Centralisers of Dehn twist automorphisms of free groups

Abstract

We 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(F_n). This gives restrictions to actions of Aut(F_n) on CAT(0) spaces.

33 pages, revised section 5, added section 6.5. Other minor revisions

References in corpus (3)

• Automorphisms of free groups with boundaries
• McCool groups of toral relatively hyperbolic groups
• Abelian subgroups of \Out(F_n)

Cited by in corpus (2)

• The Conjugacy Problem for $Out(F_3)$
• Loxodromic elements in the cyclic splitting complex and their centralizers