Geometric & Functional Analysis GAFA

, Volume 10, Issue 5, pp 1071-1089

First online:

Hyperbolic automorphisms of free groups

  • P. BrinkmannAffiliated withDepartment of Mathematics, University of Illinois at Urbana—Champaign, 273 Altgeld Hall, 1409 W. Green Street, Urbana, IL 61801, USA, e-mail:

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We prove that an automorphism \( {\not o} : F \to F \) of a finitely generated free group F is hyperbolic in the sense of Gromov if it has no nontrivial periodic conjugacy classes. This result was previously claimed (but not proved) in [BF1].