An action of the Grothendieck-Teichmuller group on the operad of stable curves of genus zero

Marcy Robertson – 6 September 2017

In this talk, we show that the group of homotopy automorphisms of the profinite completion of the (cyclic) framed little 2-discs operad is isomorphic to the (profinite) Grothendieck-Teichmuller group. We deduce that the Grothendieck-Teichmuller group acts nontrivially on an operadic model of the genus zero Teichmuller tower.

This talk will be aimed at a general audience and will not assume previous knowledge of the Grothendieck-Teichmuller group. We will emphasise that this work requires, in a fundamental way, the use of \infty-cyclic operads developed with Philip Hackney and Donald Yau. This is joint work with Pedro Boavida and Geoffroy Horel.