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

Details On the Andreadakis-Johnson filtration of the automorphism group of a free group On the Andreadakis-Johnson filtration of the automorphism group of a free group

2010-04-14

arxiv.org/abs/1004.2435v2

Mathematics

Group Theory

Corrections; revisions to proof of main theorem

Scientific paper

The Johnson filtration of the automorphism group of a free group is composed of those automorphisms which act trivially on nilpotent quotients of the free group. We compute cohomology classes as follows: (i) we analyze analogous classes for a subgroup of the pure symmetric automorphism group of a free group, and (ii) we analyze features of these classes which are preserved by the Johnson homomorphism. One consequence is that the ranks of the cohomology groups in any fixed dimension between 1 and n-1 increase without bound for terms deep in the Johnson filtraton.

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