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AN EQUIVARIANT WHITEHEAD ALGORITHM AND CONJUGACY FOR ROOTS OF DEHN TWIST AUTOMORPHISMS
Published online by Cambridge University Press: 20 January 2009
Abstract
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
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 117 - 141
- Copyright
- Copyright © Edinburgh Mathematical Society 2001
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