Wednesday, March 30th, 2011
2:30pm - 4:00pm, in McCormack 2-116

Alexandru Suciu

Northeastern University

On the Johnson filtration of the automorphism group of a free group

Abstract: Given any group G, the commutator defines a descending filtration on G, known as the lower central series. The automorphism group, Aut(G), supports yet another filtration: an automorphism belongs to the k-th term of this ``Johnson filtration'' if it has the same k-jet as the identity, with respect to the lower central series of G. In this talk, I will discuss the Johnson filtration of the automorphism group of a finitely generated free group F_n, with emphasis on the homological finiteness properties of the first few terms in the filtration. The automorphism group of the abelianization, GL_n(Z), and the representation theory of the corresponding Lie algebra, gl_n(C), will play an important role in the story. This is joint work with Stefan Papadima (arXiv:1011.5292).