Journal of the London Mathematical Society



Notes and Papers

CERF THEORY FOR GRAPHS


ALLEN HATCHER a1 and KAREN VOGTMANN a1
a1 Department of Mathematics, Cornell University, Ithaca, NY 14853-7901, USA

Abstract

We develop a deformation theory for k-parameter families of pointed marked graphs with fixed fundamental group Fn. Applications include a simple geometric proof of stability of the rational homology of Aut(Fn), computations of the rational homology in small dimensions, proofs that various natural complexes of free factorizations of Fn are highly connected, and an improvement on the stability range for the integral homology of Aut(Fn).

(Received February 20 1996)
(Revised November 12 1996)