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 ? , two complexity functions ?? and ?? are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of ? and the norm of its inverse. Restricting attention to free groups ?? , the exact asymptotic behaviour of ?2 and ?2 is computed. For rank ?⩾3 , polynomial lower bounds are provided for ?? and ?? , and the existence of a polynomial upper bound is proved for ?? .