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THE FACTORIZABLE BRAID MONOID

Published online by Cambridge University Press:  25 January 2007

James East
James East
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
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Abstract

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In this paper we study the factorizable braid monoid (also known as the merge-and-part braid monoid) introduced by Easdown, East and FitzGerald in 2004. We find several presentations of this monoid, and uncover an interesting connection with the singular braid monoid. This leads to the definition of the flexible singular braid monoid, which consists of ‘flexible-vertex-isotopy’ classes of singular braids. We conclude by defining and studying the pure factorizable braid monoid, the maximal subgroups of which are (isomorphic to) quotients of the pure braid group.

Keywords

Primary 20F36Secondary 20F05braidssingular braidsfactorizable inverse monoidspresentations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 3 , October 2006 , pp. 609 - 636
Copyright
Copyright © Edinburgh Mathematical Society 2006