A class of Garside groupoid structures on the pure braid group

2005/09/07 by Daan Krammer, Krammer, Daan · 1 citation
Mathematics · #06Bxx (Secondary) #20F05 #20F36 (Primary) 57M07 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:06Bxx #msc:20F05 #msc:20F36 #msc:57M07

paper · pdf · doi:10.48550/arxiv.math/0509165

Final version. To appear in Transactions AMS. 32 pages, 19 figures, uses pstricks

arxiv created 2006/04/04 · arxiv updated 2009/12/01

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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