A Partial Order on the Symmetric Group and New K(π, 1)'s for the Braid Groups☆

By Tom D. Brady. 2001

108 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93b082f0576717cc1d0dd1718b45d97a63b8bc2b

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Finite complex reection arrangements are K(; 1) (2015, background): “Brady and Charney-Meier-Whittlesey, the Garside structure provides a convenient simplicial Eilenberg-McLane K(B(W ), 1) space ([29], [10], [13], [23]).”
GEOMETRIC PRESENTATIONS FOR THE PURE BRAID GROUP (2006, background): “rtin in the 1920s [3]. In 1998, Birman, Ko, and Lee [5] gave a more symmetrical presentation for the braid group on a larger generating set that has become fashionable of late (see, for example, [4], [7], [8], or [11]). Our goal is to apply a similar idea to the pure braid group. The standard ﬁnite ”
Shellability of noncrossing partition lattices (2005, unknown): “C O ] 1 M ar 2”
The dual braid monoid (2001, methodology): “For type A, this isomorphism was observed in [ 5 ] and [2]; for type B, in [7] (see also [25]).”
Braids: A Survey (2004, background): “See [36], which describes the construction of a finite CW -complex Kn of dimension”
Poset Topology: Tools and Applications (2006, background): “Interest in the absolute length order is a fairly recent development, which arose in work on the braid group [48], [49], [17].”
Finite complex reflection arrangements are $K(\pi,1)$ (2006, unknown): “tions Here again, Wis an irreducible well-generated complex reﬂection group. When W is of type An−1, the lattice (S,4) is isomorphic to the lattice of non-crossing partitions of a regular n-gon ([8], [14]). Following [49], [4] and [7], we call lattice of generalized non-crossing partitions of type W”
K(π, 1) for Artin Groups of Finite Type (2002, methodology): “on. This paper is a continuation of a programme to construct new K(π,1)’s for Artin groups of ﬁnite type which began in [4] with Artin groups on 2 and 3 generators and was extended to braid groups in [3]. These K(π,1)’s diﬀer from those in [6] in that their universal covers are simplicial complexes.”
A categorification of non-crossing partitions (2013, methodology): “s in this category are described in terms of non-crossing partitions. Non-crossing partitions were introduced by Kreweras [29] and later generalised in the context of Coxeter groups by Brady and Watt [7, 8], and independently by Bessis [4]; see also Armstrong’s memoir [1]. A beautiful link between n”
Braids, posets and orthoschemes (2009, background): “We should note that we originally proved that the 5-string braid group is a CAT(0) group in a more direct fashion (unpublished) shortly after the first author introduced his new Eilenberg-MacLane spaces for the braid groups [4], a direct computation carried out independently and contemporaneously by”
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, methodology): “We have based this introduction on results of Carter [39], Brady and Watt [34, 35] and Bessis [17].”