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A class of Garside groupoid structures on the pure braid group

Author: Daan Krammer
Journal: Trans. Amer. Math. Soc. 360 (2008), 4029-4061
MSC (2000): Primary 20F36; Secondary 20F05, 20F60, 57M07
Published electronically: March 20, 2008
MathSciNet review: 2395163
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Abstract: We construct a class of Garside groupoid structures on the pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1. The object set of the groupoid is the set of ball decompositions of the punctured disk; the labels are the perimeters of the regions. Our construction generalises Garside's original Garside structure, but not the one by Birman-Ko-Lee. As a consequence, we generalise the Tamari lattice ordering on the set of vertices of the associahedron.

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Additional Information

Daan Krammer
Affiliation: Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom

Received by editor(s): September 28, 2005
Received by editor(s) in revised form: March 27, 2006
Published electronically: March 20, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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