Grothendieck-Teichmüller group, operads and graph complexes: a survey

Abstract

The paper offers a more or less self-contained introduction into the theory of the Grothendieck-Teichmüller group and Drinfeld associators using the theory of operads and graph complexes.

Wheel graph homology classes via Lie graph homology

“…This includes the theory of Grobner bases [DK10], since our main calculation could be recast as the Koszulity of Lie graph homology in genus 1, viewed as an infinitesmal bimodule over its underlying genus 0 operad. The novice reader should also be advised that this article has largely bypassed a discussion of the influential and sophisticated literature on graph complexes for which the works [Kon94], [Wil15], [KWZ17], [Mer21] may serve as a possible starting point for further reading.…”