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Some new-type equations in the Grothendieck-Teichmüller group arising from geometry \(\mathcal M_{0,5}\). (English) Zbl 1130.14023

Kohno, Toshitake (ed.) et al., Primes and knots. Proceedings of an AMS special session, Baltimore, MD, USA, January 15–16, 2003 and the 15th JAMI (Japan-US Mathematics Institute) conference, Baltimore, MD, USA, March 7–16, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3456-8/pbk). Contemporary Mathematics 416, 263-284 (2006).
Summary: It is a fascinating problem to determine the image of the absolute Galois group \(G_\mathbb{Q}\) of the rationals in the Grothendieck-Teichmüller group \(\widehat{\text{GT}}\). In this article we give some new-type equations satisfied by the Galois images in \(\widehat{\text{GT}}\) arising from various embeddings of a punctured projective line with five marked points.
For the entire collection see [Zbl 1102.11001].

MSC:

14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
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