Bounding the Gap between a Free Group (outer) Automorphism and Its Inverse
نویسندگان
چکیده
For any finitely generated group G, two complexity functions αG and βG are defined to measure the maximal possible gap between the norm of an automorphism (respectively outer automorphism) of G and the norm of its inverse. Restricting attention to free groups, Fr, the exact asymptotic behaviour of α2 and β2 is computed. For rank r > 3, polynomial lower bounds are provided for αr and βr, and the existence of a polynomial upper bound is proved for βr. E-mail addresses: [email protected], [email protected], [email protected]. 2010 Mathematics Subject Classification. 20E05, 20E36, 20F65.
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