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Seminar: "Inverting automorphisms of the free group" (E. Ventura, UPC)

Date: Thursday February 27th, 16-17.

Place: CRM, room C1/028
Títle: "Inverting automorphisms of the free group".
Speaker: Enric Ventura, UPC.

Abstract: We introduce a complexity function α (resp. β) to measure the maximal possible gap between the norm of an automorphism (resp. an outer automorphism) of a finitely generated group G, and the norm of its inverse. We shall concentrate in the case of free groups Fr and prove some results about the growth of these functions αr and βr: for rank r=2, α2 is quadratic and β2 is linear; and for higher rank, we will give polynomial lower bounds for both functions, and a polynomial upper bound for βr (the lower bounds use just manipulation of automorphisms and counting techniques, while the proof of the upper bound makes use of a recent result by Algom-Kfir and Bestvina about the asymetry of the metric in the Outer Space). This is joint work with P. Silva and M. Ladra.

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