Vasily Dolgushev, Temple University
GT-shadows are morphisms of a groupoid GTSh who objects are finite index $B_3$-invariant subgroups of the free group on two generators. They may be thought of as approximations of elements of the Grothendieck-Teichmueller group GT. After a brief reminder of the groupoid GTSh, I will introduce the dihedral poset as a concrete subposet of the poset of objects of GTSh. For every element of the dihedral poset, we will describe its connected component in the groupoid GTSh. We will use connected components of certain objects of the dihedral poset to produce the first examples of finite non-abelian quotients of GT. My talk is based on the joint paper with Ivan Bortnovskyi, Borys Holikov and Vadym Pashkovskyi.