Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T02:13:16.793Z Has data issue: false hasContentIssue false

AN EQUIVARIANT WHITEHEAD ALGORITHM AND CONJUGACY FOR ROOTS OF DEHN TWIST AUTOMORPHISMS

Published online by Cambridge University Press:  20 January 2009

Sava Krstić
Affiliation:
Department of Computer Science and Engineering, Oregon Graduate Institute, PO Box 91000, Portland, OR 97291, US ([email protected])
Martin Lustig
Affiliation:
Laboratoire de Mathématiques, Université d’Aix–Marseille III, Ave. E. Normandie-Niemen, 13397 Marseille 20, FR ([email protected])
Karen Vogtmann
Affiliation:
Department of Mathematics, 555 Malott Hall, Cornell University, Ithaca, NY 14853, US ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given finite sets of cyclic words $\{u_1,\dots,u_k\}$ and $\{v_1,\dots,v_k\}$ in a finitely generated free group $F$ and two finite groups $A$ and $B$ of outer automorphisms of $F$, we produce an algorithm to decide whether there is an automorphism which conjugates $A$ to $B$ and takes $u_i$ to $v_i$ for each $i$. If $A$ and $B$ are trivial, this is the classic algorithm due to Whitehead. We use this algorithm together with Cohen and Lustig’s solution to the conjugacy problem for Dehn twist automorphisms of $F$ to solve the conjugacy problem for outer automorphisms which have a power which is a Dehn twist. This settles the conjugacy problem for all automorphisms of $F$ which have linear growth.

AMS 2000 Mathematics subject classification: Primary 20F32. Secondary 57M07

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2001