J. Aust. Math. Soc.
79 (2005), 183212

Conjugacy in singular Artin monoids

Ruth Corran
Institut de Géométrie, Algèbre et Topologie
Batiment BCH
École Polytechnique Fédérale de Lausanne
CH1015
Switzerland
ruth.corran@epfl.ch



Abstract

We define a notion of conjugacy in singular
Artin monoids, and solve the corresponding
conjugacy problem for finite types. We show that
this definition is appropriate to describe type
(1) singular Markov moves on singular braids.
Parabolic submonoids of singular Artin monoids
are defined and, in finite type, are shown to be
singular Artin monoids. Solutions to
conjugacytype problems of parabolic submonoids
are described. Geometric objects defined by Fenn,
Rolfsen and Zhu, called
bands, are algebraically characterised, and a
procedure is given which determines when a word
represents a
band.

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