On the inverse braid monoid

Vladimir Vershinin (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to the inverse braid monoids. Namely we prove an inclusion into a monoid of partial monomorphisms of a free group. This gives a solution of the word problem. Another solution is obtained by an approach similar to that of Garside. We give also the analogues of Artin presentation with two generators and Sergiescu graph-presentations.

Mots clés: presentation; singular braid monoid; Braid; inverse braid monoid; word problem

Domaines: Topologie algébrique [math.AT]

Vladimir Vershinin. On the inverse braid monoid. Topology and its Applications, 2009, 156 (6), pp.1153-1166. ⟨10.1016/j.topol.2008.10.007⟩. ⟨hal-00795122⟩