Commentarii Mathematici Helvetici
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Published online: 1999-06-30
The conjugacy problem for Dehn twist automorphisms of free groupsM. M. Cohen and M. Lustig (1) Cornell University, Ithaca, USA
(2) Ruhr-Universität Bochum, Germany
A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For $ G = F_n $, a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of $ F_n $.
Keywords: Free group, Dehn twist automorphism, normal form, algorithm, conjugacy problem, graph of groups decomposition, centralizer, index, fixed subgroup
Cohen M., Lustig M.: The conjugacy problem for Dehn twist automorphisms of free groups. Comment. Math. Helv. 74 (1999), 179-200. doi: 10.1007/s000140050085