Let α be an automorphism of a free group of rank n. The Scott conjecture, proved by Bestvina-Handel, asserts that the fixed subgroup of α has rank at most n. We give a short alternative proof of this result using R-trees.
AbstractWe refine Cohen and Lustig's description of centralisers of Dehn twists of free groups. We show that the centraliser of a Dehn twist of a free group has a subgroup of finite index that has a finite classifying space. We describe an algorithm to find a presentation of the centraliser. We use this algorithm to give an explicit presentation for the centraliser of a Nielsen automorphism in Aut(Fn). This gives restrictions to actions of Aut(Fn) on CAT(0) spaces.