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An equivariant Whitehead algorithm and conjugacy for roots of Dehn twist automorphisms

为 DEHN 的根的一个 EQUIVARIANT WHITEHEAD 算法和 CONJUGACY 扭曲自守

作     者:Krstic, S Lustig, M Vogtmann, K 

作者机构:Oregon Grad Inst Dept Comp Sci & Engn Portland OR 97291 USA Univ Aix Marseille 3 Math Lab F-13397 Marseille 20 France Cornell Univ Dept Math Ithaca NY 14853 USA 

出 版 物:《PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY》 (爱丁堡数学会会报)

年 卷 期:2001年第44卷第1期

页      面:117-141页

核心收录:

学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基  金:Matematicki Institut Belgrade Science Fund of Serbia National Science Foundation, NSF, (DMS-9971607) 

主  题:automorphisms of free groups conjugacy problem Dehn twists Whitehead algorithm 

摘      要:Given finite sets of cyclic words {u(1), ..., u(k)} and {nu (1), ..., nu (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 nu (i) for each i. If 4 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 serve 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.

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