An index for counting fixed points of automorphisms of free groups

D. Gaboriau, A. Jaeger, G. Levitt, M. Lustig

Article publié :

Duke Math. J. 93 no. 3 (1998) 425-452.

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Let a be an automorphism of a free group F of rank n. The Scott conjecture, proved by Bestvina-Handel, states that the fixed subgroup Fixa= {w Fn | a (w) = w} has rank at most n. Using R-trees, we show the stronger inequality rkFix a+1/2 a (a) £ n, where a(a) is the number of Fix a-orbits of attracting fixed points for the action of a on the boundary of F.