Fixed points of automorphisms of free groups
The author gives a full proof of the theorem that the set of fixed points of an automorphism \(\phi\) of a finitely generated free group is a finitely generated subgroup. This was announced previously by him [Bull. Am. Math. Soc., New Ser. 8, 451-454 (1983; Zbl 0512.20014)] and settles in the affirmative a conjecture of G. P. Scott. Previously this was established in particular cases, for example in the case where \(\phi\) was of finite order or it was induced by a certain homeomorphism of the pair (M,x), where M is a compact bounded orientable two-manifold and \(x\in M\). For the proof he uses graphical representations of the automorphism, after he has written it as a product of Whitehead automorphisms, and then gives an algorithm to construct a finite set which generates the subgroup of fixed points of \(\phi\).
scientific article; zbMATH DE number 3998079