# Braids and factorizable inverse monoids

Easdown, D, East, J and FitzGerald, DG 2004 , 'Braids and factorizable inverse monoids', in Isabel M Araujo and Mario J J Branco and Vitor H Fernandes and Gracinda M S Gomes (eds.), Semigroups and languages: Proceedings of the Workshop Semigroups and Languages, Lisboa, Portugal, 27 - 29 November 2002 , World Scientific Press, pp. 86-105.

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## Abstract

What is the untangling effect on a braid if one is allowed to snip a string, or if two specified strings are allowed to pass through each other, or even allowed to merge and part as newly reconstituted strings? To calculate the effects, one works in an appropriate factorizable inverse
monoid, some aspects of a general theory of which are discussed in this
paper. The coset monoid of a group arises, and turns out to have a universal
property within a certain class of factorizable inverse monoids. This theory
is dual to the classical construction of fundamental inverse semigroups from
semilattices. In our braid examples, we will focus mainly on the merge and
part'' alternative, and introduce a monoid which is a natural preimage of
the largest factorizable inverse submonoid of the dual symmetric inverse
monoid on a finite set, and prove that it embeds in the coset monoid of the
braid group.

Item Type: Book Section Easdown, D and East, J and FitzGerald, DG factorizable inverse monoid, merge and part monoid, coset monoid World Scientific Press View statistics for this item