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

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Pedro V. Silva (Author) FCUP; Manuel Ladra (Author) Other; Enric Ventura (Author) Other

Journal

Title: Collectanea Mathematica

Vol. 67 No. 3

Pages: 329-346

ISSN: 0010-0757

Publisher: Springer Nature

Indexing

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Other information

Authenticus ID: P-00K-S0A

DOI: 10.1007/s13348-015-0133-3

Abstract (EN): 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 >= 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).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18