A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms...
Transactions of the American Mathematical Society
Jensen, Craig; McCammond, Jon; Meier, John The Euler characteristic of the Whitehead automorphism group of a free product. Trans. Amer. Math. Soc. 359 (2007), no. 6, 2577–2595 (electronic).