The Complex of Free Factors of a Free Group

Allen Hatcher and Karen Vogtmann

Quart. J. Math. Oxford Ser. (2) 49 (1998), no. 196, 459--468.

We show that the geometric realization of the partially ordered set of proper free factors in a finitely generated free group of rank n is homotopy equivalent to a wedge of spheres of dimension n-2.