| Cerf Theory for Graphs |
| Allen Hatcher and Karen Vogtmann |
| J. London Math. Soc. (2) 58 (1998), no. 3, 633--655. |
| This paper develops a deformation theory for k-parameter families of pointed marked graphs with fixed fundamentalgroup F_n. Applications include a simple geometric proof of stability of the rational homology of Aut(F_n), computations of the rational homology of Aut(F_n) in small dimensions, proofs that various natural complexes of free factorizations of F_n are highly connected, and an improvement on the stability range for the integral homology of Aut(F_n). |