0,4}$ and $\mathfrak M_{0,5}$, introduced in Deligne and Terasoma's 2005 preprint, and its extension to the Betti setup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
