Description
In 2001, Brady, McCammond, Meier and Miller computed the l²-cohomology of the group of pure symmetric automorphisms of a free group, also known as the group of motions of the trivial n-component link in the 3-dimensional sphere. Their computation relies on the computation of the Möbius function of posets of hypertrees. After recalling this historical context, I will present further results on the computation of the homology of the hypertree poset, and the related action of the symmetric group, which is also deeply linked with the pre-Lie operad.
