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A class of Garside groupoid structures on the pure braid group | | Daan Krammer
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7 Sep 2005 | | Subject: | Group Theory MSC-class: 20F36 (Primary) 57M07, 20F05, 06Bxx (Secondary) | math.GR | | 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/Dehornoy lattice orderings on the set of vertices of the associahedron. | | Source: | arXiv, math.GR/0509165 | | Services: | Forum | Review | PDF | Favorites | |
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