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Automorphisms of free groups have finitely generated fixed point sets. (English) Zbl 0628.20029
As the title indicates this paper deals with the problem of the subgroup of the fixed points of an automorphism of a free group. It was first proved by S. Gersten [Adv. Math. 64, 51-85 (1987; Zbl 0616.20014)] that the subgroup of fixed points of an automorphism of a finitely generated free group is finitely generated settling thus a conjecture of G. P. Scott. In the present paper the author gives a new proof based on new ideas. More precisely the author considers the end completion of the free group F (the set of infinite reduced words for a suitable metric), he studies the homeomorphism induced on this completion by the given automorphism and proves first the analogous result for the fixed set of this homeomorphism.
Reviewer: S.Andreadakis

MSC:
20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
20F28 Automorphism groups of groups
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References:
[1] \scD. Cooper, Dynamics of automorphisms of free groups, in preparation.
[2] \scS. Gersten, Fixed points of automorphisms of free groups, preprint. · Zbl 0616.20014
[3] Dyer, J.L; Scott, G.P, Periodic automorphisms of free groups, Comm. algebra, 3, 195-201, (1975) · Zbl 0304.20029
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