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Homological finiteness in the Johnson filtration of the automorphism group of a free group

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S. Papadima, A. I. Suciu

Editorial: Journal of Topology, 5 (4), p.909-944, 2012.


We examine the Johnson filtration of the (outer) automorphism group of a finitely generated group. In the case of a free group, we find a surprising result: the first Betti number of the second subgroup in the Johnson filtration is finite. Moreover, the corresponding Alexander invariant is a non-trivial module over the Laurent polynomial ring. In the process, we show that the first resonance variety of the outer Torelli group of a free group is trivial. We also establish a general relationship between the Alexander invariant and its infinitesimal counterpart.

Cuvinte cheie: Automorphism group of free group, Torelli group, Johnson filtration, Johnson homomorphism, resonance variety, characteristic variety, Alexander invariant