The Complex of Free Factors of a Free Group

A. Hatcher, K. Vogtmann
1998 Quarterly Journal of Mathematics  
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.
doi:10.1093/qmathj/49.4.459 fatcat:5nbuqrresncsxdoh2tkfbjaa6e