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.
 Publication:

arXiv eprints
 Pub Date:
 June 2012
 DOI:
 10.48550/arXiv.1206.5728
 arXiv:
 arXiv:1206.5728
 Bibcode:
 2012arXiv1206.5728R
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Geometric Topology;
 20E36;
 20F65
 EPrint:
 33 pages, revised section 5, added section 6.5. Other minor revisions