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Centralisers of Dehn twist automorphisms of free groups

Published online by Cambridge University Press:  08 May 2015

MORITZ RODENHAUSEN  and
RICHARD D. WADE
MORITZ RODENHAUSEN
Affiliation:
Mathematisches Institut, Endenicher Allee 60, 53115, Bonn, Germany. e-mail: moritz.rodenhausen@gmx.de
RICHARD D. WADE
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, 84113, U.S.A. e-mail: wade@math.utah.edu
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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(Fn). This gives restrictions to actions of Aut(Fn) on CAT(0) spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 1 , July 2015 , pp. 89 - 114
Copyright
Copyright © Cambridge Philosophical Society 2015 

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