QM Research Seminar: Grothendieck- Teichmüller group and the (Cyclic) Ribbon group operad

Speaker: Chandan Singh
(University of Melbourn)


Abstract:
In this talk, we show that a groupoid model based on the operad of
parenthesized ribbons admits a cyclic structure. This extends the action of
GT from braids to ribbons, thus providing a new characterization of GT as
an automorphism group of the prounipotent cyclic operad of parenthesized
ribbons. As a consequence, we exploit this GT action to provide a simple
proof of the formality of the cyclic-framed little disk operad. Finally, this
action extends to the category of parenthesized tangles, which verifies the
conjecture of Kessel-Turaev about Galois actions on framed tangles.
The work discussed here lays foundation to exploring GT actions on a
broader class of knotted objects such as B-tangles, virtual tangles and
welded tangles, which will be addressed in our future work. This is a joint
work with Marcy Robertson.