The hypertree poset and the l 2-Betti numbers of the motion group of the trivial link.

We give explicit formulae for the Euler characteristic and l ²-cohomology of the group of motions of the trivial link, or isomorphically the group of free group automorphisms that send each standard generator to a conjugate of itself. The method is primarily combinatorial and ultimately relies on a computation of the Möbius function for the poset of labelled hypertrees. [ABSTRACT FROM AUTHOR]