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

• Autores: Marcelino Ladra González , P. V. Silva, Emanuele Ventura
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 3, 2016, págs. 329-346
• Idioma: inglés
• DOI: 10.1007/s13348-015-0133-3
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• Resumen

  • 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.