J. Aust. Math. Soc.  79 (2005), 183-212
Conjugacy in singular Artin monoids

Ruth Corran
  Institut de Géométrie, Algèbre et Topologie
  Batiment BCH
  École Polytechnique Fédérale de Lausanne
  CH-1015
  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 conjugacy-type problems of parabolic submonoids are described. Geometric objects defined by Fenn, Rolfsen and Zhu, called $(j,k)$-bands, are algebraically characterised, and a procedure is given which determines when a word represents a $(j,k)$-band.
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