Resumen de Bounding the gap between a free group (outer) automorphism and its inverse

Marcelino Ladra González , P. V. Silva, Emanuele Ventura

• For any finitely generated group G, two complexity functions \alpha _G and \beta _G 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 F_r, the exact asymptotic behaviour of \alpha _2 and \beta _2 is computed. For rank r\geqslant 3, polynomial lower bounds are provided for \alpha _r and \beta _r, and the existence of a polynomial upper bound is proved for \beta _r.