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https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Teichm%C3%BCller_group
Grothendieck–Teichmüller group
In mathematics, the Grothendieck–Teichmüller group GT is a group closely related to (and possibly equal to) the absolute Galois group of the rational numbers. It was introduced by Vladimir Drinfeld (1990) and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his 1984 essay Esquisse d'un Programme to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids Tg,n, the fundamental groupoids of moduli stacks of genus g curves with n points removed. There are several minor variations of the group: a discrete version, a pro-l version, a k-pro-unipotent version, and a profinite version; the first three versions were defined by Drinfeld, and the version most often used is the profinite version.
References

Further reading
Relation to algebraic topology via the little disks operads
Fresse, Benoit (2017), Homotopy of Operads and Grothendieck-Teichmüller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods, Mathematical Surveys and Monographs, vol. 217, American Mathematical Society, p. 704, ISBN 9781470434823
Relation to combinatorial anabelian geometry
Hoshi, Yuichiro; Minamide, Arata; Mochizuki, Shinichi (2022). "Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups". Kodai Mathematical Journal. 45 (3): 295-348. doi:10.2996/kmj45301.