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A class of garside groupoid structures on the pure braid group
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Krammer, Daan (2008) A class of garside groupoid structures on the pure braid group. Transactions of the American Mathematical Society, Vol.360 (No.8). pp. 4029-4061. doi:10.1090/S0002-9947-08-04313-4 ISSN 0002-9947.
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Official URL: http://dx.doi.org/10.1090/S0002-9947-08-04313-4
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.360 | ||||
Number: | No.8 | ||||
Number of Pages: | 33 | ||||
Page Range: | pp. 4029-4061 | ||||
DOI: | 10.1090/S0002-9947-08-04313-4 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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