منابع مشابه
Bestvina’s Normal Form Complex and the Homology of Garside Groups
A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of ...
متن کاملA New Garside Structure for Braid Groups
We describe a new presentation for the complex reflection groups of type (e, e, r) and their braid groups. A diagram for this presentation is proposed. The presentation is a monoid presentation which is shown to give rise to a Garside structure. A detailed study of the combinatorics of this structure leads us to describe it as post-classical.
متن کاملGröbner-Shirshov basis for the braid group in the Artin-Garside generators
In this paper, we give a Gröbner-Shirshov basis of the braid group Bn+1 in the Artin–Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup B + n + 1 is the subsemigroup in Bn+1.
متن کاملGröbner-shirshov Basis for the Braid Group in the Birman-ko-lee-garside Generators
In this paper, we obtain Gröbner-Shirshov (non-commutative Gröbner) bases for the braid groups in the Birman-Ko-Lee generators enriched by new “Garside word” δ ([2]). It gives a new algorithm for getting the Birman-KoLee Normal Form in the braid groups, and thus a new algorithm for solving the word problem in these groups.
متن کاملA class of Garside groupoid structures on the pure braid group
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–...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2016
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-016-1769-8